Performance of Semiconductor Optical Amplifier

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This text tries to give a brief ideal about the SOA, its realization based on matlab simulation with the reservoir model and cross-gain modulation

This text tries to give a brief ideal about the SOA, its realization based on matlab simulation with the reservoir model and cross-gain modulation

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  • 1. Performance ofSemiconductor Optical AmplifierA report submitted for the partial fulfilment of the 4th year syllabus of the fouryear B.tech. course under West Bengal University of TechnologybyPranab Kumar Bandyopadhyay (univertsy roll no : 071690103020)Md. Taushif (univertsy roll no : 071690103039)Samadrita Bhattacharyya (univertsy roll no : 071690103040)Sanghamitra Bhattacharjee (univertsy roll no : 071690103046)Prakash Kumar (univertsy roll no : 071690102033)
  • 2. AcknowledgementIt is a pleasure to thank the many people who made this project work possiblefor us. It is difficult to overstate our gratitude to our guide, Prof. SuranjanaBanerjee, Lecturer, Dept. of Electronics & Communication, Academy OfTechnology. With her enthusiasm, her inspiration and her great efforts toexplain things simply and clearly, she has helped to make this project workconvenient for us. Throughout my project work period, she providedencouragement, sound advice, good teaching, good company and lots of goodideas. We would have been lost without her.We would like to thank our director Prof. Santu Sarkar, Head of The Dept.Electronics & Communication Engg., Academy Of Technology, for giving us anopportunity to carry out the project work here. We are indebted to our teachersfor providing a stimulating and challenging environment in which to learn andgrow.Last, but by no means least, we thank our friends for their support andencouragement throughout.Date:- Signature of students i
  • 3. Certificate by the SupervisorThis is to certify that this technical report “Performance of Semiconductor Optical Amplifier” is a recordof work done by Pranab Kumar Bandyopadhyay, Md. Taushif, Samadrita Bhattacharyya, SanghamitraBhattacharjee & Prakash Kumar, during the time from August 2010 to April 2011as a partial fulfillmentof the requirement of the final year project at Academy of Technology, affiliated under West BengalUniversity of Technology.These candidates have completed the total parameters and requirement of the entire project.This project has not been submitted in any other examination and does not from a part of any othercourse undergone by the candidates. ______________________________ (Prof. Suranjana Banerjee) Lecturer, Dept. of Electronics & Communication Engineering, Academy of Technology, West Bengal ii
  • 4. Preface In this report, we are going to discuss, simulate and realize an popularly know opticalamplifier, the SOA. SOAs have been in use for the purpose of cheap, reliable andenvironment suitable optical amplifiers in the field of long distance optical communication.In the practical field, where the distance between the two successive optical amplifiers aremore than 100 km , SOAs have been very useful to provide a low maintenance, low cost andless fragile system for signal boosting. Our report on the project continuous to discuss on the performance of SOA on the aspectof gain, cross-gain modulation & BER as well as power penalty for the system comprising ofa WDM ring network. All the necessary theories to derive or to simulate the SOA features are tried to bedescribed on the following chapter. With a grateful heart we are expressing our feelings of gratude to our respected teacherProf. Mrs. Suranjana Banerjee for her kind help and guide to us in the simulation throughtthe span of the project, without which this work was almost impossible. iii
  • 5. indexChapter no. Topic Page no. 1 Introduction 1 2 History 4 3 Why SOA? 5 4 Basic Principle 10 5 Fundamental device characteristics & Materials used in SOA 15 6 Modelling of SOA 21 7 Cross-gain modulation 46 8 Work done 51 9 Power penalty & BER in SOA receiver 88 10 Summary 94 11 Bibliography 95
  • 6. Introduction Chapter1Communications can be broadly defined as the domain, are required in transparent opticaltransfer of information from one point to networks.another. In optical fiber communications, thistransfer is achieved by using light as theinformation carrier. There has been an In this chapter we begin with the reasons whyexponential growth in the deployment and optical amplification is required in opticalcapacity of optical fiber communication communication networks. This is followed by atechnologies and networks over the past brief history of semiconductor optical amplifierstwenty-five years. This growth has been made (SOAs), a summary of the applications of SOAspossible by the development of new and a comparison between SOAs and opticaloptoelectronic technologies that can be fiber amplifiers (OFAs).utilized to exploit the enormous potentialbandwidth of optical fiber. Today, systems are WHY WE NEED OPTICALoperational which operate at aggregate bit AMPLIFICATION? :-rates in excess of 100 Gb/s. Such highcapacity systems exploit the optical fiber Optical fiber suffers from two principal limitingbandwidth by employing wavelength division factors: Attenuation and dispersion. Attenuationmultiplexing. leads to signal power loss, which limits transmission distance. Dispersion causes optical Optical technology is the dominant carrier ofglobal information. It is also central to the pulse broadening and hence inter symbolrealization of future networks that will have interference leading to an increase in the systemthe capabilities demanded by society. These bit error rate (BER). Dispersion essentiallycapabilities include virtually unlimited limits the fiber bandwidth. The attenuationbandwidth to carry communication services of spectrum of conventional single-mode silicaalmost any kind, and full transparency that fiber, shown in Fig. 1.1, has a minimum in theallows terminal upgrades in capacity and 1.55 µm wavelength region. The attenuation isflexible routing of channels. Many of the somewhat higher in the 1.3 µm region. Theadvances in optical networks have been made dispersion spectrum of conventional single-possible by the advent of the optical amplifier. mode silica fiber, shown in Fig. 1.2, has aIn general, optical amplifiers can be divided minimum in the 1.3 µm region. Because theinto two classes: optical fiber amplifiers and attenuation and material dispersion minima aresemiconductor amplifiers. The former has located in the 1.55 µm and 1.3 µm ‘windows’,tended to dominate conventional system these are the main wavelength regions used inapplications such as in-line amplification used commercial optical fiber communicationto compensate for fiber losses. However, due systems. Because signal attenuation andto advances in optical semiconductor dispersion increases as the fiber length increases,fabrication techniques and device design, at some point in an optical fiber communicationespecially over the last five years, the link the optical signal will need to besemiconductor optical amplifier (SOA) is regenerated. 3R (reshaping-retiming-showing great promise for use in evolvingoptical communication networks. It can be retransmission).Regeneration involves detectionutilized as a general gain unit but also has (photon-electron conversion), electricalmany functional applications including an amplification, retiming, pulse shaping andoptical switch, modulator and wavelength retransmission (electron-photon conversion).converter. These functions, where there is noconversion of optical signals into the electrical 1
  • 7. Fig 1.1: Typical attenuation spectrum of low-loss single-mode silica optical fiber. 2
  • 8. This method has some disadvantages- improve receiver sensitivity. Besides these basic►Firstly, it involves breaking the optical link system applications optical amplifiers are alsoand so is not optically transparent. useful as generic optical gain blocks for use in larger optical systems. The improvements in►Secondly, the regeneration process is optical communication networks realizeddependent on the signal modulation format and through the use of optical amplifiers providesbit rate and so is not electrically transparent. new opportunities to exploit the fiberThis in turn creates difficulties if the link needs bandwidth.to be upgraded. Ideally link upgrades should There are two types of optical amplifier: Theonly involve changes in or replacement of SOA and the OFA. In recent times the latter hasterminal equipment (transmitter or receiver). dominated; however SOAs have attracted►Thirdly, asregenerators arecomplex systemsand oftensituated inremote ordifficult to accesslocation, as is thecase in underseatransmissionlinks, networkreliability isimpaired.In systems wherefiber loss is thelimiting factor,an in-line opticalamplifier can beused instead of aregenerator. Asthe in-lineamplifier hasonly to carry out one function (amplification ofthe input signal) compared to full regeneration,it is intrinsically more reliable and lessexpensive device. Ideally an in-line optical renewed interest for use as basic amplifiers andamplifier should be compatible with single- also as functional elements in opticalmode fiber, impart large gain and be optically communication networks and optical signaltransparent (i.e. independent of the input processing devices.optical signal properties).In addition optical amplifiers can also be usefulas power boosters, for example to compensatefor splitting losses in optical distributionnetworks, and as optical preamplifiers to 3
  • 9. HISTORY Chapter2The first studies on SOAs were carried out around the time of the invention of the semiconductor laser inthe 1960’s. These early devices were based on GaAs homo-junctions operating at low temperatures. Thearrival of double hetero-structure devices spurred further investigation into the use of SOAs in opticalcommunication systems. In the 1970’s Zeidler and Personick carried out early work on SOAs. In the1980’s there were further important advances on SOA device design and modeling. Early studiesconcentrated on AlGaAs SOAs operating in the 830 nm range. In the late 1980’s studies on InP/InGaAsPSOAs designed to operate in the 1.3 µm and 1.55 µm regions began to appear.Developments in anti-reflection coating technology enabled the fabrication of true travelling-wave SOAs.Prior to 1989, SOA structures were based on anti-reflection coated semiconductor laser diodes. Thesedevices had an asymmetrical waveguide structure leading to strongly polarization sensitive gain.In 1989 SOAs began to be designed as devices in their own right, with the use of more symmetricalwaveguide structures giving much reduced polarization sensitivities. Since then SOA design anddevelopment has progressed in tandem with advances in semiconductor materials, device fabrication,antireflection coating technology, packaging and photonic integrated circuits, to the point where reliablecost competitive devices are now available for use in commercial optical communication systems.Developments in SOA technology are ongoing with particular interest in functional applications such asphotonic switching and wavelength conversion. The use of SOAs in photonic integrated circuits (PICs) isalso attracting much research interest. 4
  • 10. WHY SOA? Chapter3 As optical technology has become an integral advantages including smaller size and the abilitypart of telecommunications, the need for reliable to easily integrate with semiconductor lasers.optical signal transmission has become more and The latest step in semiconductor amplifiers camemore pronounced. In order to transmit over long with the introduction of a SOA that operated as adistances, it is necessary to account for linear amplifier (LOA). Thus far this hasattenuation losses. Initially, this was done eliminated many of the downfalls of SOAs suchthrough an expensive conversion from optical to as cross talk and high signal to noise ratio.electrical and back. This was soon remediedwith the creation of optical amplifiers. 1. EDFA: Erbium doped fiber amplifiers are commonly used optical amplifier. An EDFAThe optical amplifiers we have today are consists of a pump laser coupled to an input signal and passed through an optical fiber1.EDFA. slightly doped with erbium ions. The pump laser is used to excite erbium ions which emit photons2. SOA. in phase with the input signal which acts to amplify it. EDFA’s amplify in the 1520-16003. LOA. nm range which corresponds to the energy difference between the excited and ground states One of the first widely adopted optical of the erbium ions.amplifiers was the Erbium Doped FiberAmplifier (EDFA). This revolutionized theoptical communications industry. The next big 2. SOA: The semiconductor optical amplifierstep in optical amplifiers came with is an amplifier with a laser diode structure that issemiconductor optical amplifiers (SOA). used to amplify optical signals passing throughAlthough these didn’t perform as well as the its optical region. Amplification occurs throughEDFAs in some conditions, they had many stimulated emission in the active region as input 5
  • 11. signal energy propagates through the wave a feedback device, preventing carrier depletionguide. This can be seen below even when the input power varies. This can be seen in Figure Why SOA is better? 1. In the practical applications in the rigorous field of the industry, it is easier to use SOA, because it uses direct electrical drive current as its energy pump that is more robust in structure than the laser as used as the energy pump in EDFA. 2.The switching characteristics of EDFA is not very good. SOAs & LOAs show better switching properties under continuous on& on signal. SOA are seen to be tolerant upto a switching speed varying from 0.5 to 5 GHz. 3. LOA: The linearoptical amplifier(LOA) is actually a SOA with an integratedvertical cavity surface emitting laser (VCSEL).The amplifier and the VCSEL share the sameactive region, which causes the VCSEL to act as 6
  • 12. 3. The channel toBit-error channel, which israte characteristics of the SOAs are much better unlikely in SOAs. SOAs can operate at thethan the EDFA. In the EDFA, the BER lowest Bi- error rate of 10-15.progressively gets worse from 7
  • 13. 4. One of the main drawbacks of SOA devices is the need for8
  • 14. polarization matching. Thepolarization of the incidentlaser must match thepolarization of thesemiconductor. From the abovediscussion we can be sure tochoose SOA instead of the ofthe other device, i.e. EDFA orLOA. 9
  • 15. Basic Principle Chapter 4 An SOA is an optoelectronic device that reflections are negligible (i.e. the signalunder suitable operating conditions can undergoes a single-pass of the amplifier).amplify an input light signal. A schematic Anti-reflection coatings can be used to creatediagram of a basic SOA is shown in Fig. 2.1. SOAs with facet reflectivities <10-5.The TW-The active region in SOA is not as sensitive as thethe device imparts FP-SOA to fluctuations ingain to an input bias current, temperature andsignal. An external signal polarisation.electric currentprovides the energysource that enablesgain to take place. Principles of OpticalAn embedded waveguide Amplification:-is used to confine thepropagating signal wave to the active region. In an SOA electrons (more commonlyHowever, the optical confinement is weak so referred to as carriers) are injected from ansome of the signal will leak into the external current source into the active region.surrounding lossy cladding regions. The output These energised region material, leaving holessignal is accompanied by noise. This additive in the valence band (VB). Three radiativenoise is produced by the amplification process mechanisms are possible in the semiconductor.itself and so cannot be entirely avoided. The These are shown in Fig 2.3 for a material withamplifier facets are reflective causing ripples an energy band structure consisting of twoin the gain spectrum. discrete energy levels. SOAs canbe classifiedinto two maintypes shownin Fig. 4.02:The Fabry-Perot SOA(FP-SOA)wherereflectionsfrom the endfacets aresignificant(i.e.the signalundergoesmany passesthrough theamplifier) andthe travelling-wave SOA(TW-SOA)where 10
  • 16. In stimulated absorption an incident light proportional to the intensity of the inducingphoton of sufficient energy can stimulate a radiation whereas the spontaneous emissioncarrier from the process isVB to the CB.This is a lossprocess as theincident photonisextinguished. If a photonof light ofsuitable energyis incident onthesemiconductor,it can causestimulatedrecombinationof a CB carrier independent ofwith a VB hole. it.The recombining carrier loses its energy in theform of a photon of light. This new stimulated Spontaneous and induced transitions:-photon will be identical in all respects to theinducing photon (identical phase, frequency The gain properties of opticaland direction, i.e. a coherent interaction). Both semiconductors are directly related to thethe original photon and stimulated photon can processes of spontaneous and stimulatedgive rise to more stimulated transitions. If the emission. To quantify this relationship weinjected current is sufficiently high then a consider a system of energy levels associatedpopulation inversion is created when the with a particular physical system. Let N1 andcarrier population in the CB exceeds that in the N2 be the average number of atoms per unitVB. In this case the likelihood of stimulated volume of the system characterised by theemission is greater than stimulated absorption average number of atoms by energies E1 andand so semiconductor will exhibit optical gain. E2 respectively, with E2 > E1 .If a particular atom has energy E2 then there is a finite In the spontaneous emission process, there probability per unit time that it will undergo ais a non-zero probability per unit time that a transition from E2 to E1 and in the process emitCB carrier will spontaneously recombine with a photon. The spontaneous carrier transitiona VB hole and thereby emit a photon with rate per unit time from level 2 to level 1 israndom phase and direction. Spontaneously given byemitted photons have a wide range offrequencies. Spontaneously emitted photons 4.1are essentially noise and also take part inreducing the carrier population available for where A21 is the spontaneous emissionoptical gain. Spontaneous emission is a direct parameter of the level 2 to level 1 transition.consequence of the amplification process and Along with spontaneous emission it is alsocannot be avoided; hence a noiseless SOA possible to have induced transitions. Thecannot be created. Stimulated processes are 11
  • 17. induced carrier transition rate from level 2 to l(v)dv is the probability that a particularlevel 1 (stimulated emission) is given by spontaneous emission event from is level 2 to level 1 will result in a photon with a frequency 4.2 between v and v+dv. The inducing field where B21 is the stimulated emission intensity (w/m3) isparameter of the level 2 to level 1 transitionand ρ(v) the incident radiation energy density 4.9at frequency v. The induced photons haveenergy hv = E2 – E1 The induced transitionrate from level 1 to level 2 (stimulated So (4.7) becomesabsorption) is given by 4.9 4.3 where B12 is the stimulated emissionparameter of the level 2 to level 1 transition. Itcan be proved, from quantum-mechanical Absorption and amplification :-considerations [1,2], that By using the expression for the stimulated B12 = B21 4.4 transition rates developed in previously, it is now possible to derive an equation for the optical gain coefficient for a two level system. 4.5 We consider the case of a monochromatic plane wave propagating in the z-direction where ηr is the material refractive index through a gain medium with cross-section areaand the speed of light in a vacuum. Inserting A and elemental length dz. The net power dPv(4.5) into (4.2) gives generated by a volume Adz of the material is simply the difference in the induced transition rates between the levels multiplied by the 4.6 transition energy hv and the elemental volume i.e. In the case where the inducing radiation is 4.11monochromatic at frequency v, then theinduced transition rate from level 2 to level 1is This radiation is added coherently to the propagating wave. This process of amplification can then be described by the 4.7 differential equation where ρv is the energy density (T/m3) of the 4.12electromagnetic field inducing the transitionand l(v) is the transition lineshape function,normalised such that gm(v) is the material gain coefficient given by 4.8 4.13 12
  • 18. (4.13) implies that to achieve positive gain 4.15a population inversion (N2 > N1) must existbetween level 2 and level 1. It also shows, bythe presence of A21, that the process of optical A volume element, with cross-section area Again is always accompanied by spontaneous and length dz at position z, of the gain mediumemission, i.e. noise. spontaneously emits a noise power 4.16 Spontaneous emission noise :- This noise is emitted isotropically over a 4πAs shown above, spontaneous emission is a solid angle. Each spontaneously emitteddirect consequence of the amplification photon can exist with equal probability in oneprocess. In this section an expression is of two mutually orthogonal polarisation states.derived for the noise power generated by anopticalamplifier. Weconsider thearrangement ofFig. 4.4, whichshows an inputmonochromaticsignal offrequency vtravellingthrough a gainmedium havingthe energy levelstructure of Fig4.03. Apolariser andoptical filter ofbandwidth B0centred about vare placedbefore thedetector. Theinput beamis focussedsuch that its waist occupies the gain medium. The polariser passes the signal, while reducingIf the beam is assumed to have a circular the noise by half. Hence the total noise powercross-section with waist diameter D then the emitted by the volume element into a solidbeam divergence angle is angle dΩ and bandwidth B0 is 4.17 4.14 The smallest solid angle that can be usedwhere λ0 is the free space wavelength. The net without losing signal power ischange in the signal power due to coherentamplification by an elemental length dz of thegain medium is 13
  • 19. The noise can also be reduced by the use of a narrowband optical filter. 4.18This solid angle can be obtained by the use ofa suitably narrow output aperture. In this case(4.17) can be rewritten as 4.19The total beam power P (signal and noise) canthen be described by 4.20where the spontaneous emission factor nsp isgiven by 4.21The solution of (2.20), assuming that gm isindependent of z, is 4.22where Pm is the input signal power. If theamplifying medium has length L then the totaloutput power is 4.23where G = egmL is the single-pass signal gain.The amplifier additive noise power is 4.23(4.24) shows that increasing the level ofpopulation inversion can reduce SOA noise. 14
  • 20. Fundamental Device Characteristics & Chapter 5 Materials Used in SOA The most common application of SOAs isas a basic optical gain block. For such anapplication, a list of the desired properties is v0 is the closest cavity resonance to v. Cavitygiven in Table 2.1. The goal of most SOA resonance frequencies occur at integer multiples of Δv. The sin2 factor in (5.1) isresearch and development is to realise these equal to zero at resonance frequencies andproperties in practical devices. equal to unity at the anti-resonance frequencies (located midway between successive resonance frequencies). The effective SOA gain coefficient is 5.3 where Γ is the optical mode confinement factor (the fraction of the propagatingTable 5.01: Desirable Properties of a practical SOA signal field mode confined to the active region) and α the absorption coefficient.Small-signal gain and gain bandwidth Gs=egl is the single-pass amplifier gain. In general there are two basic gain An uncoated SOA has facet reflectivitiesdefinitions for SOAs. The first is the intrinsic approximately equal to 0.32. The amplifiergain G of the SOA, which is simply the ratio gain ripple Gr is defined as the ratio betweenof the input signal power at the input facet to the resonant and non-resonant gains. Fromthe signal power at the output facet. The (5.1) we getsecond definition is the fibre-to-fibre gain,which includes the input and output couplinglosses. These gains are usually expressed in 5.4dB. The gain spectrum of a particular SOAdepends on its structure, materials andoperational parameters. For most applications From (5.4) the relationship between thehigh gain and wide gain bandwidth are geometric mean facet reflectivitydesired. The small-signal (small here meaning and Gr isthat the signal has negligible influence on theSOA gain coefficient) internal gain of a Fabry-Perot SOA at optical frequency v is given by 5.5 Curves of Rgeo versus Gs are shown in Fig. 5.02 with Gs as parameter. For example, to 5.1 obtain a gain ripple less than 1 dB at an amplifier single-pass gain of 25 dB requires Where R1 and R2 are the input and output that Rgeo < 3.6 x 10-4. Facet reflectivities of thisfacet reflectivities and Δv is the cavity order can be achieved by the application oflongitudinal mode spacing given by anti-reflection (AR) coatings to the amplifier facets. The effective facet reflectivities can be 5.2 15
  • 21. reduced further by the use of specialised SOA Cascaded SOAs accentuate this polarisationstructures. dependence. The amplifier waveguide is characterised by two mutually orthogonal A typical TW-SOA small-signal gain polarisation modes termed the Transversespectrum is shown in Fig. 5.01. The gain Electric (TE) and Transverse Magnetic (TM)bandwidth Bopt of the amplifier is defined as modes. The input signal polarisation statethe wavelength range over which the signal usually liesgain is not less than half its peak value. Widegain bandwidthSOAs areespecially usefulin systems wheremultichannelamplification isrequired such asin WDMnetworks. A widegain bandwidthcan be achieved inan SOA with anactive regionfabricated fromquantum-well ormultiple quantum-well (MQW)material. Typicalmaximum internalgains achievablein practicaldevices are in therange of 30 to 35 dB.Typical small-signalgain bandwidths are inthe range of 30 to 60 nm. Polarisationsensitivity In general the gain ofan SOA depends on thepolarisation state of theinput signal. Thisdependency is due to anumber of factorsincluding the waveguidestructure, the polarisationdependent nature of anti-reflection coatings and the gain material. Fig 5.02: Geometric mean facet reflectivity 16
  • 22. somewhere between these two extremes. The In the limiting case where the amplifierpolarisation sensitivity of an SOA is defined as gain is much larger than unity and thethe magnitude of the difference between the amplifier output is passed through aTE mode gain GTE and TM mode gain GTM i.e. narrowband optical filter, the noise figure is given by 5.6 5.8Signal gain saturationThe gain of an SOA isinfluenced both by theinput signal power andinternal noise generatedby the amplificationprocess. As the signalpower increases thecarriers in the activeregion become depletedleading to a decrease inthe amplifier gain. Thisgain saturation can causesignificant signaldistortion. It can also limitthe gain achievable whenSOAs are used asmultichannel amplifiers. A The lowest value possible for nsp is unity,typical SOA gain versus output signal power which occurs when there is complete inversioncharacteristic is shown in Fig. 5.03. A useful of the atomic medium, i.e. N1=0, giving F = 2parameter for quantifying gain saturation is the (i.e. 3 dB). Typical intrinsic (i.e. not includingsaturation output power Po,sat which is defined coupling losses) noise figures of practicalas the amplifier output signal power at which SOAs are in the range of 7 to 12 dB. The noisethe amplifier gain is half the small-signal gain. figure is degraded by the amplifier inputValues in the range of 5 to 20 dBm for are coupling loss. Coupling losses are usually oftypical of practical devices. the order of 3 dB, so the noise figure of typical packaged SOAs is between 10 and 15 dB. Noise figure Dynamic effects A useful parameter for quantifying opticalamplifier noise is the noise figure. F, defined SOAs are normally used to amplifyas the ratio of the input and output signal to modulated light signals. If the signal power isnoise ratios, i.e. high then gain saturation will occur. This would not be a serious problem if the amplifier gain dynamics were a slow process. However 5.7 in SOAs the gain dynamics are determined by the carrier recombination lifetime (average The signal to noise ratios in (5.7) are those time for a carrier to recombine with a hole inobtained when the input and output powers of the valence band). This lifetime is typically ofthe amplifier are detected by an ideal a few hundred picoseconds. This means thatphotodetector. the amplifier gain will react relatively quickly 17
  • 23. to changes in the input signal power. This momentum vector. Direct bandgapdynamic gain can cause signal distortion, semiconductors are used because thewhich becomes more severe as the modulated probability of radiative transitions from the CBsignal bandwidth increases. These effects are to the VB is much greater than is the case forfurther exacerbated in multichannel systems indirect bandgap material. This leads to greaterwhere the dynamic gain leads to interchannel device efficiency, i.e. conversion of injectedcrosstalk. This is in contrast to doped fibre electrons into photons. A simplified energyamplifiers, which have recombination band structure of this material type is shown inlifetimes of the order of milliseconds leading Fig. 5.04, where there is a single CB and threeto negligible signal distortion. VBs. The three VBs are the heavy-hole band, light-hole band and a split-off band. The heavy and light-hole bands are Nonlinearities degenerate; SOAs also exhibit that is theirnonlinear behaviour. In maxima havegeneral these nonlinearities the samecan cause problems such as energy andfrequency chirping and momentum.generation of second or thirdorder intermodulationproducts. However,nonlinearities can also be ofuse. in using SOAs asfunctional devices such aswavelength converters. Fig 5.04: Carrier and optical confinement in DH SOA BULK MATERIAL PROPERTIES An SOA with an active region whosedimensions are significantly greater than thedeBroglie wavelength λB=h/p.( where p is thecarrier momentum) of carriers is termed a bulkdevice. In the case where the active region hasone or more of its dimensions (usually thethickness) of the order of λB the SOA istermed a quantum-well (QW) device. It is alsopossible to have multiple quantum-well(MQW) devices consisting of a number ofstacked thin active layers separated by thinbarrier (non-active) layers. Bulk material band structure and gaincoefficient Fig 5.05: Energy band structure of direct band The active region of a bulk SOA is gap semiconductorfabricated from a direct band-gap material. Insuch a material the VB maximum and CBminimum energy levels have the same 18
  • 24. In this model the energy of a CB electron Where nc and nv are constants given byor VB hole, measured from the bottom or topof the band respectively is given by 5.15 ħ2 ∗ ^2 Ea = 2∗ 5.9 and 5.16 ħ2 ∗ ^2 = 2∗ 5.10 and where kp is the magnitude of themomentum vector, mc the CB electron 5.17effective mass and mv VB hole effective mass. where mhh and mlh and are the VB heavy Under bias conditions the occupationprobability f(c)of an electron with energy E in and light-hole effective masses.the CB is dictated by Fermi-Dirac statistics For a two-level system we have from angiven by expression for the optical gain coefficient at frequency υ 5.11 5.18 Where Efc is the quasi-Fermi level of the This expression applies to any particularCB relative to the bottom of the band, k is the transition. Without lack of generality we canBoltzmann constant and T the temperature. apply it to transitions, having the sameSimilarly the occupation probability of an momentum vector, between a CB energy levelelectron in the VB with energy E, increasing Ea and VB energy level Eb whereinto the band, is given by 5.19 5.12 Thus we obtain the relations: ℎℎ where Efv is the quasi-Fermi level of the Ea= (hυ-Eg(n))*( + ℎℎ )) 5.20VB relative to the top of the band. The quasi-Fermi levels can also be estimated using theNilsson approximation Eb = -(h(υ)-Eg(n))*( + ℎℎ ) = + 64 + 0.05524 64 + −1 5.21 /4} 5.13 Where mhh is the effective mass of heavy Efv = -{ ln ε+ ε [64 +0.05524ε (64+ )]^- hole and me is the effective mass of electrons.1/4}KT 5.14 It is assumed that heavy-holes dominate over light-holes due to their much greater effective Where δ = and ε = mass. 19
  • 25. Thus the optical gain coefficient of theamplifier is given by 5.22 The above equations are used to computethe fitting parameters in farther calculations. 20
  • 26. Modeling of SOA CHAPTER66.1. MODELING Models of SOA steady-state anddynamic behavior are important tools that allowthe SOA designer to develop optimized deviceswith the desirable characteristics.They also allow the applications engineer topredict how an SOA or cascade of SOAsbehaves in a particular application.Some models are amenable to analytical solutionwhile others require numerical solution. Themain purpose of an SOA model is to relate theinternal variables of the amplifier to measurable The band gap energy Eg can be expressed asexternal variables such as the output signalpower, saturation output power and amplifiedspontaneous emission (ASE) spectrum. 6.2In this chapter two important model of SOA are Where Eg0 the band gap energy with no injecteddiscussed. carriers, is given by the quadratic approximation  Steady state numerical model proposed by M.J. Connelly or Connelly model  Dynamic model of SOA or Reservoir 6.3 model Where a, b and c are the quadratic coefficients and e is the electronic charge. ΔEg (n) is the6.1.1. STEADY STATE NUMERICAL band gap shrinkage due to the injected carrierMODEL density given byThis model uses a comprehensive widebandmodel of a bulk InP–InGaAsP SOA. The modelcan be applied to determine the steady-stateproperties of an SOA over a wide range of 6.4operating regimes. A numerical algorithm isdescribed which enables efficient where Kg is the band gap shrinkage coefficient.implementation of the model. The Fermi-Dirac distributions in the CB and VB A. The InGaAsP direct band gap bulk- are given by material active region has a material gain coefficient gm(υ) given by 6.5 6.6 6.7 6.8 Efc is the quasi-Fermi level of the CB relative to the bottom of the band. It is the quasi-Fermi level of the VB relative to the top of the band. 6.1 They can be estimated using the Nilsson approximation. 21
  • 27. = + 64 + 0.05524 64 + −1 /4} 6.9 6.15 Thus we obtain the relations:Efv = -{ ln ε+ ε [64 +0.05524ε (64+ )]^- ℎℎ Ea= (hυ-Eg(n))*( + ℎℎ )) 6.161/4}KT 6.10 Eb = -(h(υ)-Eg(n))*( + ℎℎ ) 6.17 Where δ = and ε = Where mhh is the effective mass of heavy hole and me is the effective mass of electrons. It is assumed that heavy-holes dominate over light-Where nc and nv are constants given by holes due to their much greater effective mass. Thus the optical gain coefficient of the amplifier is given by 6.11 6.12 6.18 The above equations are used to compute the fitting parameters in farther calculations.And gm (υ) is composed of two components one is the gain coefficient And another is the absorption coefficient 6.13 SoWhere mhh and mlh and are the VB heavy andlight-hole effective masses. 6.19For a two-level system we have from anexpression for the optical gain coefficient atfrequency υ 6.14 6.20 9This expression applies to any particulartransition. Without lack of generality we canapply it to transitions, having the samemomentum vector, between a CB energy level 6.21Ea and VB energy level Eb where Plot for gm and gm´ is given in the fig.6.1. 22
  • 28. valid for SOAs with narrow active regions. In the model, the left (input) and right (output) facets have power reflectivity R1 and R2, respectively. Within the amplifier, the spatially varying component of the field due to each input signal can be decomposed into two complex traveling-waves Es+ and Es-, and, propagating in the positive and negative directions, respectively lies along the amplifier axis with its origin at the input facet. The modulus squared of the amplitude of a traveling-wave is equal to the photon rate (s) of the wave in that direction, so The light wave representing the signal must beFigure.6.1. Typical InGaAsP bulk treated coherently since its transmission throughsemiconductor gain spectra. the amplifier depends on its frequency and phase when reflecting facets are present Esk+ and Esk-The SOA parameters used in Connelly model is obey the complex traveling-wave equationsgiven in the table 6.23The material loss coefficient α is modeled as alinear function of carrier density And 6.22K0 and K1 are the carrier-independent and 6.24carrier-dependent absorption loss coefficients,respectively. Boundary conditions B. TRAVELLING WAVE EQUATION FOR SIGNAL FIELD 6.25 6.26In the model, signals are injected with opticalfrequencies υk ( k=1 to Ns) and power Pink Where the k-th input signal field to the left ofbefore coupling loss. The signals travel through the input facet isthe amplifier, aided by the embeddedwaveguide, and exit at the opposite facet. TheSOA model is based on a set of coupleddifferential equations that describe the 6.27interaction between the internal variables of theamplifier, i.e., the carrier density and photonrates. The solution of these equations enables The k-th output signal field to the right of theexternal parameters such as signal fiber-to-fiber output facet isgain and mean noise output to be predicted. In 6.28the following analysis, it is assumed thattransverse variations in the photon rates andcarrier density are negligible. This assumption is 23
  • 29. The k-th output signal power after coupling loss carrier population and helps saturate the gain.is However, it is not necessary to treat the spontaneous emission as a coherent signal, since it distributes itself continuously over a relatively wide band of wavelengths with random phases 6.29 between adjacent wavelength components. When reflecting facets are present, theηin and ηout are the input and output coupling spontaneously emitted noise will show theefficiencies, respectively. presence of longitudinal cavity modes. For thisThe amplitude reflectivity coefficients are reason, it may be assumed that noise photons only exist at discrete frequencies corresponding to integer multiples of cavity resonances. These frequencies are given byThe kth signal propagation coefficient is Where the cutoff frequency at zero injected carrier density is given by 6.30 6.34neq is the equivalent index of the amplifier Δυc is a frequency offset used to match υ0 to awaveguide resonance. Km and Nm are positive integers. The values of Km and Nm chosen depend on the gain bandwidth of the SOA and accuracy required from the numerical solution of the model equations. The longitudinal mode frequency spacing is 6.31 n2 is the refractive index of the InP material 6.35surrounding the active region. neq is modeled asa linear function of carrier density This technique can be applied to both resonant and near-traveling-wave SOAs and greatly reduces computation time. It can be shown that averaging the coherent signal over two adjacent 6.32 cavity resonances is identical to treating the signal coherently in terms of traveling-waveneq0 is the equivalent refractive index with no power (or photon rate) equations. It is sufficientpumping. The Differential in given to describe the spontaneous emission in terms of power, while signals must be treated in terms of waves with definite amplitude and phase. Nj+ and Nj- and are defined as the spontaneous 6.33 emission photon rates (s) for a particular polarization [transverse electric (TE) or C. TRAVELING-WAVE EQUATIONS transverse magnetic (TM)] in a frequency FOR THE SPONTANEOUS spacing centered on frequency, traveling in the EMISSION positive and negative directions, respectively.The amplification of the signal also depends on And obey the traveling-wave equationsthe amount of spontaneously emitted noisegenerated by the amplifier. This is because thenoise power takes part in draining the available 24
  • 30. If the single-pass gain is at , then the signal gain for frequencies within spacing Δυm around υj 6.36 6.42 6.37Subject to the boundary conditions Where the single-pass phase shift is 6.38 6.43The function Rsp(vj,n) represents the At resonance, the signal gain isspontaneously emitted noise coupled into N j+ or -Nj . An expression for Rsp can be derived by acomparison between the noises outputs from anideal amplifier obtained using with the quantummechanically derived expression. An idealamplifier has no gain saturation (which implies a 6.44constant carrier density throughout the Let the amplifier have a noise input spectralamplifier), material gain coefficient, and zero density (photons/s/Hz) distributed uniformlyloss coefficient, facet reflectivities, and coupling over centered. The total output noise (photons/s)losses. In this case, is obtained from the solution in is thento 6.39The output noise power at the single frequency 6.45band If the input noise power were concentrated at (resonance), then the output noise photon rate would be 6.40 Where 6.46The equivalent quantum mechanical expression where 6.47 6.41The traveling-wave power equations describingand assume that all the spontaneous photons in 6.48spacing are at resonance frequencies. In a realdevice the injected spontaneous photons,originating from, are uniformly spread over. Thenoise is filtered by the amplifier cavity. To Kj is equal to unity for zero facet reflectivities.account for this, and are multiplied by anormalization factor which is derived as follows. 25
  • 31. D. CARRIER DENSITY RATE EQUATIONThe carrier density at obeys the rate equation Figure.6.2. the ith section of the SOA model. Signal fields and spontaneous emission are 6.49 estimated at the section boundaries. The carrierWhere I is the bias current and R (n(z)) is the density is estimated at the center of the sectionrecombination rate given by The first step in the algorithm is to initialize the signal fields and spontaneous emission photon rates to zero. The initial carrier density is Rrad(n) and obtained from the solution of carrier density rateRnrad(n) carrier recombination rates, respectively, equation with all fields set to zero, using theboth of which can be expressed as polynomial Newton–Raphson technique. The coefficients offunctions the traveling-wave equations are computed. In the gain coefficient calculations, the radiative 6.50 carrier recombination lifetime is approximated by 6.51Arad and Brad are the linear and bimolecular 6.52radioactive recombination coefficients. Next, the signal fields and noise photon densities are estimated. The noise normalization factors E. STEADY STATE NUMERICAL are then computed. Q (i) is then calculated. This SOLUTION OF CONNELLY process enables convergence toward the correct MODEL value of carrier density by using smaller carrier density increments. The iteration continues untilAs the SOA model equations cannot be solved the percentage change in the signal fields, noiseanalytically, a numerical solution is required. In photon rates and carrier density throughout thethe numerical model the amplifier is split into a SOA between successive iterations is less thannumber of sections labeled from i=1 to Nz as the desired tolerance. When the iteration stops,shown in Fig.6.2. The signal fields and the output spontaneous emission power spectralspontaneous emission photon rates are estimated density is computed using the method of Sectionat the section interfaces. In evaluating Q (i) in VII and parameters such as signal gain, noisethe i-th section the signal and noise photon rates figure and output spontaneous noise power areused are given by the mean value of those calculated. The algorithm shows goodquantities at the section boundaries. In the convergence and stability over a wide range ofsteady-state Q (i) is zero. To predict the steady- operating conditions. A flowchart of thestate a characteristic, an algorithm is used which algorithm is shown in Fig. 6.3.adjusts the carrier density so the value ofthroughout the amplifier approaches zero. Aflowchart of the algorithm is shown in Fig. 6.3. 26
  • 32. Figure.6.3. SOA steady-state model algorithm 27
  • 33. F. ESTIMATION OF THE OUTPUT G. OUTPUT OF THE CONNELLY SPONTANEOUS EMISSION MODEL POWER SPECTRAL DENSITYThe average output noise photon rate spectraldensity (photons/ s/Hz) after the coupling lossover both polarizations and Bandwidth KmΔυmcentered on υj is 6.53 Figure 6.6. predicted and experimental SOA fiber-to-fiber gain versus bias current characteristics. The input signal has a wavelength of 1537.7 nm and power of -25.6 dBm.Figure.6.4. SOA output spectrum. Resolutionbandwidth is 0.1 nm. The input signal has awavelength of 1537.7 nm and power of -25.6dBm. Bias current is 130 mA. The predicted and Figure 6.7. predicted SOA noise figureexperimental fiber-to-fiber signal gains are both spectrum. Input parameters are as for Fig.25.0 dB. The experimental gain ripple of 0.5 dB 5. A noise figure of 11.4_0.5 dB at 1537.7 nm isis identical to that predicted. The difference predicted compared to an experimental value ofbetween the predicted and experimental ASE 8.8_0.3 dB.level is approximately 2.5 dB. 28
  • 34. Figure 6.8. SOA predicted fiber-to-fiber gainand output ASE power versus inputsignal power. Signal wavelength is 1537.7 nmand bias current is 130 mA. 29
  • 35. Figure 6.10. predicted SOA output ASE spectrawith the input signal power as parameter,showing non-linear gain compression. Signalwavelength is 1537.7 nm and the bias current is130 mA. Resolution bandwidth is 0.1 nm.A wideband SOA steady-state model andnumerical solution has been described. Themodel predictions show good agreement withexperiment. The model can be used toinvestigate the effects of different material andgeometrical parameters on SOA characteristicsand predict wideband performance under a widerange of operating conditions. 30
  • 36. SOA PARAMETERS USED IN STEADYSTATE CONNELLLY MODEL 31
  • 37. saturation, and it may significantly affect the SOA steady-state and dynamic responses. Scattering losses also have an impact on the dynamic response of the SOA. Moreover, Agrawal and Olsson’s model was originally cast for single-wavelength-channel6.2. RESERVIOR MODEL amplification, although it can be extended to multi wavelength operation by assuming that theAnother important SOA model is the Reservoir channels are spaced far enough apart to neglectmodel proposed by Walid Mathlouthi, Pascal FWM beating in the co propagating case. SalehLemieux, Massimiliano Salsi, Armando arrived independently at the same model asVannucci, Alberto Bononi, and Leslie A. Agrawal and Olsson’s coincides with and thenRusch. introduced further simplifying approximations toThis model is the dynamic version of the steady get to a very simple block diagram of the single-state Connelly model. We are interested in channel SOA, which was exploited for aanalyzing the response of SOAs to optical mathematically elegant stochastic performancesignals that are modulated at bit rates not analysis of single-channel saturated SOAs. Theexceeding 10 Gb/s, such as those planned for loss of accuracy due to Saleh’s extranext-generation metropolitan area networks. approximations with respect to Agrawal’s modelTherefore, ultrafast intra band phenomena such was quantified in Saleh’s model was lateras carrier heating (CH) and spectral hole burning extended to cope with injection current(SHB) can be neglected, and only carrier modulation, scattering losses, and ASE. Ininduced gain dynamics need to be included, as addition, Agrawal’s model was extended towas done in several SOA models developed in include ASE in both and ASE was addedthe past. Such models can be divided into two phenomenologically at the output of the SOAbroad categories: 1) space-resolved numerically and did not influence the gain dynamics, therebyintensive models, which take into account facet limiting the application to very small saturationreflectivity as well as forward and backward levels.propagating signals and amplified spontaneous In this paper, we first develop a dynamic versionemission (ASE) and offer a good fit to of the steady-state wideband SOA Connellyexperimental data simplified analytical models model which is shown to fit quite well with ourwith a coarser fit to experimental data but dynamic SOA experiments with OOK channels.developed to facilitate conceptual understanding The Connelly model was selected because itand performance analysis. For the purpose of derives the SOA material gain coefficient fromcarrying out extensive Monte Carlo simulations quantum mechanical principles without thefor statistical signal analysis and bit-error rate assumption of linear dependence on carrier(BER) estimation, the accurate space-resolved density that was made in.models are ruled out because of their Our dynamic Connelly model serves then as aprohibitively long simulation times. However, a benchmark to test the accuracy andsimplified model with a satisfactory fit to computational-speed improvement of a novelexperimental results would be highly desirable. state-variable SOA dynamic model, whichMost simplified models can be derived from the represents the most important contribution ofwork of Agrawal and Olsson. Under suitable this paper. The novel model is an extension ofassumptions, Agrawal and Olsson managed to Agrawal’s model, with the inclusion ofreduce the coupled propagation and rate approximations for scattering loss and ASE toequations into a single ordinary differential better fit the experimental results and theequation (ODE) for the integrated gain. The dynamic Connelly model predictions. In such asimplicity of the solution is due to the fact that model, the SOA dynamic behavior is reduced towaveguide scattering losses and ASE were the solution of a single ODE for the single stateneglected. ASE has an important effect on the variable of the system, which is proportional tospatial distribution of carrier density and the integrated carrier density, which, for WDM 32
  • 38. operation is a more appropriate variable than the provides a new entry aside from the alreadyintegrated gain used in. Once the state-variable known models for EDFAs and for Ramandynamic behavior is found, the behavior of all amplifiers .A challenge in our reservoir model,the output WDM channels is also obtained. The as in all simplified SOA models, is to correctlystate variable is called ―reservoir‖ since it plays choose the values of the wavelength-dependentthe same role as the reservoir of excited erbium coefficients that give the best fit to theions in an erbium-doped fiber amplifier (EDFA). experimental results. We propose and describeQuite interestingly, then, the SOA for WDM here a methodology to extract the neededoperation admits almost the same block diagram wavelength-dependent coefficients from thedescription as that of an EDFA suggested by parameters of the dynamic Connelly model.Such a novel SOA block diagram is shown in This paper is organized as follows. In Section II,Fig. 6.11 (without ASE for ease of drawing) and the dynamic Connelly model is introduced, andwill be derived in the next sections. Note that a procedure to derive its parameters fromthis model treats the intensity of the electrical experiments is described. In Section III, thefield, but the field phase can be indirectly SOA reservoir model is derived first withoutobtained since it is a deterministic function of ASE and then with ASE that is resolved over athe reservoir. In the SOA, the role of the optical large number of wavelength bins. Simulationspump for EDFAs is played by the injected show good accordance between the reservoircurrent I. The most striking difference between model predictions and experiments, and goodthe two kinds of amplifiers is the fluorescence improvement in calculation time with respect totime τ, which is of the order of milliseconds in the Connelly model. However, inclusion ofEDFAs and of a fraction of nanosecond in many ASE wavelength channels makes even theSOAs. Such a huge difference accounts for most reservoir model too slow for the BERof the disparity in the dynamic behavior between estimations we have in mind. Hence, in order tothe two kinds of amplifiers and explains why further simplify the model, we introduce theSOAs have not been used for WDM applications reservoir model with a single equivalent ASEfor a long time]. However, recent cheap gain- channel. The ASE can be seen as an independentclamped SOAs] are likely to promote the use of input-signal channel (with proper input powerSOAs for WDM metro applications. As already and wavelength) that depletes the reservoir of amentioned, the reservoir model requires the (co- noiseless SOA. Results show that this last modelpropagating) WDM channels to have minimum is the most efficient one since it can be made tochannel spacing in excess of a few tens of accurately predict experimental results with angigahertz, in order to neglect the carrier-induced execution time that is 20 times faster than that ofFWM fields generated in the SOA. This should the dynamic Connelly model for single-channelnot be a problem for channels allocated on the operation, with the savings increasing with theInternational Telecommunications Union grid number of WDM signal channels. In Section III-with 50 GHz spacing or more. However, an C, we examine a model that was obtained byintrinsic limit of the reservoir model is its dividing the SOA into several sections, eachneglecting SHB and CH, which generate FWM characterized by its own reservoir. Here again,and XPM interactions among WDM channels the ASE can be modeled as a single channel thateven when the minimum channel spacing is propagates through the different reservoir stages.large enough to rule out any carrier-induced Results show better precision, although theinteraction. The predictions of the reservoir increase in precision is not worth, in most cases,model will be accurate whenever the carrier the loss in execution time. Most of the numericalinduced XGM mechanism dominates over FWM results are reported in Section IV. Finally,and XPM. It is worth mentioning that state- Section V summarizes the main findings of thisvariable amplifier block diagrams are very paper.important simulation tools that enable thereliable power propagation of WDM signals inoptical networks with complex topologies;therefore, the present reservoir SOA model 33
  • 39. 6.56 where I is the bias current; q is the electron charge; d, L, andW are the active-region thickness, length, and width, respectively, and R(N) is the recombination rate. The reservoirFigure6.11. Block diagram of the reservoir model of Section III uses a linear approximationmodel. ASE contribution not shown for ease of for R (N) in (9); nsig is the number of WDMdrawing. signals; nASE is the number of spectral components of the ASE; and Kj is an ASE multiplying factor, which equals 1 for zero facet6.2.2 DYNAMIC CONNELLY MODEL reflectivity [12]. The factor 2 in accounts for two A. Theory ASE polarizations. Note that equation containsIn this paper, we adopt the wideband model for a an important approximation: it is the sum of thebulk SOA proposed in Connelly model, which is signals and ASE powers (fluxes), instead of—based on the numerical solution of the coupled more correctly—the power of the sum of theequations for carrier-density rate and photon signals and ASE fields, which depletes carrierflux propagation for both the forward and density N. Therefore, (3) neglects the carrier-backward signals and the spectral components of density pulsations due to beating among WDMASE. At a specified time t and position z in the channels that generate FWM and XPM in SOAsSOA, the propagation equation of photon flux [9]. Although such an approximation isQ±k [photons/s] of the kth forward (+) or inappropriate for extremely dense or high-powerbackward (−) signal is WDM channels, it is accurate for typical wavelength spacing of 0.4 nm or more. The material gain gk(N) ≡ g(νk,N) is calculated as in Connelly model. Fig.6.12 plots the material gain 6.54 N versus wavelength λk = c/νk (with c being thewhere Γ is the fundamental mode confinement speed of light) using the SOA parameters.factor, gk is the material gain coefficient at theoptical frequency νk of the kth signal, α is thematerial-loss coefficient, and both are functionsof carrier density N(z, t). The power of thepropagating signal is related to its photon flux asP±k = hνkQ± k (in watts), where h is Planck’sconstant. The ASE photon flux on each ASEwavelength channel obeys a similar propagationequation given by 6.55where Rsp,j(N) is the spontaneous emission ratecoupled into the ASE channel at frequency νj.The expression of Rsp,j(N) will be used inSection III-B to develop a reservoir modelequation that takes ASE into account. The Figure.6.12. Gain coefficient g(λ,N) versuscarrier density at coordinate z evolves as wavelength and carrier density 34
  • 40. B. Parameterization 3) The parameters of the carrier-dependentIn order to fit the experimental results that we material-loss coefficient, i.e.obtained with a commercial Optospeed SOAmodel 1550MRI X1500, we used the SOA α (N(z)) = K0 +ΓK1Nparameters provided in the Table in Connellymodel, except for a subset of different values where chosen so that the maximum simulatedreported in Table I in this paper; the most critical gain matched the measured one.of such parameters were determined as follows. 4) The active-region thickness and width were1) The active-region length L was determined by set so as to match the experimental andmeasuring the frequency spacing between two simulated curves of gain as a function of themaxima of the gain spectrum ripples: L = λ20 injection current./2nrΔλ, where λ0 is the central wavelength(1550 nm), nr is the average semiconductor 5) The band gap shrinkage coefficient Kg wasrefractive index, and Δλ is the ripple wavelength set so that the peak gain wavelength equals thespacing. measured value of 1560 nm at an injection current of 500 mA.2) The band gap energy Eg0 was set so that theexperimental cutoff wavelength of the gainspectrum (which was about 1605 nm) matchedthe simulated one. 35
  • 41. Figure.6.13. Fiber to fiber unsaturated gain versus wavelength. Measured (dashed) and simulation (solid) results using Connelly model. ensuing Fig. 4 fiber to fiber gain versus inputC. Simulations with Connelly Model optical power. Measured (dashed) and ConnellyWe present simulation results obtained with the model (solid). Experiments and simulations, theConnelly model and compare them against input signal will be fixed at the gain peakexperimental measurements. wavelength of 1560 nm.The experiment consisted in amplifying atunable continuous wave (CW) laser whose 2) Gain Saturation: Fig. 6.13. shows the fiber-wavelength was varied around the Optospeed to-fiber gain as a function of the input power.SOA peak gain wavelength. Laser polarization The wavelength of the input laser was 1560 nm,was controlled so as to obtain maximum gain. and the injection current was 500 mA.1) Unsaturated Gain Spectrum: Fig. 3 shows the 3) Dynamic Response: The experimental setup issimulated and measured unsaturated gain spectra depicted in Fig. 5. The input laser at 1560 nmat a signal input power of −30 dBm and an was externally modulated at 1 Gb/s. The laserinjection current of 500 mA. A good match power was varied from −25 to −10 dBm in stepsbetween the simulations and experiments was of 5 dB. The measured photo receiverobtained when using the values of Table I. In the responsively was 400 mV/mW. The injection 36
  • 42. current was 500 mA. Since we are interested in Figure.6.15. Response to square wave input (seetesting the action of the SOA on the propagating inset representing optical input power in dBm).signal power in this paper, no optical filter was Measured (dashed) and dynamic Connellyinserted before detection. model (solid).The measured experimental input pulses to theSOA were replicated in the simulator. The 6.3. RESERVOIR MODELlength of the input-signal time series was 1350 We now derive the reservoir model for apoints over a 2-ns time window. In Fig. 6, we traveling-waveplot the experimental and the simulated output SOA (zero facet reflectivity) fed by WDMpulses at an input power of −18 dBm. At this signals. For k =1, . . . , nsig, the propagation andpower level, the SOA is not heavily saturated by carrier density updatethe signal; thus, the ASE-induced saturationsignificantly contributes to the dynamicresponse.Fig. 6.15 demonstrates that the dynamic 6.57Connelly model is also able to accurately predictthe amplified output pulse shape.Similar results were also obtained for manydifferent input powers and signal wavelengths. 6.584) Computation Time: The major drawback of where A and V = AL are the active waveguidethe Connelly model is its long execution time. area and volume, respectively, and weOur Matlab code, which was run on a 3-GHz introduced the propagation direction variable uk,Intel processor, took about 12 s to calculate an which equals +1 for forward signals and −1 foroutput bit resolved over 1350 points. Similar backward signals. · QASE j stands for ancalculations for a time series of 50 000 points equivalent ASE flux that accounts for the impact(37 bits) took about 432 s. This presents a major of both forward and backward ASE on thelimitation when typical Monte Carlo BER carrier-density update equation. The formalestimations are sought, which require solution of the propagation equation is obtainedtransmission of millions of bits. A drastic by multiplying both sides by uk, dividing themsimplification of the gain dynamics calculation by Qk, integrating both sides in dz from z = 0 tois required in order to significantly decrease z = L for each k, and obtain an equivalentexecution time. Reduced computation time and equation of the form Qout k = Qin k Gk, wherethe facility of analysis motivate our introduction the gainof the reservoir model. 6.59 is independent of the signal propagation direction. For convenience, we will let 6.60 denote the net gain coefficient per unit length in the SOA. Now, define the SOA reservoir as 6.61 which physically represents the total number of carriers in the SOA that are available for 37
  • 43. conversion into signal photons by the stimulated plot of gnet k (λ,N) would have a similar form;emission process. If one approximates both the in particular, a rigid shift downward wouldrecombination rate and the material gain as result if K1 = 0, i.e., if α did not depend on N.linear functions of N then Fig. 7 gives a slice of the surface in Fig. 2 at a 6.62 wavelength of 1560 nm, which was plotted over a wide range of carrier density N. As shown, a linear approximation of the gain coefficient is 6.63 well justified especially as the physicallywhere τ is the fluorescence time and σk[m2] and achievable range of carrier densities is muchN0k[m−3] are wavelength-dependent fitting smaller than the range shown. Our task is now tocoefficients, then one obtains provide good estimates of the wavelength- dependent coefficients σk and N0k. First, we identify the achievable range of N over which we will restrict our linear fit. To this aim, usingWhere 6.64 the steady-state Connelly model, we calculated the maximum and minimum values of the ―average carrier density,‖ i.e., 6.65 6.66 6.69are two dimensionless parameters. In addition, which were obtained for the extreme cases of aone can multiply both sides of the second single input signal at very low (−40 dBm) andequation in (5) by A and integrate in very high (0 dBm) input power at 1560 nm.dz to obtain These extremes cover the small-signal regime and saturation at an injection current of 500 mA without ASE was used to find N (z) at steady state (dN/dt = 0) for a small signal and saturation 6.67 at λk. The carrier density was integrated across zFor the time being, the contribution of ASE will to give the extreme values Nmax,k and Nmin,k,be neglected. which are depicted in Fig. 7. The process wasIt will be tackled in Section III-B. Now, repeated at each wavelength from 1450 to 1600integrating in dz both sides of the first equation nm in intervals of 5 nm. The parameters of thein (5) gives gain coefficient linear fit were then extracted from the extreme values as follows: 6.68the ―reservoir dynamic equation‖ given by 6.70 where gmax,k_= g(λk,Nmax,k) and gmin,k is similarly defined.Note that the reservoir dynamic equation is quite In Fig. 8, we provide the wavelengthsimilar to the EDFA reservoir equation. dependence of the extracted fitting parameters σk and N0,k for our Optospeed SOA. Once theA. Extraction of Reservoir Parameters from liberalized gain parameters are calculated, weConnelly Model can investigate the steady state and the dynamicWe next explain how to extract the fitting behavior predicted by the reservoir model and,parameters of the gain linearization from the as explained in the Appendix, look for the valueConnelly gain g (λ,N), whose plot versus of τ that best fits the steady-state and dynamicwavelength and carrier density was already experimental curves. However, before doing so,given in Fig.6.12 for our Optospeed SOA. A the fundamental role of spontaneous emission in 38
  • 44. the rate equation must be properly accounted previous section. The ASE flux at z is obtainedfor. by solving the propagation (2) with zero initial condition 6.71 where Gj(z) = exp[_z 0 Γgnetj (N(z ))dz] is the gain from 0 to z. If, for this calculation, we assume that the carrier density is constant along z at the average carrier density N = r/V, then the preceding equation simplifies to 6.72 Such an expression can now be used to evaluate the ASE IntegralsFigure.6.16. Connelly gain coefficient g(dashed) and net gain coefficient gnet in(7) (solid) versus carrier density N for λ = 1560 where G(r) = exp{Γgnet j (N)L} is the gain andnm. SOA parameters as in is a function of the reservoir only.Table I. Dotted is the linear approximation used If we linearize gin the reservoir model. j(N) ∼ =γj(N − N1j) and use the linearization 6.73 where r1j_= N1jV . As a dimensional check, γj and A are measured in [m2], while aj is dimensionless so as to correctly obtain a dimensionless nsp,j . Fig. 6.17. also shows the values of the wavelength-dependent coefficients γj and N1j in the linearization of g , which were obtained using exactly the same procedure that yields the linearization coefficients of g detailed in Section III-A. Finally the reservoir dynamic equation including ASE becomesFigure.6.17. Coefficients σk (squares solid) andN0, k (triangle solid) of the linearization of thegain coefficient g versus wavelength for ourOptospeed SOA. Also shown are the coefficientsγk and N1,k of the linearization of the emissiongain coefficient g_ 6.74B. Including ASE C. Multistage Reservoir ModelWe now take into account the ASE-induced The multistage reservoir model consists ofsaturation term in (5) that was neglected in the subdividing the SOA into several cascaded 39
  • 45. sections or ―stages,‖ each characterized by its Fig. 6.18. . Variation of the total output ASEown reservoir (Fig. 10). Let ns be the number of power for a square input pulse train simulationstages. Then, the reservoir equation for each results with dynamic Connelly model (solid) andstage i is with reservoir model including ASE (dashed). 6.74where ri is the reservoir of the ith stage withlength Li = L/ns and Gk(ri) is its gain given in(10) and (11) (where Li is used instead of L), andnsp,j is the spontaneous emission factor in (21). Figure.6.19. Multi stage reservoir model.For the signal channels, the flux Qin k,i+1 inputto the (i + 1)th stage is the output flux of the ith D. Reservoir Model with Single-Channel ASEstage, which is in turn equal to the ith reservoir Consider the single-stage reservoir model. Ingain Gk(ri) multiplied by its input flux Qin k,i. order to further speed up calculations, we nowFor the ASE channels, the first-stage input flux introduce a single fictitious CWinput ASEis zero. The output ASE of one stage becomes channel. Once its wavelength is fixed, the poweran input ASE signal to the next stage, which is of such a CW channel should be chosen so thataccounted for in (23) by the second summation the time behavior of reservoir r (t) in a noiselessterm. The third summation term is, as usual, the SOA is as close as possible to r(t) in the actualASE generated inside stage i. considering SOA that is saturated by signals and ASE. Weforward ASE only has the advantage of call such an input channel the ―ASE depletingsimplicity, but the approximation brought into a channel’multistage scenario is evident: Each stage issaturated by forward ASE from the upstreamstages. Modeling the SOA with multiple stagesis similar to the algorithm used in the space 6.4. RESULTSresolved models, which provide the carrier- The purpose of this paper is to demonstrate thatdensity evolution N(t, zi) at discrete positions zi calculations using the SOA reservoir model arealong the SOA. Hence, the multistage reservoir much faster than the space resolved Connellymodel is expected to give similar results to the model and hence, are suitable for Monte CarloConnelly model. simulations. We also demonstrate that using the correct wavelength-dependent parameters, the reservoir model is sufficiently accurate. In this section, we first compare the computation speed of both models. Then, we assess the accuracy of the reservoir models that were developed in the previous sections by comparing gain spectrum, gain saturation, and dynamic response with the predictions of our experiments. A. Calculation Speed We present the calculation times required for different models, namely, the dynamic Connelly model presented in Section II, the reservoir model with multiple ASE channels in Section III-B, and the reservoir model with a single ASE channel in Section III-D. For the reservoir model, we determined the computation time for 40
  • 46. a single-stage SOA, as well as three multistageSOAs (two, five, and ten stages). Thecalculation times in Table II refer to theresponse to a single input pulse with a durationof 2 ns that was resolved over 1350 temporalpoints. As a reference, the execution time for theConnelly model was 11.95 s. The calculationtimes in Table III refer to the response to a stringof multiple pulses with the same time step asbefore, for a total of 50 000 temporal points. Asa reference, the execution time for the Connellymodel was 432.54 s. In the Connelly model, wealways used a space resolution of 43.33 μm,with the ASE resolved over 30 channels in binsof 2.5 nm each, which were symmetricallyarranged around the gain peak. As shown, thereservoir model with single-stage ASE is always Fig. 6.21. Fiber to fiber gain versus inputthe fastest model. The simulation is 20 times optical power. Measured (dashed) andfaster than the Connelly model when a single simulation (solid) results using the singleASE channel is used. However, when several (squares) and five-stage (circles) reservoir withreservoir stages are used, the calculation speed 20 ASE channels.of the single-ASE model becomes of the sameorder as that of the multiple-ASE case. In thiscase, the use of multiple ASE channels is betterfor accuracy.The improvement in computation time in allreservoir models with respect to the Connellymodel is predicted to significantly increase whenincreasing the number of propagated WDMsignal channels. Fig. 6.22. Response to square wave input. Measured (dashed) and simulation (solid) results using the single (squares) and five-stage (circles) reservoir with 20 ASE channels. B. Single-Stage Reservoir with ASE 1) Gain Spectrum: Fig. 6.20 shows both simulated (solid lines with markers) andFig. 6.20. Fiber to fiber gain spectrum versus experimental fiber-to-fiber (dashed dotted line)wavelength. Measured (dashed) and simulation gain versus wavelength. The input laser power(solid) results using the single (squares) and was −25 dBm. We can see a reasonable matchfive-stage (circles) reservoir with 20 ASE between simulations and experiments. A slightchannels gap between simulation and experiment is 41
  • 47. observed at shorter wavelengths. The peak gainwavelength was the same in both simulationsand experiment. We also see that the five-stagereservoir model is slightly more accurate thanthe single-stage reservoir one.2) Gain Saturation: Fig. 6.21 shows bothsimulated and experimental fiber-to-fiber gainsversus input power at a signal wavelength of1560 nm. We see that the simulations reasonablypredict the small-signal gain. A slightdiscrepancy is observed when saturation sets in.This is attributed to the fact that the ratio gk/gnetk is larger than one in deep saturation since thedenominator tends to zero. In such cases, it is Fig. 6.23. fiber to fiber gain versus optical inputpreferable to include the term gk(r)/gnet k (r) in power. Measured (dashed) and simulated (solid)the reservoir equation rather than set it to 1 and results using a three-stage reservoir with singleplay with the fitting parameter τ, as we did in channel ASE.this paper. Here again, we see that the five-stagereservoir is closer to the experimental data.3) Dynamic Response: Fig. 6.22 shows thesimulated (solid with squared markers) andexperimental (dashed) response in mill watts to asquare-wave input (see inset in Fig. 6).Simulations include the ASE total detectedpower, which plays a fundamental role in thereservoir equation, since it partially saturates theamplifier, hence reducing the amplifier gain. Wesee that the CW levels (zero and one levels) arewell predicted in Fig. 6.22. This suggests thatthe approximation that we used to calculate theASE power is valid, although the simulated andexperimental output pulses are slightly different. Fig. 6.24. Response to a square wave input.We see that the pulse’s overshoot and Measured (dashed) and simulated (solid) resultsundershoot are better predicted by the five-stage using a three-stage reservoir with ASE depletingreservoir model. channel. C. Multistage Reservoir With ASE Figs. 6.20–6.22 show the gain spectrum, gain saturation at 1560 nm, and the output pulse power for the five-stage (solid with circle markers) reservoir with ASE, respectively. The parameters used in the simulations are the same as those considered in the single-stage reservoir model. Increasing the stage number beyond five does not increase the accuracy, which might be attributed to the neglect of ASE that propagates backward across the stages. In these figures, we see that the dynamic and steady-state fits are 42
  • 48. more accurate than those in the single stage. Fig. 16 shows the measured power at the outputParticularly, the simulated gain spectrum shape of our Optospeed SOA as well as simulation(Fig. 6.20) is closer to the experimental one results using the Connelly model and (a) a one-compared with the single-stage reservoir. stage reservoir model and (b) a three-stageMoreover, the overshoot and undershoot of the model, in which the fluorescence τ was set at theoutput pulse are much closer to the experimental value of 360 ps to best match the measurements.one. However, this precision comes at the price The SOA was fed with four synchronouslyof simulation speed: The larger the number of OOK-modulated WDM signals with astages, the longer the execution time. An wavelength spacing of 3 nm (λ1 = 1550 nm, λ2 =advantage of the multistage model is that it 1553 nm, λ3 = 1556 nm, and λ4 = 1559 nm).allows trading execution time for precision, The SOA output is optically filtered so that theeventually reaching a comparable precision (and ASE is eliminated, and the desired channel isa comparable computational burden) as the selected. The optical filter is 1.2 nm wide, so itsspace-resolved Connelly model. effect on the pulse shape is negligible at an experimental bit rate of 1 Gb/s. The averageD. Multistage Reservoir With ASE Depleting input power of each channel is −20 dBmChannel (experimentally, lower input power showedIn order to fit the experimental results, we noisy pulses). Under such conditions, wearbitrarily fixed the ASE-depleting-channel observe a good match between thewavelength at 1520 nm and then found the value measurements and the Connelly modelof its input flux, which gave the minimum mean predictions. A reasonable match is also obtainedsquare error fit with the prediction of the between the experiment and the reservoirConnelly model. As shown in Figs. 14 and 15, models. However, we verified that at lower inputthe simulation results are not far from the powers, the simulations give a less exact fit.experimental ones, but they are less accurate The lack of accuracy during the transients is duethan those in the multichannel ASE case. To to the linear approximations of the gain andinvestigate the dynamic response, we cascaded recombination rate.three reservoir stages and propagated both the Note the different slopes of measured andsignal and the ASE depleting channel. simulated pulses after the overshoot in Fig. 15.We note from the figures that simulations fit We believe the reason for this to lie in the linearmeasurements in a way comparable to the approximation of R(N) is when the signalmultistage reservoir with ASE, which proves the reaches a maximum (and the carrier densityeffectiveness of the ASE-depleting-channel reaches a minimum), the actual time constant ofapproach. Moreover, the advantage of this the SOA is larger than that employed in (9).approach is the computation speed. In fact, ASE- Moreover, ultrafast phenomena (neglected indepleting-channel simulations are twice as fast this paper) will have an increasing impact foras those for the multichannel ASE case (see overshoots and undershoots on the order of aTables II and III). The use of more than three few picoseconds.stages does not improve accuracy.E. WDM AmplificationIn order to verify the efficiency of our model fora wider range of simulation scenarios, weinvestigated the case of WDM-signalamplification. We recall that both the Connellyand the reservoir models are not able toreproduce carrier induced nonlinear effects suchas FWM and XPM and can only model theeffects of carrier-induced self-gain modulationand XGM. 43
  • 49. Fig. 6.25. Response of four WDM channels (with a spacing of 3 nm) to a square wave input (see inset showing input optical powers in dBm). (a) Measured (dashed) and dynamic Connelly model (solid). (b) Measured (dashed), one stage reservoir with single channel ASE (solid with squares) and three-stage reservoir with single channel ASE(solid with circles).6.5. CONCLUSION A critical step in the SOA reservoir model is theA novel state-variable SOA model that is appropriate selection of the values of itsamenable to block diagram implementation for wavelength-dependent parameters that provide aWDM applications and with fast execution times good fit with the experiments. We proposed andwas presented and discussed. We called the described at length a procedure to extract suchnovel model the reservoir model, in analogy parameters from the parameters of a detailed andwith similar block oriented models for EDFAs accurate space-resolved SOA model due toand Raman amplifiers. While ASE self- Connelly, which we extended to cope with thesaturation can be simply included in the EDFA time-resolved gain transient analysis. It isreservoir model [28], an added complexity in important to note that our reservoir model is notSOAs with respect to EDFAs is that scattering entirely dependent on the space resolvedlosses cannot be neglected. These increases the simulator. The key wavelength-dependentdifficulty in developing a reservoir model for parameter for the reservoir model is the materialSOAs, and we proposed innovative solutions to gain as a function of both wavelength andtackle the problem. inversion. A detailed knowledge of this dependence allows accurate linearization around 44
  • 50. the working point and hence, more accuracy for induced by ASE. To speed up the emulation ofthe reservoir model. A procedure to extract the transmission of long bit sequences in themodel parameters directly from the reservoir model, we introduced a singlemeasurements would be of great practical value. equivalent input ASE channel with appropriateA number of other issues remain to be explored power and gain parameters, which feeds aand deserve further research. The presence of noiseless reservoir model to give equivalentnonzero facet reflectivity was not considered dynamics.and would be important for modeling reflective We showed that at a comparable accuracy, theSOAs with the reservoir. In addition, a different reservoir model with the single ASE channel canapproximation for the recombination rate, be 20 times faster than theaccounting for a reservoir-dependent time Connelly model in single-channel operation andconstant, could increase the reliability of the much more significant time savings are expectedmodel. In this paper, we assumed a linear for WDM operation. The accuracy of the modeldependence of this parameter on the inversion. is limited to modulation rates per channel notA better approximation (R(r) = a1(r) + a2r2 + exceeding 10 Gb/s since ultrafast phenomenaa3r3 + . . .) could be obtained if we assume a such as CH and SHB are neglected. However,constant inversion such rates are of interest for next-generationN = r/V over the SOA length (as we did for ASE metropolitan optical networks. In addition,calculations in Section III-B). However, the beating-induced carrier gratings that generateaccuracy obtained with such approximations will FWM and XPM in SOAs are not captured by thebe at the cost of slower execution time. reservoir model, which then is reliable wheneverThe raison d’être of the reservoir model is to XGM dominates over such effects. The truefind a tradeoff between accuracy and calculation value of the SOA reservoir model is thatspeed. To achieve this goal, we considered together with block diagram descriptions ofseveral variations of the model, with increasing EDFA and Raman amplifiers, it provides acomplexity, which allow the accurate inclusion unique tool with reasonably short computationof both scattering losses and gain saturation times. 45
  • 51. Cross-gain modulation Chapter 7 The material gain spectrum of an SOA is In order to suppress the sensitivity tohomogenously broadened. This means that polarization inherent to planar structures,carrier density changes in the amplifier will especially when quantum-well active regionsaffect all of the input signals. The carrier are used, SOAs require specific designs thatdensity temporal response is dependent on the make their coupling efficiency to optical fiberscarrier lifetime. Asdiscussed in thepreceding chapter,carrier density changescan give rise to patterneffects and interchannelcrosstalk inmultiwavelengthamplification. The mostbasic cross-gainmodulation (XGM)scenario is shown in Fig.7.01 where a weak CW Fig 7.01 (Simple Wavelength converter using XGM in SOA)probe light and a strong pump light, with a quite low.small-signal harmonic modulation at angularfrequency ω are injected into an SOA. XGMin the amplifier will impose the pump All-optical wavelength converters aremodulation on the probe. This means that expected to become key components in futurethe amplifier is acting as a wavelength broadband networks. Wavelength conversionconverter, i.e. transposing information at one techniques include cross-gain modulationwavelength to another signal at a different (XGM) or cross-phase modulation (XPM) inwavelength. semiconductor optical amplifiers (SOA), four- wave mixing (FWM) in passive waveguides, The most useful figure of merit of the SOAs, or semiconductor lasers, gain-converter is the conversion efficiency η suppression mechanism in the semiconductorwhich is defined as the ratio between the lasers such as DBR lasers, and T-Gate lasers,modulation index of the output probe to the laser-based wavelength conversion, andmodulation index of the input pump. difference frequency generation (DFG). Optical XGM in SOAs has beenSemiconductor optical amplifiers (SOA) intensively studied in the past. However, theredisplay nonlinear optical response on short are relatively few papers on XGM intime scales which arises from the changes semiconductor lasers, especially small-signalinduced by the injected optical field in both the modulation.total carrier density and its distribution over An intensity-modulated input signal at athe energy bands. These ultrafast optical pump wavelength λ2 is used to modulate thenonlinearities may allow for efficient all- carrier density and consequently also the gainoptical signal processing. Actually, all-optical of a test laser due to gain saturation. In the testwavelength conversion of the signal, data- laser, a continuous wave (CW) beam at desiredformat translation and add-drop functionalities test wavelength λ1 (called the test signal) ishave been demonstrated by using SOAs via modulated by the gain variation. In this way,cross-gain modulation (XGM), cross-phase information is transferred from the pumpmodulation, or four-wave mixing. SOAs are wavelength to the test wavelength. The XGMusually of the travelling-wave type, which response, which is obtained by pumping in themaximizes the optical bandwidth by strongly gain region of the quantum wells (QWs), is ofsuppressing the ripples due to facet great practical significance for wavelengthreflectivities. conversion. The modulation response in this case will suffer virtually no adverse transport 46
  • 52. effects; hence, the response is practically νg group velocity;intrinsic in nature, and shows a clear picture of τp photon lifetime;the physical interactions taking place in the Γ optical confinement factor;semiconductor laser. Our theoretical model G1,2 gain at the test and pump laser wavelength, respectively.also focuses on small-signal analysis, which is In order to take into account the effects ofused to study the modulation bandwidth or nonlinear gain suppression with cross-gain-wavelength conversion speed. If one is saturation, we include ε11 and ε22,which areinterested in bit-error rate, however, a large- the self-nonlinear gain saturation coefficients,signal approach is required. Several groups and ε12 and ε21, which are the cross-nonlinearhave measured the optical-absorption gain saturation coefficients. The cross-modulation response of a semiconductor laser saturation properties of the gain due to pump-for optical pumping within the QW region, test-laser interactions describe how the pumpwhere the pump photons create electron-hole and test signals interact with each other in thepairs as they are absorbed. The newly created active region. The gain suppression at acarriers relax into the lower states of the QW, wavelength λ1 will be due to the presence ofmodulating the QW carrier density and the both the test and pump photon densities,laser output. When the optical pump although not necessarily to the same degree.wavelength is within the gain region of the test The spontaneous emission term has beenlaser, the pump signal will be amplified neglected because the test laser is abovethrough stimulated recombination of carriers threshold.rather than the creation of carriers throughabsorption. The amplification of the pump A. Steady-State Solutionsignal will have two major effects. First, the In the steady state, the time-varying termscarrier lifetime will decrease because of are set to zero in the rate equations 7.1 and 7.2.stimulated recombination. Second, the test- The equation for the photon density is used tolaser intensity will decrease at a given bias define the steady-state gain–loss relationwhen the pump signal is injected. The test-laser photon density and carrier lifetimesignificantly impact the modulation response 7.3of the laser. Moreover, there are effects whicharise from cross-gain saturation due to the For simplicity in notation, capital letters S1presence of more than one intense laser field and S 2 stand for steady-state values. Thewhich can also influence the modulation equation for the carrier density can also beresponse. used to solve for the light–current (L-I) Consider a pump laser (denoted by the characteristics of the test laser, after setting thesubscript 2) with a photon density S2 time-varying terms to zerocompeting for the gain with a test laser(denoted by the subscript 1) with a photondensity S1. The rate equations for the carrierdensity N(1/cm3 ) and the photon density 7.4S1(1/cm ) of the lasing mode (test signal) are where, is the original 7.1threshold current without an external pump. With cross saturation, the L-I relationship may not behave as a simple, linear function. For a given test-laser current I, the photon density of 7.2 the test-laser S1 will be less than what it would be if S2 were not present, since the pump where, competes for carriers, causing both a shift in I test-laser current; threshold for the test laser and a change in the V volume of the active region; slope of its L-I curve. q unit charge of the carrier; τn carrier lifetime; 47
  • 53. B. Small-Signal Solution in which the effective carrier lifetime τn’ due In this section, the changes in the lasing to stimulated recombination by the pump S2 ismode photon densities and carrier density due defined asto the pump signal variation are assumed to bemuch smaller than the steady-state value of the 7.13photon and carrier densities. To solve for thesmall-signal modulation response, theexpressions for carrier and photon densities are and the cross-gain saturation term X is 7.5 7.6 7.14 7.7 Now the damping factor can be defined, and by linearizing the gain function after simplification, as 7.8 where g’1,2 is the differential gain at 7.15wavelength λ1 or λ2. For the small-signal and the resonant frequency squared may beanalysis, the quantity N-N0 will equal the written assmall-signal change in carrier density, denotedby η. Taylor’s series expansion is used to simplifythe small-signal form of the rate equations.Note that the source of modulation is the pump 7.16photon density. Terms containing products of or, replacing 1/τn’ by 1/τn using 7.13steady-state and small-signal components arelinearized, and only first-order terms areretained. The small-signal rate equations canbe expressed as follows: where, 7.17 7.9 7.18 7.10 The expression for the damping factor remains almost the same, except for the After eliminating the carrier density n and reduced carrier lifetime. The relaxationsolving for s1/s2, the response is obtained frequency ( ωr = 2πfr), however, depends on pump laser photon density S2. The overall 7.11 response is simply the “intrinsic” form of the response in the denominator, but with different Where, the numerator N(ω) is values defining the relaxation frequency ωr and the damping factor γ. Equations 7.13, 7.15, and 7.16 indicate new analytical results on the effective inverse carrier lifetime (1/τn’), γ and ωr respectively. The numerator N(ω) remains almost constant within the frequency range of 7.12 48
  • 54. interest. As a final step, the overall response is also listed in table 7.01for comparison. Inormalized, and the magnitude is written as should be noted that the two sets of modulation responses are identical when the photon density S2 approaches zero. Therefore, the expressions for the small-signal optical 7.12 gain modulator response are actually the intrinsic modulation response of the The equations are summarized in Table semiconductor laser and are useful in studying7.01. The expressions for the conventional the physics of XGM.intrinsic small-signal modulation response are Table 7.01: COMPARISON OF INTENSITY MODULATION RESPONSES: INTRINSIC AND XGM 49
  • 55. Table 7.02: Structure of a Common Test Laser fro lab use 50
  • 56. Work Done Chapter 8 Analysis of the performance of the Phase 1Semiconductor Optical Amplifier includesseveral phases of realization of the behaviour In this phase we are only sending oneof the same under different input signal signal of single pulse through a singlecondition. SOA along with a continuous wave reference signal. So, before realizing the In our case as the final result should SOA for the simulation we need to definehave been based on the simulation under input some parameters used for defining theas 4 signals WDM multiplexed with one SOA using the reservoir model of SOA asreference wave and the whole signal path described earlier. These are as follows:-including 3 SOAs connected as a ring networkwith standard difference between tow SOA of symbol Parameter name valueabout 200 KM, we divided our simulationdevelopment into 3 phases to ease out the Length of the SOA 1300 µmdifficulties arising due to programming Number of sections 3complexities. Velocity of light 3 x 108 m/s The three phase are:- Planck‟s constant 6.626068 x 1. Simulation with 1 signal, 1 continuous 10-34 wave (as reference1), and signal Active region width 0.7 µm passing through only 1 SOA. Input facet reflectivity 0.9 x 10-6 2. Simulation with 4 signals (WDM multiplexed), 1 continuous wave and Output facet reflectivity 0.5 x 10-6 signal passing through 1 SOA. 3. Simulation with 4 signals (WDM Carrier independent 6000 m-1 multiplexed), 1 continuous wave as absorption loss reference and signal path consisting of coefficient a ring network containing 3 SOAs. Active region thickness 0.7 µm Now, while realizing the SOA basedWDM ring network with identical SOAs the Carrier dependant 6000 x 10-24 m2SOA, though show identical performance for absorption losseach of the stages, each SOA show different coefficientbehaviour for different signals input onto it, Linear radiative 3.5 x 108 s-1possibly caused due to the cross-gain recombination coefficientmodulation. This cross-gain modulation can beobserved as soon as several signals are fed into Bimolecular radiative 4 x 10-16 m3s-1the SOA. Now, on the way to describe each of recombination coefficientthe phases to the simulation we need to give Linear non-radiative 7.5 x 108 s-1the theory used by us to generate the code for recombination coefficientthe simulation, and then to make the procedure Bimolecular non- 7.5 x 10-16 m3s-1understandable, we are going to describe it radiative recombinationthrough folw charts of each of the simulation coefficientstages. Band gap energy 0.773 eV 1. SOAs describe the effect cross-gain modulation the variation of gain for one signal due amplification of the other, which is easily determined by feeding an extra continuous wave onto Table 8.01 the SOA as reference signal. 51
  • 57. The program flowchart is as follows :-Fit Parameters:- Now, the primary parameters of the SOAs Wavelength of the launched power: - 1550nm Length of the SOA: - 10-4 mare defined, not our primary objective is to Pump Current: - 0.25 Adescribe the SOA by the equations given in the Fundamental mode confinement factor: -0.36reservoir model. On this step, the first way isto get the fit parameters out the given data for The given can be implemented using thethe SOA simulation:- following matlab function:-function [sigma N0k gamma N1k]=fit_parameter(Wavel,L,I,Con_F)Carr_Den = 0.5:.1:3.5;inguess = 1;Pin_low=-40;Pin_high=0;for i=1:length(Carr_Den) gain_res(i) = matgain_res (Wavel,Carr_Den(i));end;fit_data=polyfit(Carr_Den,gain_res,1);Nmax =fzero(@(N)calculate_avg(N,Pin_low,Wavel,fit_data,I,L,Con_F),inguess)Nmin =fzero(@(N)calculate_avg(N,Pin_high,Wavel,fit_data,I,L,Con_F),inguess)sigma = ( matgain_res (Wavel,Nmax*1E-24) - matgain_res (Wavel,Nmin*1E-24) ) /(Nmax-Nmin); 52
  • 58. N0k = Nmax - (matgain_res(Wavel,Nmax*1E-24)/sigma);gamma = ( mat_gbar_res (Wavel,Nmax*1E-24,L,Con_F) - mat_gbar_res(Wavel,Nmin*1E-24,L,Con_F) ) / ( Nmax-Nmin ) ;N1k = Nmax - mat_gbar_res(Wavel,Nmax*1E-24,L,Con_F)/gamma; 4. Con_F :- fundamental mode As the function signifies, the function, confinement factor;known by the name “ fit_parameter”, has 4arguments, namely:- The function outputs the fit parameter for the given input signal. Now, we can define the 1. Wavel :- the wavelength of the input parameters by the previously derived signal; equations by Connelly as:- 2. L :- the length of the SOA; 3. I :- input pump current; σk = ( matgain_res (Wavel,Nmax*1E-24) - matgain_res (Wavel,Nmin*1E-24) ) /(Nmax-Nmin);where,Nmax= fzero(@(N)calculate_avg(N,Pin_low,Wavel,fit_data,I,L,Con_F),inguess); &Nmin= fzero(@(N)calculate_avg(N,Pin_high,Wavel,fit_data,I,L,Con_F),inguess); Here, the function “fzero” gives the initial “calculate_avg” is a function that is used tovalue of the function defined within it, in this calculate the average value of the dN(z, t)/dtcase be it “calculate_avg.” , described in the Connelly model of SOA. The function “calculate_avg” is defined as under:-function out = calculate_avg(N,PindB,Wavel,fit_data,I,L,Con_F);Pin = dbtoc(PindB);q = 1.602177E-19; % Electronic charge (Coulomb)d = 0.7E-6; % Active region thickness (m)W = 0.7E-6; % Central active region width (m)Arad = 3.5E8; % Linear radiative recombination coefficient(S^-1)Brad = 4E-16; % Bimolecular radiative recombinationcoefficient (m^3*s^-1)Anrad = 7.5E8; % Linear non-radiative recombinationcoefficient due to traps (S^-1)Bnrad = 7.5E-16; % Bimolecular non-radiative recombinationcoefficient (m^3*s^-1)Caug = 0.2E-42; % Auger recombination co-efficient (m^6*s^-1)h = 6.6260755E-34; % Plancks constant (J*s)vel_light = 2.99792458E8; % Velocity of light (m/s)Freq_use = vel_light/(Wavel*1E-9);Qin = Pin/(h*Freq_use);% ========= Calculation of Wavelength Dependent Gain ========= %% ============================================================ %K = 1.3806505E-23; % Boltzmann constant (Joule/kelvin) 53
  • 59. T = 300; % Absolute temperature (kelvin)n1 = 3.22; % InGaAsP active region refractive indexneq0 = 3.22; % Equivalent refractive index at 0 carrier densitydelneq_n = -1.34E-26; % Differential of equivalent refractive index WRTcarrier density (m^-3)me = 4.10E-32; % Effective Mass of Electron in CB (Kg)mhh = 4.19E-31; % Effective Mass of a heavy hole in VB (Kg)mlh = 5.06E-32; % Effective Mass of a light hole in VB (Kg)Kg = 0.1E-10; % Bandgap shrinkage coefficient (eVm)R1 = 0.9E-6; % Input facet reflectivityR2 = 0.5E-6; % Output facet reflectivityEg0 = 1.237E-19; % Bandgap Energydeln1_n = -1.8E-26; % Differential of active regionrefractive index WRT carrier density (m^-3)h1 = h/(2*pi);mdh = (mhh^(3/2) + mlh^(3/2))^(2/3);Nc = 2 * (((me*K*T) / (2*pi*h1^2)) ^ (3/2));Nv = 2 * (((mdh*K*T) / (2*pi*h1^2)) ^ (3/2));Delta = N/Nc;Efsilon = N/Nv;Efc = (log(Delta)+Delta*(64+0.05524*Delta*(64+sqrt(Delta)))^(-1/4))*K*T;Efv = -(log(Efsilon)+Efsilon*(64+0.05524*Efsilon*(64+sqrt(Efsilon)))^(-1/4))*K*T;Del_EgN = q*Kg*(N^(1/3));EgN = Eg0 - Del_EgN;Ea = (h*Freq_use - EgN) * (mhh/(mhh + me));Eb = - (h*Freq_use - EgN) * (me/(mhh + me));fcF = (exp((Ea - Efc)/(K*T))+1)^-1;fvF = (exp((Eb - Efv)/(K*T))+1)^-1;Tow = 1/(Arad + N*Brad); % From Equation 52 [Connelly]gain = ((vel_light^2)/(4*sqrt(2)*(pi^(3/2))*(n1^2)*Tow*(Freq_use^2)))... *(((2*me*mhh)/(h1*(me+mhh)))^(3/2))*sqrt(Freq_use-EgN/h)*(fcF-fvF);% ============================================================ %f1 = I/(q*L*d*W); % First Part of the Steady-state Equationf2 = N * (Arad+Anrad+Brad*N+Bnrad*N+Caug*N^2); % Second Part of theSteady-state Equationf4 = (Con_F/(d*W))*Qin*polyval(fit_data,N)*1E-24; %Third Part of theSteady-state Equationf3 = (Con_F/(d*W))*Qin*matgain_res(1560,2);matgain_res(1560,2);out = f1-f2-f4;and the function “matgain_res” gives the given as the argument. This function is definedmaterial gain value of the current active as :-medium, under the given particular conditionfunction out = matgain_res(Wavel,Carr_Den); 54
  • 60. N = Carr_Den*1E24;wavel_use = Wavel*1E-9;% Important parameters needed to calculate the material gain% ==========================================================h = 6.6260755E-34; % Plancks constant (J*s)me = 4.10E-32; % Effective Mass of Electron in CB (Kg)mhh = 4.19E-31; % Effective Mass of a heavy hole in VB (Kg)mlh = 5.06E-32; % Effective Mass of a light hole in VB (Kg)K = 1.3806505E-23; % Boltzmann constant (Joule/kelvin)T = 300; % Absolute temperature (kelvin)e = 1.602177E-19; % Electronic charge (Coulomb)Kg = 0.1E-10; % Bandgap shrinkage coefficient (eVm)vel_light = 2.99792458E8; % Velocity of light (m/s)Arad = 3.5E8; % Linear radiative recombination coefficient (S^-1)Brad = 4E-16; % Bimolecular radiative recombination coefficient (m^3*s^-1)n1 = 3.22; % InGaAsP active region refractive indexEg0 = 1.237E-19; % Bandgap energy% ==========================================================h1 = h/(2*pi);mdh = (mhh^(3/2) + mlh^(3/2))^(2/3);Nc = 2 * (((me*K*T) / (2*pi*h1^2)) ^ (3/2));Nv = 2 * (((mdh*K*T) / (2*pi*h1^2)) ^ (3/2));Delta = N/Nc;Efsilon = N/Nv;Efc = (log(Delta)+Delta*(64+0.05524*Delta*(64+sqrt(Delta)))^(-1/4))*K*T;Efv = -(log(Efsilon)+Efsilon*(64+0.05524*Efsilon*(64+sqrt(Efsilon)))^(-1/4))*K*T;Del_EgN = e*Kg*(N^(1/3));EgN = Eg0 - Del_EgN;Freq_use = vel_light/wavel_use;Ea = (h*Freq_use - EgN) * (mhh/(mhh + me));Eb = - (h*Freq_use - EgN) * (me/(mhh + me));fcF = (exp((Ea - Efc)/(K*T))+1)^-1;fvF = (exp((Eb - Efv)/(K*T))+1)^-1;Tow = 1/(Arad + N*Brad); % From Equation 52 [Connelly]out = ((vel_light^2)/(4*sqrt(2)*(pi^(3/2))*(n1^2)*Tow*(Freq_use^2)))... *(((2*me*mhh)/(h1*(me+mhh)))^(3/2))*sqrt(Freq_use-EgN/h)*(fcF-fvF); In this way, we can also define the other three fit parameters as :- N0k = Nmax - (matgain_res(Wavel,Nmax*1E-24)/sigma); gamma = (mat_gbar_res(Wavel,Nmax*1E-24,L,Con_F)-mat_gbar_res(Wavel,Nmin*1E- 24,L,Con_F))/(Nmax-Nmin); N1k = Nmax - mat_gbar_res(Wavel,Nmax*1E-24,L,Con_F)/gamma; 55
  • 61. Input Signal :- Here, we need to parameterize the inputsignal to be fed into the SOA. Now the severalspecification we are abiding by are :- The number of bits for the simulation is 1. Modulation frequency(Fm)=0.5E9 chosen to be 1 with the consent of the project 2. Samples per bit = 80 guide 3. Duty ratio = 1 We define the input signal with the following coding:-[ti,sig]=signalin(no_of_bits,Fm,samples_per_bit,Duty_ratio,effective_power)sig_voltage1 = sig1;the function “signalin” is auser defined function definedto generate a two dimensionalarray of time and signalamplitude that take inputargument as number of bits,modulation frequency of theinput wave, samples to bedrawn per bit, duty ratio ofthe step pulse to begenerated and the effectivepower. The function“signalin” can realize as:-function[ti,sig]=fn1(a1,a2,a3,a4,a5);% Initialization ofthe parameters fordifferent ModulationFormats Fig: - 8.01% =================================================================no_of_bits = a1;Fm = a2; %Modulation frequency in bpssamples_per_bit = a3;Duty_ratio = a4;effective_power = a5; %Power launched in dBmbit_period = 2/Fm; %Bit period of the modulated signalN = no_of_bits*samples_per_bit; %Total no of samplessample_interval = bit_period/samples_per_bit; %Sampling period (1/Fs)P_av = (10^(effective_power/10))*(10^(-3));%Average launched power in wattsP_peak = P_av/Duty_ratio; 56
  • 62. %%%%%% GENERATION OF SIGNAL %%%%%%%%%%%%%%=======================================%%bit_pattern = pnseq7(no_of_bits);T0 = 0.5E-9;m = 20; %Defines the super-gaussianity of the envelope point_array=[-(bit_period/2):sample_interval:(bit_period/2)- sample_interval];gauss_env = exp(-0.5*((point_array./T0).^(2*m)));%&&&&&&&&&&&&&&&&&&&&&&&&figure;plot(point_array,gauss_env);T = 0;sample_point = 1;A = zeros(1,N);DUTY = round(samples_per_bit*Duty_ratio);Amp=P_peak; %Amplitude of the envelope of the lunched electric fieldfor (n=1:no_of_bits) du = 1; for(t = T:sample_interval:T + bit_period - sample_interval if (du <= A(1,sample_point) = Amp*gauss_env(1,du); sample_point = sample_point + 1; else A(1,sample_point) = 0; sample_point = sample_point + 1; end; du = du + 1; end; T = T + bit_period;end;ti=0:sample_interval:(sample_interval*N)-sample_interval;sig=A;the generated wave look like one in the Fig:-8.01. The figure, based on a Gaussian envelopdefined as :- e (-0.5*((point_array./T0).^(2*m)));where, the point_array is defined over the bitperiod with a resolution of the sample interval. Solve Rate Equation :-Introduce Continuous Wave:- As the continuous wave is defined already, we noe can proceed towards the solution of the rate equation defined in the Reservoir model,Now, here we are to introduce a continuous as:-wave signal so that we can witness thephenomenon of the cross-gain modulation, as:-PindB_cw = -6; The solution of this rate equation gives us thepav= (10^(PindB_cw/10))*1E-3; rate of generation of the carrier in the SOA. ToL4=length(p1); solve the equation with the matlab functionfor (k=1:L4-1) “ode45” we need to first determine the value p_cw(k)= pav; of the function at t=0; i.e., the initial condition.end To determine that we use a matlab function 57
  • 63. named “fzero”. This is used in the simulationas :-inguess=1; y1=fzero(@(r)sol_ase(r,Lz,p1(1),pin2(1),pav,lamdak,sigmaK,nok,gammaK,n1k,gamma,I, lifetime), inguess); Here, the function sol_ase gives the value of the of the rate equation. This is defined by thecodes below :-function reservoir=sol_ase(r,Lz, Pin,Pin2, p_cw,lamdak,sigmaK,nok,gammaK,n1k,gamma,I,lifetime)deltanu = 30*(1E-9)/130 ; % assumed SOA BW 30 nm%----------------q= 1.602E-19; % electronic charge in [C]c= 2.99E8; % velocity of light [m/s]h= 6.626068E-34 ; % Planck Constant in [m^2-kg/s]A= ( 0.7^2)*1E-12; % area in [m^2]ko= 6000; %absorption constant indep of n in [m^-1]k1= 6000*1E-24 ; %k1=6000*1E-24 ; in m^2ak= (gamma*(sigmaK-k1))/A ;% gain constant of the reservoir model,unitless.rok= ((gamma*sigmaK*nok + ko)*Lz)/ak ; % in [m^-2]r1k= n1k *(A*Lz);Qin=(lamdak*Pin*1E-9)/ (h*c);Qin2=(lamdak*Pin2*1E-9)/ (h*c);Qin_cw=(lamdak*p_cw*1E-9)/ (h*c); nsp = ( gamma*gammaK*(r-r1k))/(A*ak*(r-rok));Gr=exp(gamma*r*(sigmaK -k1)/A - (gamma*sigmaK*nok+ko)*Lz ); reservoir= I/q - r/lifetime- (Qin +Qin2+ Qin_cw)*( exp(ak*(r-rok))-1 )- 4*deltanu * nsp*(Gr -1-log(Gr)); the function “solve_rateq_ase” and the Now, as the initial value of the is function returns the in a mere time versusderived, we can proceed towards the solution amplitude array. The amplitude signifies theof it. We shall solve it for every instance of rate of generation of carrier in the bulktime over the timespan of the wave for each material of SOA, which can be simply passedstage of the SOA separately (we devided the on to a separate user-defined function namedSOA in three stages or sections of same “single_pass_gain_ase” to calculate the gain.length). The approach passes the arguments, This function calculates the gain of the SOAi.e. the power readings of the signal, the same for a single pass or stage. The codes to realizeof the continuous wave, the length of each the solution of the rate equatin can besection, the fit parameters, the pump current, described as follows :-the lifetime of the carriers and the initial valuetoj=1; for (i= 1:1:T1-1) a=0; b=0; [a,b] =solve_rateeq_ase(p(i),p_cw(i),Lz,lamdak,sigmaK,nok,gammaK,n1k,gamma,I,lifetime,t1(i),t1(i+1),y1); % return a as time and b as r values L2=length(b); % length of the each time division y1=b(L2); % y1=b(L2);final value of the solution of differentialeq.for that time division r1(j)=b(1); % r1(j)=b(1);collecting one value of r in each passof the solution of diff. Eqn 58
  • 64. x2(j)=a(1); % x2(j)=a(1);collecting time instants. arrayr(k,j)=r1(j); j=j+1; end The rate of generation of carrier isoutputted by the array „r1‟. Now the function including the noise power of ASE. The“single_pass_gain_ase” shall calculate the gain function can be realized as follows :-% calculation of gainfunction value1 = single_pass_gain_ase(r,Lz,sigmaK, nok,gamma);A= ( 0.7^2)*1E-12;ko= 6000; % 6000 m^-1k1= 6000*1E-24 ; %k1=6000*1E-24 ; in m^2ak= (gamma*(sigmaK-k1))/A ;rok= ((gamma*sigmaK*nok + ko)*Lz)/ak ; % in [m^-2]value1 = exp(ak*(r - rok)); % Value1 is Gk, which is a function of time tat wavelength lamda k Gain Calculation:- Once the gain is out it is easy to calculatethe power outputfor each of the stageof SOA by justmultiplying the gainto the input poweras the input powerto each stage issignified by thepower out by theprevious stage.As the described inthe Fig 8.02, thegraph gives thegenerated carriersin the reservoir, forthree consecutivestages. Similarly,the next figure Fig8.03 gives theamount of photonsgenerated in thereservoir, whichgive the idea of thegain for that signal.In the figure the Fig 8.02photons generated due to the signal isdescribed by the blue graph while the red onegives the amount of photons generated due to signal of each stage we get the output powerthe inserted continuous wave. Now, we can for each stage.define an three dimensional array to store thevalues of the gain versus time for three stage As shown in the Fig 8.04, 8.05 & 8.06, thesimultaneously, multiplying which to the input figures give the amount of power outputted from the 1st, 2nd, 3rd stage respectively. 59
  • 65. Fig 8.03Fig 8.04 60
  • 66. Fig 8.05Hence, we are successful to realize a simple wave as input, and complete the Phase 1 of ourSOA with 1 signal & 1 continuous reference simulation. Fig 8.06 61
  • 67. Phase 2 So, the coding includes several stages of the previous codings edited. Our second phase of simulation continues 1. Firstly we are to derive the fitwith the simulation with 4 input signals, parameters for different wavelength byinstead of only one for the previous one, the passing them on to the functionsame previously added continuous wave signal “fit_parameter” and saving the fitthat is used for reference to the effect of cross- parameters for different fit parametersgain modulation and a single SOA to pass by. for different wavelength under different The simulation starts with those previously variable length, like the following :-described coding but the only difference is the [a11, a12, a13, a14]=input. The input is WDM multiplexed. fit_parameter(lamdak1,L,I,gamma) ; In fiber-optic communications, wavelength sigmaK1= a11 ;division multiplexing (WDM) is a technology nok1= a12 ;which multiplexes a number of optical carrier gammaK1= a13 ; n1k1= a14;signals onto a single optical fiber by usingdifferent wavelengths (colours) of laser light. [a21, a22, a23, a24]=This technique enables bidirectional fit_parameter(lamdak2,L,I,gamma)communications over one strand of fiber, as ; sigmaK2= a21 ;well as multiplication of capacity. nok2= a22 ; gammaK2= a23 ; The term wavelength-division multiplexing n1k2= a24;is commonly applied to an optical carrier(which is typically described by its [a31, a32, a33, a34]= fit_parameter(lamdak3,L,I,gamma)wavelength), whereas frequency-division ;multiplexing typically applies to a radio carrier sigmaK3= a31 ;(which is more often described by frequency). nok3= a32 ;Since wavelength and frequency are tied gammaK3= a33 ; n1k3= a34;together through a simple directly inverserelationship, the two terms actually describe [a41, a42, a43, a44]=the same concept. A WDM system uses a fit_parameter(lamdak4,L,I,gamma)multiplexer at the transmitter to join the ; sigmaK4= a41 ;signals together, and a demultiplexer at the nok4= a42 ;receiver to split them apart. With the right type gammaK4= a43 ;of fiber it is possible to have a device that does n1k4= a44;both simultaneously, and can function as anoptical add-drop multiplexer. The optical 2. as the input is ready with for signals,filtering devices used have traditionally been the next problem comes with theetalons, stable solid-state single-frequency solution of the rate equation.Fabry–Pérot interferometers in the form ofthin-film-coated optical glass. We can remember the rate equation that we have already used for the coding during the Now, here we are multiplexing 4 signals in first phase of the work, there we used thethe SOA, with there carrier optical signal equation:-wavelength as 1548 nm, 1552 nm, 1556 nm,1560 nm. 62
  • 68. The equation already contained the term 1 signal for that phase. This time we are using 4 signals (and the continuous wave signal as well). which signified input of n number of signals numbering from 1 to nsig. The difference was that we used only So the function to derive changes to:-function reservoir=sol_ase(r,Lz,Pin1,Pin2,Pin3,Pin4,p_cw,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4, nok1, nok2, nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma,I,lifetime)deltanu = 30*(1E-9)/130 ; % assumed SOA BW 30 nmq= 1.602E-19; % electronic charge in [C]c= 2.99E8; % velocity of light [m/s]h= 6.626068E-34 ; % Planck Constant in [m^2-kg/s]A= ( 0.7^2)*1E-12; % area in [m^2]ko= 6000; %absorption constant indep of n in [m^-1]k1= 6000*1E-24 ; %k1=6000*1E-24 ; in m^2ak1= (gamma*(sigmaK1-k1))/A ;ak2= (gamma*(sigmaK2-k1))/A ;ak3= (gamma*(sigmaK3-k1))/A ;ak4= (gamma*(sigmaK4-k1))/A ;% gain constant of the reservoir model,unitless.rok1= ((gamma*sigmaK1*nok1 + ko)*Lz)/ak1 ; % in [m^-2]rok2= ((gamma*sigmaK2*nok2 + ko)*Lz)/ak2 ; % in [m^-2]rok3= ((gamma*sigmaK3*nok3 + ko)*Lz)/ak3 ; % in [m^-2]rok4= ((gamma*sigmaK4*nok4 + ko)*Lz)/ak4 ; % in [m^-2]r1k1= n1k1 *(A*Lz);r1k2= n1k2 *(A*Lz);r1k3= n1k3 *(A*Lz);r1k4= n1k4 *(A*Lz);Qin1=(lamdak1*Pin1*1E-9)/ (h*c);Qin2=(lamdak2*Pin2*1E-9)/ (h*c);Qin3=(lamdak3*Pin3*1E-9)/ (h*c);Qin4=(lamdak4*Pin4*1E-9)/ (h*c);Qin_cw=((lamdak1*p_cw*1E-9)+(lamdak2*p_cw*1E-9)+(lamdak3*p_cw*1E-9)+(lamdak4*p_cw*1E-9))/ (h*c);nsp1 = ( gamma*gammaK1*(r-r1k1))/(A*ak1*(r-rok1));nsp2 = ( gamma*gammaK2*(r-r1k2))/(A*ak2*(r-rok2));nsp3 = ( gamma*gammaK3*(r-r1k3))/(A*ak3*(r-rok3));nsp4 = ( gamma*gammaK4*(r-r1k4))/(A*ak4*(r-rok4));Gr1=exp(gamma*r*(sigmaK1 -k1)/A - (gamma*sigmaK1*nok1+ko)*Lz );Gr2=exp(gamma*r*(sigmaK2 -k1)/A - (gamma*sigmaK2*nok2+ko)*Lz );Gr3=exp(gamma*r*(sigmaK3 -k1)/A - (gamma*sigmaK3*nok3+ko)*Lz );Gr4=exp(gamma*r*(sigmaK4 -k1)/A - (gamma*sigmaK4*nok4+ko)*Lz );reservoir= I/q - r/lifetime- (Qin1+Qin_cw)*( exp(ak1*(r-rok1))-1 )-(Qin2+Qin_cw)*( exp(ak2*(r-rok2))-1 )-(Qin3+Qin_cw)*( exp(ak3*(r-rok3))-1)-(Qin4+Qin_cw)*( exp(ak4*(r-rok4))-1 )- 4*deltanu * nsp1*(Gr1 -1- 63
  • 69. log(Gr1))- 4*deltanu * nsp2*(Gr2 -1-log(Gr2))- 4*deltanu * nsp3*(Gr3 -1-log(Gr3))- 4*deltanu * nsp4*(Gr4 -1-log(Gr4));Now, once we have determined the initial “solve_rateq_ase”, where the different parameters and 4 different signals are passed.value of the we can proceed toward The function can be called as following:-deriving its solution to get the value of „r‟ ofthe rate of generation of the carriers in thereservoir. This is again done by the functionfor (i= 1:1:T1-1) a=0; b=0; [a,b] =solve_rateeq_ase(pin1(i),pin2(i),pin3(i),pin4(i),p_cw(i),Lz,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4,nok1, nok2, nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma,I,lifetime,t1(i),t1(i+1),y1); % return a as time and b as r values L2=length(b); % length of the each time division y1=b(L2); % y1=b(L2);final value of the solution of differentialeq.for that time division r1(j)=b(1); % r1(j)=b(1);collecting one value of r in each passof the solution of diff. Eqn x2(j)=a(1); % x2(j)=a(1);collecting time instants. arrayr(k,j)=r1(j); j=j+1; endand realized as following:-function [t,r] =solve_rateeq(pw1,pw2,pw3,pw4,pcw,Lz,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4,nok1, nok2, nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma,I,lifetime,dt1,dt2,yi);deltanu = 30*(1E-9)/130 ; % assumed 30 nm SOA bw % bw=1.5 times bitrate.A= ( 0.7^2)*1E-12; % area in [m^2]ko= 6000; %absorption constant indep of n in [m^-1]k1= 6000*1E-24 ; %k1=6000*1E-24 ; in m^2q= 1.602E-19; % electronic charge in [C]c= 2.99E8; % velocity of light [m/s]h= 6.626068E-34 ; % Planck Constant in [m^2-kg/s]ak1= (gamma*(sigmaK1-k1))/A ; % gain constant of the reservoir model,unitless.ak2= (gamma*(sigmaK2-k1))/A ; % gain constant of the reservoir model,unitless.ak3= (gamma*(sigmaK3-k1))/A ; % gain constant of the reservoir model,unitless.ak4= (gamma*(sigmaK4-k1))/A ; % gain constant of the reservoir model,unitless.%-----------------------------%finding rokrok1= ((gamma*sigmaK1*nok1 + ko)*Lz)/ak1 ; % in [m^-2]rok2= ((gamma*sigmaK2*nok2 + ko)*Lz)/ak2 ; % in [m^-2]rok3= ((gamma*sigmaK3*nok3 + ko)*Lz)/ak3 ; % in [m^-2]rok4= ((gamma*sigmaK4*nok4 + ko)*Lz)/ak4 ; % in [m^-2]%finding r1kr1k1= n1k1 *(A*Lz); 64
  • 70. r1k2= n1k2 *(A*Lz);r1k3= n1k3 *(A*Lz);r1k4= n1k4 *(A*Lz);%-----------------------------% finding Qin from input power pwQin1 = (lamdak1*(pw1+pcw)*1E-9)/ (h*c);Qin2 = (lamdak2*(pw2+pcw)*1E-9)/ (h*c);Qin3 = (lamdak3*(pw3+pcw)*1E-9)/ (h*c);Qin4 = (lamdak4*(pw4+pcw)*1E-9)/ (h*c);%-----------------------------tspan = [dt1 dt2];y0=yi; % initial value of the differential equation, updated in each timeinterval [t,r]=ode45(@rateeq ,tspan,y0 ); function drdt = rateeq(t,r) nsp1 = ( gamma*gammaK1*(r-r1k1))/(A*ak1*(r-rok1)); Gr1=exp(gamma*r*(sigmaK1 -k1)/A -(gamma*sigmaK1*nok1+ko)*Lz ); nsp2 = ( gamma*gammaK2*(r-r1k2))/(A*ak2*(r-rok2)); Gr2=exp(gamma*r*(sigmaK2 -k1)/A -(gamma*sigmaK2*nok2+ko)*Lz ); nsp3 = ( gamma*gammaK3*(r-r1k3))/(A*ak3*(r-rok3)); Gr3=exp(gamma*r*(sigmaK3 -k1)/A -(gamma*sigmaK3*nok3+ko)*Lz ); nsp4 = ( gamma*gammaK4*(r-r1k4))/(A*ak4*(r-rok4)); Gr4=exp(gamma*r*(sigmaK4 -k1)/A -(gamma*sigmaK4*nok4+ko)*Lz ); drdt = [-r(1)/lifetime + I/q - Qin1* ( exp( ak1*(r(1)-rok1))-1) -Qin2* ( exp( ak2*(r(1)-rok2))-1) - Qin3* ( exp( ak3*(r(1)-rok3))-1) - Qin4*( exp( ak4*(r(1)-rok4))-1)- 4*deltanu * nsp1*(Gr1 -1-log(Gr1))- 4*deltanu *nsp2*(Gr2 -1-log(Gr2))- 4*deltanu * nsp3*(Gr3 -1-log(Gr3))- 4*deltanu *nsp4*(Gr4 -1-log(Gr4)) ]; end figure(2) plot(t,r); % plot for each time division hold on; % holding the plot for each time division xlabel(time in seconds); ylabel(Number of carriers in reservoir);endnow, we calculate the gain likewise we did in 8.03, we can observe that the amplitude if thethe previous phase and determine the output constant amplitude continuous wave signal,power for each stage of the SOA. The that is inputted, has changed during there is agenerated carrier vs. Time graph will look like high amplitude in the inputted optical messageFig 8.07, whereas the output power vs. Time signal. The amplitudes can be analysed by thegraph for 1st, 2nd and 3rd stage will be like Fig following table 8.02.8.08, 8.09 and 8.10 respectively. Time(10-8 Photons/sec Photons/sec sec) (x1.018)(signal) (x1.020)(cont. Effect of Cross-gain Modulation wave)so far:- 0 0 3.2725 0.005 0 0.0134 From the first phase of simulation, we have 0.01 0 0.0207observed the effect of cross-gain modulation 0.015 0 0.0209on the inputted signal. On reviewing the Fig 0.02 0 0.0210 65
  • 71. 0.025 0 0.0210 0.29 0 0.02100.03 0 0.0210 0.295 0 0.02100.035 0 0.0210 0.3 0 0.02100.04 0 0.0210 0.305 0 0.02100.045 0 0.0210 0.31 0 0.02100.05 0 0.0210 0.315 0 0.02100.055 0 0.0210 0.32 0 0.02100.06 0 0.0210 0.325 0 0.02100.065 0 0.0210 0.33 0 0.02100.07 0 0.0210 0.335 0 0.02100.075 0 0.0210 0.34 0 0.02100.08 0 0.0210 0.345 0 0.02100.085 0 0.0210 0.35 0 0.02100.09 0 0.0210 0.355 0 0.02100.095 0 0.0210 0.36 0 0.02100.1 0 0.0210 0.365 0 0.02100.105 0 0.0210 0.37 0 0.02100.11 0 0.0210 0.375 0 0.02100.115 0 0.0210 0.38 0 0.02100.120 0 0.0210 0.385 0 0.02100.125 0 0.0210 0.39 0 0.02100.13 0 0.0210 Tabale 8.02: Reading of the photons per0.135 0 0.0210 second graph0.14 0 0.02100.145 0 0.0210 Cross-phase modulation can be relevant0.15 5.7278 0.0210 under different circumstances:0.155 1.3498 0.0030  It leads to an interaction of optical0.16 1.5272 0.0034 pulses in a medium, which allows e.g.0.165 1.8586 0.0041 the measurement of the optical0.17 1.8163 0.0040 intensity of one pulse by monitoring a0.175 1.8072 0.0040 phase change of the other one (without0.18 1.8056 0.0040 absorbing any photons of the first0.185 1.8053 0.0040 beam).  The effect can also be used for0.19 1.8053 0.0040 synchronizing two mode-locked lasers0.195 1.8053 0.0040 using the same gain medium, in which0.2 1.8053 0.0040 the pulses overlap and experience0.205 1.8053 0.0040 cross-phase modulation.0.21 1.8053 0.0040  In optical fiber communications,0.215 1.8053 0.0040 cross-phase modulation in fibers can0.22 1.8053 0.0040 lead to problems with channel0.225 1.8053 0.0040 crosstalk.0.23 1.8053 0.0040  Cross-phase modulation is also0.235 1.8053 0.0040 sometimes mentioned as a mechanism0.24 1.8051 0.0040 for channel translation (wavelength0.245 1.7921 0.0040 conversion), but in this context the0.25 1.1057 0.0040 term typically refers to a kind of cross-0.255 0 0.0076 phase modulation which is not based0.26 0 0.0514 on the Kerr effect, but rather on0.265 0 0.0221 changes of the refractive index via the0.27 0 0.0206 carrier density in a semiconductor0.275 0 0.0208 optical amplifier.0.28 0 0.02090.285 0 0.0209 66
  • 72. So, the effect of the cross-gain modulation Because a ring topology provides only oneis clearly visible. pathway between any two nodes, ring networks may be disrupted by the failure Phase 3 of a single link. A node failure or cable break might isolate every node attached to On the third phase of our simulation we the ring.will continue to edit of matlab coding byinserting 4 waves in the input along with the A ring network has some advantages as:-previously present continuous wave and passthe signal through a ring network consisting of  Very orderly network where every3 SOAs. device has access to the token and the Let us first describe a bit about a ring opportunity to transmitnetwork, in brief.  Performs better than a bus topology under heavy network load  Does not require network server toThe following Fig 8.07 best describes a manage the connectivity between thering network. A ring network is a computersnetwork topology in which each nodeconnects to exactly two other nodes, But it also has some disadvantages as :-forming a single continuous pathway for  One malfunctioning workstation orsignals through each node - a ring. Data bad port in the MAU can createtravels from node to node, with each node problems for the entire networkalong the way handling every packet.  Moves, adds and changes of devices can affect the network  Network adapter cards and MAUs are much more expensive than Ethernet cards and hubs  Much slower than an Ethernet network under normal load Now, for an SOA based ring network simulation, we assume that the signal is flowing from 1 SOA to another but, an optical path realized in this way does not seem to have the same loosy characteristics like a practical one. So, we add some attenuators in between the SOAs to practically realize the network. 67
  • 73. In case we assume the optical signal to have a represented as Fig 8.08.bandwidth of 1550 nm, or more genericallysaid to beoperating in thethird window,most of thefibres presentindustriallyshow anattenuation of0.2 dB/km. So,if we assume agap of 200 kmbetween twoconsecutivefibres, therewill be total 40dB loss of the Now, we can move forwardsignal to reach to briefly describe our finalanother SOA, coding to achieve this goal.or the signal amplitude will be 1/10000 time Our algorithm of the total simulation canthat of the signal launched. So the actual ring be described as :-network we are using to simulate can be 68
  • 74. As the coding is a replication of thepreviously used coding, we do not go intodetail of the description and start writing theactual coding used:-% Cross gain modulation%----------------------------------------% if confinement factor is increased to say 0.3 there is a sharp transient% in rise and fall time. Also power output considerably increases with the% increase of gamma.%--------------------------------clear all;clc;% dividing SOA length into number of sections L= 10E-4; % 10E-4length of SOA in [m] sections = 3; % number of sections i.e. number of loops to berun Lz= L/sections ; % length of each subdivisions%---------------------------c= 3E8; % velocity of light [m/s]h= 6.626068E-34 ;lamdak1=1548; % wavelength in [nm]lamdak2=1552; % wavelength in [nm]lamdak3=1556; % wavelength in [nm]lamdak4=1560; % wavelength in [nm]gamma= 0.36; %Confinement factor; Note gamma has been madeto 0.8 to fit with the curve in Fig 11.A= ( 0.7^2)*1E-12; % area in [m^2]ko= 6000; %absorption constant indep of n in [m^-1]k1= 6000*1E-24 ;I= 0.25; % 0.25 Alifetime= 0.310E-9; % in [s], lifetime 310 pS ,%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&% parameter extraction[a11, a12, a13, a14]= fit_parameter(lamdak1,L,I,gamma); sigmaK1= a11 ; nok1= a12 ; gammaK1= a13 ; n1k1= a14; [a21, a22, a23, a24]= fit_parameter(lamdak2,L,I,gamma); sigmaK2= a21 ; nok2= a22 ; gammaK2= a23 ; n1k2= a24; [a31, a32, a33, a34]= fit_parameter(lamdak3,L,I,gamma); sigmaK3= a31 ; nok3= a32 ; gammaK3= a33 ; n1k3= a34; [a41, a42, a43, a44]= fit_parameter(lamdak4,L,I,gamma); sigmaK4= a41 ; nok4= a42 ; gammaK4= a43 ; n1k4= a44;%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&% Control Parameters for constructing supergaussian pulseno_of_bits = 1; 69
  • 75. Fm=0.5E9;samples_per_bit = 80; % 1350 number of time domain pointsDuty_ratio1 = 1;Duty_ratio2 = 1;Duty_ratio3 = 1;Duty_ratio4 = 1;effective_power1 = -3; %peak power launched in -20 dBm (4,5,15,-12)effective_power2 = -3;effective_power3 = -3; %peak power launched in -20 dBm (4,5,15,-12)effective_power4 = -3; %peak power launched in -20 dBm (4,5,15,-12)[ti,sig1]=signalin(no_of_bits,Fm,samples_per_bit,Duty_ratio1,effective_power1);sig_voltage1 = sig1;[ti,sig2]=signalin(no_of_bits,Fm,samples_per_bit,Duty_ratio2,effective_power2);sig_voltage2 = sig2;[ti,sig3]=signalin(no_of_bits,Fm,samples_per_bit,Duty_ratio3,effective_power3);sig_voltage3 = sig3;[ti,sig4]=signalin(no_of_bits,Fm,samples_per_bit,Duty_ratio4,effective_power4);sig_voltage4 = sig4;% converting peak power in terms of voltage for 1/0 bitpatternfigure(1); % plot of single bitplot(ti(1:samples_per_bit),sig1(1:samples_per_bit), b);hold on;plot(ti(1:samples_per_bit),sig2(1:samples_per_bit), g);hold on;plot(ti(1:samples_per_bit),sig3(1:samples_per_bit), k);hold on;plot(ti(1:samples_per_bit),sig4(1:samples_per_bit), r);hold on;grid on;xlabel(Time in Seconds);ylabel(Input Pulse Amplitude in volts);B1=10*log10(sig1*(10^3));B2=10*log10(sig2*(10^3));B3=10*log10(sig3*(10^3));B4=10*log10(sig4*(10^3));figure(7);plot(ti(1:samples_per_bit),B1(1:samples_per_bit), b); % comment this forbit streamhold on; 70
  • 76. plot(ti(1:samples_per_bit),B2(1:samples_per_bit), g); % comment this forbit streamhold on;plot(ti(1:samples_per_bit),B3(1:samples_per_bit), k); % comment this forbit streamhold on;plot(ti(1:samples_per_bit),B4(1:samples_per_bit), r); % comment this forbit streamhold on;grid on;xlabel(Time in Seconds);ylabel(Input Pulse Power in dBm);t1=ti(1:samples_per_bit); % time division in arrayT1 = length(t1);p1 = sig1(1:samples_per_bit); % pulse power in arrayp2 = sig2(1:samples_per_bit); % pulse power in arrayp3 = sig3(1:samples_per_bit); % pulse power in arrayp4 = sig4(1:samples_per_bit); % pulse power in array%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&% Average power of the CW input optical power in dBmPindB_cw = -6;pav= (10^(PindB_cw/10))*1E-3;%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&% finding out initial condition inguess=1; y1 =fzero(@(r) sol_ase(r,Lz,p1(1),p2(1),p3(1),p4(1),pav,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4, nok1, nok2, nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma,I,lifetime),inguess); % p1(1)is in non dB and first value of the array p1 will besupplied to the steadystatesol,%calculation of rate equationL4=length(p1);pin1=p1(1:L4-1); % eleminate first component of the array p1 to make itslength equal to L5pin2=p2(1:L4-1);pin3=p3(1:L4-1);pin4=p4(1:L4-1);% making pav an array of same length as pfor (k=1:L4-1) p_cw(k)= pav;endfor(k=1:1:sections) j=1;for (i= 1:1:T1-1) a=0; 71
  • 77. b=0; [a,b] =solve_rateeq_ase(pin1(i),pin2(i),pin3(i),pin4(i),p_cw(i),Lz,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4,nok1, nok2, nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma,I,lifetime,t1(i),t1(i+1),y1); % return a as time and b as r values L2=length(b); % length of the each time division y1=b(L2); % y1=b(L2);final value of the solution of differentialeq.for that time division r1(j)=b(1); % r1(j)=b(1);collecting one value of r in each passof the solution of diff. Eqn x2(j)=a(1); % x2(j)=a(1);collecting time instants. arrayr(k,j)=r1(j); j=j+1; end Gk1= single_pass_gain_ase(r1,Lz,sigmaK1, nok1,gamma); % Gk is function oftime Gk2= single_pass_gain_ase(r1,Lz,sigmaK2, nok2,gamma); % Gk is function oftime Gk3= single_pass_gain_ase(r1,Lz,sigmaK3, nok3,gamma); % Gk is function oftime Gk4= single_pass_gain_ase(r1,Lz,sigmaK4, nok4,gamma); % Gk is function oftime Qkout1 =Gk1.*((lamdak1*pin1*1E-9)/ (h*c)); % output signal photons persec Qkout2 =Gk2.*((lamdak2*pin2*1E-9)/ (h*c)); % output signal photons persec Qkout3 =Gk3.*((lamdak3*pin3*1E-9)/ (h*c)); % output signal photons persec Qkout4 =Gk4.*((lamdak4*pin4*1E-9)/ (h*c)); % output signal photons persec Qkout_cw = (Gk1.*((lamdak1*p_cw*1E-9)/ (h*c)))+(Gk2.*((lamdak2*p_cw*1E-9)/ (h*c)))+(Gk3.*((lamdak3*p_cw*1E-9)/ (h*c)))+(Gk4.*((lamdak4*p_cw*1E-9)/(h*c))); Pkout1 =Gk1.*pin1; % output power for each multistage Pkout2 =Gk2.*pin2; % output power for each multistage Pkout3 =Gk3.*pin3; % output power for each multistage Pkout4 =Gk4.*pin4; % output power for each multistage arrayPkout1(k,:)=Pkout1; arrayPkout2(k,:)=Pkout2; arrayPkout3(k,:)=Pkout3; arrayPkout4(k,:)=Pkout4; Pkout_cw =(Gk1.*p_cw)+(Gk2.*p_cw)+(Gk3.*p_cw)+(Gk4.*p_cw); arrayPkout_cw(k,:)=Pkout_cw; 72
  • 78. Pase =asepower(r1,Lz,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4,nok1, nok2, nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma); %output ase power in watt pin1=Pkout1; pin2=Pkout2; pin3=Pkout3; pin4=Pkout4;endL8=length(x2);L9=length(Qkout1);L10=length(Qkout2);L11=length(Qkout3);L12=length(Qkout4);L17=length(Qkout_cw);L13=length(Pkout1);L14=length(Pkout2);L15=length(Pkout3);L16=length(Pkout4);L18=length(Pkout_cw);Pkout_voltage1= (Pkout1); % converting optput power in voltagePkout_voltage2= (Pkout2); % converting optput power in voltagePkout_voltage3= (Pkout3); % converting optput power in voltagePkout_voltage4= (Pkout4); % converting optput power in voltagePkout_voltage_cw= (Pkout_cw);figure(4)subplot(5,1,1);plot(x2(20:L8),arrayPkout1(1,20:L13), b);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,2)plot(x2(20:L8),arrayPkout2(1,20:L14), g);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,3)plot(x2(20:L8),arrayPkout3(1,20:L15), k);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,4) 73
  • 79. plot(x2(20:L8),arrayPkout4(1,20:L16), r);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,5)plot(x2(20:L8),arrayPkout_cw(1,20:L18), m);axis auto;grid on;figure(5)subplot(5,1,1);plot(x2(20:L8),arrayPkout1(2,20:L13), b);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage second stage volts);subplot(5,1,2)plot(x2(20:L8),arrayPkout2(2,20:L14), g);grid on;axis auto;xlabel(time in seconds);ylabel(Output voltage from second stage in volts);subplot(5,1,3);plot(x2(20:L8),arrayPkout3(2,20:L15), k);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage second stage volts);subplot(5,1,4);plot(x2(20:L8),arrayPkout4(2,20:L16), r);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage second stage volts);subplot(5,1,5)plot(x2(20:L8),arrayPkout_cw(2,20:L18), m);grid on;axis auto;xlabel(time in seconds);ylabel(Output voltage from second stage in volts);figure(6)subplot(5,1,1);plot(x2(20:L8),arrayPkout1(3,20:L13), b);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage); 74
  • 80. subplot(5,1,2)plot(x2(20:L8),arrayPkout2(3,20:L14), g);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);subplot(5,1,3);plot(x2(20:L8),arrayPkout3(3,20:L15), k);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);subplot(5,1,4);plot(x2(20:L8),arrayPkout4(3,20:L16), r);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);subplot(5,1,5)plot(x2(20:L8),arrayPkout_cw(3,20:L18), m);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);%%second SOApin2_1=arrayPkout1(3,1:L13);pin2_2=arrayPkout2(3,1:L14);pin2_3=arrayPkout3(3,1:L15);pin2_4=arrayPkout4(3,1:L16);for(i= 1:1:79) pin2_1(i)=pin2_1(i)/10000; pin2_2(i)=pin2_2(i)/10000; pin2_3(i)=pin2_3(i)/10000; pin2_4(i)=pin2_4(i)/10000;end;p_cw_2=p_cw(1:79);for(k=1:1:sections)j=1; 75
  • 81. for (i= 1:1:T1-1)a=0;b=0;[a,b] =solve_rateeq_ase1(pin2_1(i),pin2_2(i),pin2_3(i),pin2_4(i),p_cw(i),Lz,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4,nok1, nok2, nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma,I,lifetime,t1(i),t1(i+1),y1); % return a as time and b as r valuesL2=length(b); % length of the each time divisiony1=b(L2); % y1=b(L2);final value of the solution of differentialeq.for that time divisionr1(j)=b(1); % r1(j)=b(1);collecting one value of r in each pass ofthe solution of diff. Eqnx2(j)=a(1); % x2(j)=a(1);collecting time instants.arrayr(k,j)=r1(j);j=j+1;endGk1= single_pass_gain_ase(r1,Lz,sigmaK1, nok1,gamma); % Gk is function oftimeGk2= single_pass_gain_ase(r1,Lz,sigmaK2, nok2,gamma); % Gk is function oftimeGk3= single_pass_gain_ase(r1,Lz,sigmaK3, nok3,gamma); % Gk is function oftimeGk4= single_pass_gain_ase(r1,Lz,sigmaK4, nok4,gamma); % Gk is function oftimePkout2_1 =Gk1(1:L13).*pin2_1; % output power for eachmultistagePkout2_2 =Gk2(1:L14).*pin2_2; % output power for eachmultistagePkout2_3 =Gk3(1:L15).*pin2_3; % output power for eachmultistagePkout2_4 =Gk4(1:L16).*pin2_4; % output power for eachmultistagearrayPkout2_1(k,:)=Pkout2_1;arrayPkout2_2(k,:)=Pkout2_2;arrayPkout2_3(k,:)=Pkout2_3;arrayPkout2_4(k,:)=Pkout2_4;Pkout_cw_2=(Gk1(1:L13).*p_cw_2)+(Gk2(1:L14).*p_cw_2)+(Gk3(1:L15).*p_cw_2)+(Gk4(1:L16).*p_cw_2);arrayPkout_cw2(k,:)=Pkout_cw_2;Pase =asepower(r1,Lz,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4,nok1, nok2, nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma); %output ase power in wattpin2_1=Pkout2_1; 76
  • 82. pin2_2=Pkout2_2;pin2_3=Pkout2_3;pin2_4=Pkout2_4;endL8=length(x2);L9=length(Qkout1);L10=length(Qkout2);L11=length(Qkout3);L12=length(Qkout4);L17=length(Qkout_cw);L13=length(Pkout2_1);L14=length(Pkout2_2);L15=length(Pkout2_3);L16=length(Pkout2_4);L18=length(Pkout_cw_2);figure(8)subplot(5,1,1);plot(x2(20:L8),arrayPkout2_1(1,20:L13), b);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,2)plot(x2(20:L8),arrayPkout2_2(1,20:L14), g);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,3)plot(x2(20:L8),arrayPkout2_3(1,20:L15), k);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,4)plot(x2(20:L8),arrayPkout2_4(1,20:L16), r);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,5)plot(x2(20:L8),arrayPkout_cw2(1,20:L18), m);axis auto;grid on; 77
  • 83. figure(9)subplot(5,1,1);plot(x2(20:L8),arrayPkout2_1(2,20:L13), b);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage second stage volts);subplot(5,1,2)plot(x2(20:L8),arrayPkout2_2(2,20:L14), g);grid on;axis auto;xlabel(time in seconds);ylabel(Output voltage from second stage in volts);subplot(5,1,3);plot(x2(20:L8),arrayPkout2_3(2,20:L15), k);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage second stage volts);subplot(5,1,4);plot(x2(20:L8),arrayPkout2_4(2,20:L16), r);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage second stage volts);subplot(5,1,5)plot(x2(20:L8),arrayPkout_cw2(2,20:L18), m);grid on;axis auto;xlabel(time in seconds);ylabel(Output voltage from second stage in volts);figure(10)subplot(5,1,1);plot(x2(20:L8),arrayPkout2_1(3,20:L13), b);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);subplot(5,1,2)plot(x2(20:L8),arrayPkout2_2(3,20:L14), g);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);subplot(5,1,3);plot(x2(20:L8),arrayPkout2_3(3,20:L15), k);grid on;axis auto;xlabel(time in seconds); 78
  • 84. ylabel(Output from Third Stage);subplot(5,1,4);plot(x2(20:L8),arrayPkout2_4(3,20:L16), r);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);subplot(5,1,5)plot(x2(20:L8),arrayPkout_cw2(3,20:L18), m);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);%%third SOApin3_1=arrayPkout2_1(3,1:L13);pin3_2=arrayPkout2_2(3,1:L14);pin3_3=arrayPkout2_3(3,1:L15);pin3_4=arrayPkout2_4(3,1:L16);for(i= 1:1:79) pin3_1(i)=pin3_1(i)/10000; pin3_2(i)=pin3_2(i)/10000; pin3_3(i)=pin3_3(i)/10000; pin3_4(i)=pin3_4(i)/10000;end;p_cw_3=p_cw(1:79);for(k=1:1:sections)j=1;for (i= 1:1:T1-1)a=0;b=0;[a,b] =solve_rateeq_ase2(pin3_1(i),pin3_2(i),pin3_3(i),pin3_4(i),p_cw_3(i),Lz,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4,nok1, nok2,nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma,I,lifetime,t1(i),t1(i+1),y1); % return a as time and b as r valuesL2=length(b); % length of the each time division 79
  • 85. y1=b(L2); % y1=b(L2);final value of the solution of differentialeq.for that time divisionr1(j)=b(1); % r1(j)=b(1);collecting one value of r in each pass ofthe solution of diff. Eqnx2(j)=a(1); % x2(j)=a(1);collecting time instants.arrayr(k,j)=r1(j);j=j+1;endGk1= single_pass_gain_ase(r1,Lz,sigmaK1, nok1,gamma); % Gk is function oftimeGk2= single_pass_gain_ase(r1,Lz,sigmaK2, nok2,gamma); % Gk is function oftimeGk3= single_pass_gain_ase(r1,Lz,sigmaK3, nok3,gamma); % Gk is function oftimeGk4= single_pass_gain_ase(r1,Lz,sigmaK4, nok4,gamma); % Gk is function oftimePkout3_1 =Gk1(1:L13).*pin3_1; % output power for eachmultistagePkout3_2 =Gk2(1:L14).*pin3_2; % output power for eachmultistagePkout3_3 =Gk3(1:L15).*pin3_3; % output power for eachmultistagePkout3_4 =Gk4(1:L16).*pin3_4; % output power for eachmultistagearrayPkout3_1(k,:)=Pkout3_1;arrayPkout3_2(k,:)=Pkout3_2;arrayPkout3_3(k,:)=Pkout3_3;arrayPkout3_4(k,:)=Pkout3_4;Pkout_cw_3=(Gk1(1:L13).*p_cw_3)+(Gk2(1:L14).*p_cw_3)+(Gk3(1:L15).*p_cw_3)+(Gk4(1:L16).*p_cw_3);arrayPkout_cw3(k,:)=Pkout_cw_3;Pase =asepower(r1,Lz,lamdak1,lamdak2,lamdak3,lamdak4,sigmaK1,sigmaK2,sigmaK3,sigmaK4,nok1, nok2, nok3,nok4,gammaK1,gammaK2,gammaK3,gammaK4,n1k1,n1k2,n1k3,n1k4,gamma); %output ase power in wattpin3_1=Pkout3_1;pin3_2=Pkout3_2;pin3_3=Pkout3_3;pin3_4=Pkout3_4;endL8=length(x2);L9=length(Qkout1);L10=length(Qkout2);L11=length(Qkout3);L12=length(Qkout4); 80
  • 86. L17=length(Qkout_cw);L13=length(Pkout3_1);L14=length(Pkout3_2);L15=length(Pkout3_3);L16=length(Pkout3_4);L18=length(Pkout_cw_3);figure(11)subplot(5,1,1);plot(x2(20:L8),arrayPkout3_1(1,20:L13), b);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,2)plot(x2(20:L8),arrayPkout3_2(1,20:L14), g);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,3)plot(x2(20:L8),arrayPkout3_3(1,20:L15), k);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,4)plot(x2(20:L8),arrayPkout3_4(1,20:L16), r);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage from first stage in volts);subplot(5,1,5)plot(x2(20:L8),arrayPkout_cw3(1,20:L18), m);axis auto;grid on;figure(12)subplot(5,1,1);plot(x2(20:L8),arrayPkout3_1(2,20:L13), b);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage second stage volts); 81
  • 87. subplot(5,1,2)plot(x2(20:L8),arrayPkout3_2(2,20:L14), g);grid on;axis auto;xlabel(time in seconds);ylabel(Output voltage from second stage in volts);subplot(5,1,3);plot(x2(20:L8),arrayPkout3_3(2,20:L15), k);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage second stage volts);subplot(5,1,4);plot(x2(20:L8),arrayPkout3_4(2,20:L16), r);axis auto;grid on;xlabel(time in seconds);ylabel(Output voltage second stage volts);subplot(5,1,5)plot(x2(20:L8),arrayPkout_cw3(2,20:L18), m);grid on;axis auto;xlabel(time in seconds);ylabel(Output voltage from second stage in volts);figure(13)subplot(5,1,1);plot(x2(20:L8),arrayPkout3_1(3,20:L13), b);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);subplot(5,1,2)plot(x2(20:L8),arrayPkout3_2(3,20:L14), g);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);subplot(5,1,3);plot(x2(20:L8),arrayPkout3_3(3,20:L15), k);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage);subplot(5,1,4);plot(x2(20:L8),arrayPkout3_4(3,20:L16), r);grid on;axis auto;xlabel(time in seconds);ylabel(Output from Third Stage); 82
  • 88. subplot(5,1,5) plot(x2(20:L8),arrayPkout_cw3(3,20:L18), m); grid on; axis auto; xlabel(time in seconds); ylabel(Output from Third Stage); All the functions are the same as used in of each stage of each SOA.the phase 2. The runtime of this matlab code isa bit high (nearly 5 minutes), because we are The network was first fed by a four signalsusing arrays for saving the amplitude and the of wavelength 1548 nm, 1552 nm, 1556 nm,corresponding time instances of any signal, but 1560nm and each of them of duty ratio 1. So,the arrays are dynamically defined. they look like Fig 8.09:-Preallocating may become a solution to thisproblem but preallocating such an array may Thereafter, the Fig 8.10 gives the generatedincrease the the program complexity and also carriers in the first SOA.the difficulty to dbug. The coding gives outputto the amount of generated carriers in eachSOA for the corresponding time and the output 83
  • 89. The figure Fig 8.11- Fig 8.13 gives theamplitude (in Volts) vs. time graph for theoutput of each stage of the 1 st SOA :- 84
  • 90. The output of third stageis attenuated 1/10000 times and passed ontothe next SOA which gives the response graphFig 8.14 – Fig 8.17. Fig 8.15: output voltage 1st stage 2nd SOA 85
  • 91. and, lastly, thesignal isattenuated againto be fed to thelast SOA, whichgives theresponse of thegraphs Fig 8.18– Fig 8.21. Fig 8.18:number ofcarrier in 3rdSOA 86
  • 92. 87
  • 93. Power Penalty and BER in SOA Receiver CHAPTER 9 The IM-DD receiver can be analyzed as9.1. Optical communication systems can be follows. We assume on-off keyed (OOK)classified broadly as non-coherent and coherent modulation where spaces and marks aretransmission. In non-coherent transmission represented by input powers of zero and 2Psonly the intensity of an optical carrier signal is respectively.modulated. At the receiver the signal is directlydetected, a process that is only sensitive to the Ps is the average received power assuming thatsignal intensity. Such systems are termed the transmission probabilities of a mark or aIntensity Modulation-Direct Detection (IM- space are equal.DD). The photocurrent idA schematic diagram of a basic IM-DD receiveris shown in Fig. 9.1. In this scheme intensity And the responsively of the receiver ismodulated optical carrier signal is detected by aphoto detector (p-i-n diode or avalanchephotodiode (APD)). The resulting photocurrent where η is the detector quantum efficiency.is amplified and passed to a decision circuit that Apart from the signal detection current there aredetermines whether each received bit is a mark noise due to dark current, shot noise and receiveror space. circuit current. Due to these noises and interference of the adjacent pulses, the receiver cannot always detect the digital signal correctly. BER is the measuring of rate of errors. It is defined as BER= Where Ne is the number of erroneous bits and NtFigure..9.1. IM-DD Receiver in optical is the number of bits received at a certaincommunication interval t.To make decisions on the received waveform For a conventional OOK receiver, if it isthe received waveform is sampled every bit assumed that the noise currents have Gaussianperiod, usually at the centre of the bit and probability density functions, the BER is givencompared the sampled value to a threshold bylevel. If the sampled value is less than thethreshold level the received bit is interpreted as aspace and vice versa.The usual figure of merit for an optical receiver BER=is the bit-error-rate (BER).Apart from BER the other figure of merits are  Power penalty  Quality factorAnother important figure of merit for opticalamplifier is noise figure. To an approximation it can be written as9.1.1. Bit Error Rate 88
  • 94. amplification of light. The use of an optical filter at the amplifier output can greatly reduce this9.1.2. Q-Factor noise; however it is impossible to eliminate it entirely. When the signal and accompanying Q-factor is widely used to specify the noise are detected by a photo detector thereceiver performance. It is related to the OSNR square-law detection process gives rise to beat-(optical signal to noise ratio). noise currents in addition to the usual shot-noise.If we assume that the receiver threshold be A useful figure of merit for an optical amplifieroptimized for the minimum BER then it is called is the electrically equivalent noise figure F,Q-factor. It is defined as defined as the ratio between the amplifier input and output electrical SNRsWhere S1=Is^2 and S2=0 signal power for markand space respectively. The SNRs are calculated by assuming that theIn ideal case where dark current and cicuit noise amplifier input signal and output signal plusis neglected then ASE are passed through a narrowband optical filter prior to detection by an ideal photo detector (i.e. unity quantum efficiency). In this case the only photocurrent noise terms that needWhere Be is the electrical BW of the photo to be taken into account are the signal shot noisedetector. and the signal-spontaneous beat noise.9.1.3. Power penalty Optical extinction ratioPower penalty Optical extinction ratio (re) is Anddefined as re=I1/I0=P1/P0 where P0 and P1 arethe power of bit ‘0’ and ‘1’ respectively.Ideally P0=0 making re infinity. If the extinctionratio is not optimum the transmitted power mustbe increased to maintain the same BER at the where G is the amplifier gain.receiver. This increase in power is called Power So the noise figure ispenalty. It is the excess optical power requiredto account for the degradation due to ISI,reflections, mode partition etc.9.2. Noise figure 9.3. To evaluate the SOA receiver parameter We now simulate the Q-factor, BER and otherThe addition of spontaneous emission (i.e. performance parameters. We also calculate thenoise) is an inevitable consequence of the beat current due to the shot noise in the receiver.The parameters of the SOA receiver are given as follows: 89
  • 95. Parameter symbol Parameter name Value g0 Intrinsic gain of SOA 30dB λ Input wavelength 1550 nm B0 BW of the optical filter 126 GHz nsp Spontaneous emission factor 4 M Number of SOA in ring network 3 R Responsivity 0.8 Psat Saturated output power 10 dBm9.3.1 PROGRAM OF Q-FACTOR AND BEROF A 4-CHANNEL SOA9.3.1.a. SUBPROGRAMfunction gain= sol_gain(g,g0,Pin,Psat,B0,nsp,h,fs, M)gain = g0*exp(-(g-1)*(g*Pin+(M-1)*2*nsp*(g-1)*h*fs*B0)/(g*Psat))-g; Pin2 is the signal with noise. Here only the shot noise is incorporated. The number of amplifierThe parameters are passed from the main used in the ring network is 3 and 4 WDMprogram. This program has a subprogram which channels are taken. Responsivity of the receivercalculates the gain of the SOA and the optical assumed to be 0.8.network before reception of the signal. Gain of the network is calculated by calling the subprogram. The power spectral density of ASE noise is calculated with and without shot noise.9.3.1.b. The BER of the received signal iscalculated from the Q-factor. Two signals are The photo detector current is given byconsidered here. Pin1 is the desired signal and Is =Responsivity* Incident photon power. 90
  • 96. The ASE beat-noise variance (σ) with and Power penalty is the difference in the inputwithout transient is calculated. Q-factor is given signal (in dB) to establish a particular BER withby Q=Is /σ. and without noise.BER is calculated using the formula BER=% finding out initial conditionnsp=4; %spontaneous emission factorh=6.62E-34; %unit is in J.sc=3*1E8;lamda1= 1550*1E-9;number_of_ch = 4;fs = c/lamda1;B0=126E9; %unit is in Hzg0_dB= 30; %unit is in dBg0= (10^(g0_dB/10));Psat_dbm= 10; % in dBmPsat = (10^(Psat_dbm/10))*1E-3; %unit is in wattPin_dbm= [-30 -25 -20 -15 -12 -9 -7 -5 -3 0 3 5 7];L1 =length(Pin_dbm);Pin1= (10.^(Pin_dbm/10)).*1E-3.*number_of_ch; %unit is in watt; signal input powerPin1Pin_Tr= [ 0.1*1e-4 0.7*1e-4 1.39*1e-4 4.41*1e-4 8.81*1e-4 0.0018 0.0028 0.00440.0070 0.0140 0.0279 0.04 0.070 ];% Transient power in wattPin2 = Pin1 + Pin_Tr;Pin2Pin2_dbm = 10*log10(Pin2);M=3; % number of amplifiers in the ringinguess=1;for (i=1:1:L1)gain1(i) =fzero(@(g) sol_gain(g,g0,Pin1(i),Psat,B0,nsp,h,fs, M), inguess);gain1gain2(i) =fzero(@(g) sol_gain(g,g0,Pin2(i),Psat,B0,nsp,h,fs, M), inguess);gain2endPin_temp = Pin1 + Pin_Tr./gain2;PintempdB = 10*log10(Pin_temp);Nase1=(gain1-1).*(nsp*h*fs);Nase2=(gain2-1).*(nsp*h*fs);e=1.6E-19; % electron charge n=1; R=0.8; Is1=R*Pin1; Is1 Is2= R*Pin_temp; Is2 91
  • 97. Pase1=2*B0*Nase1; % ASE power for the input signal onlyPase2=2*B0*Nase2; %ASE power for the input signal with receiver shot noiseIase1=(e*n*lamda1*Pase1)./(h*c);Iase1Iase2=(e*n*lamda1*Pase2)./(h*c);Iase2Be=1.25*1E9; % unit is in Hzase_beat1=(4*(R^2)*Be).*Nase1.*Pin1; %Beat currentsigma1=15*sqrt(ase_beat1);sigma1ase_beat2=(4*(R^2)*Be).*Nase2.*Pin2; %Beat current with transientsigma2=15*sqrt(ase_beat2);sigma2Q1=Is1./sigma1;Q1Q2=Is2./sigma2;Q2 y1=(exp(-(Q1.^2)/2)./(Q1.*sqrt(2*pi))); % BER for the signal onlyy2=(exp(-(Q2.^2)/2)./(Q2.*sqrt(2*pi) ));% BER for signal and noisey1y2 y1_dB=10*log10(exp((-Q1.^2)/2)./(Q1.*sqrt(2*pi))); % BER in dB for the signal onlyy2_dB=10*log10(exp((-Q2.^2)/2)./(Q2.*sqrt(2*pi) ));% BER in dB for signal and transientfigure(1)%plot(Pin_dbm,y1(1,:),k);plot(Pin_dbm,y1_dB,k, Pin_dbm,y2_dB,r);xlabel(Input power in dBm);ylabel(BER);%plot(Pin_dbm,y2,r);grid on;axis([-35, -5, -10, 1]); a. The resultant graph shown in the figure 9.1. 92
  • 98. Figure.9.1. Input power vs. BER graphFrom the graph we can show the power penalty i.e. the difference in input power (dBm) to maintain aconstant BER with and without noise. At -10 dB BER i.e. 0.1 BER Figure.9.2. Magnified output at -10.5 dB BER Power penalty = (-13.7-(-14.2)) = 0.5 dB 93
  • 99. b. Now for 10^-9 BER i.e.-90 dB BER the graph is Figure.9.3. Input power vs. BER graph for 10E-9 BER From the graph the power penalty for 10E-9 BER is shown Figure.9.4. Magnified output for 10e-9 BER Power penalty = (-6.9-(-7.4)) = 0.5 dB Power penalty = 0.5 dB. This power serves no additional purpose but is an extra requirement tocompensate the noise interference due to non-ideal extinction ratio. Less the power penalty, more efficient is the system. 94
  • 100. Summary Chapter 10 At the end of the report describing our project, we come to conclude about the performance of theSemiconductor Optical Amplifier. In the first and second chapter, we have introduced the SOA wit its brief history. In the thirdchapter, we have justified why we have selected the SOA. In the fourth chapter, we have given thebasic principle of the SOA. The fifth chapter describes the fundamental device characteristics and thematerial used in the SOA. The modelling of SOA is described in the sixth chapter, where widebandSOA steady-state model and numerical solution has been described, while the seventh chapter givesthe description about the cross-gain modulation . The whole of the eight and ninth chapter givesdescription about our work done on the simulation and the power penalty calculation including theBER calculation. 94
  • 101. Bibliography Chapter 111. Studies on Placement of Semiconductor Optical Amplifiers in Wavelength Division Multiplexed Star and Tree Topology Networks by Yatindra Nath Singh submitted in fulfilment of the requirement of degree of Doctor of Philosophy (Ph.D.) to Electrical Engineering Department Indian Institute of Technology, Delhi Hauz Khas, New Delhi 110016 India September 19962. Theory and Experiment of High-Speed Cross-Gain Modulation in Semiconductor Lasers by X. Jin, T. Keating, and S. L. Chuang3. Investigation of Pulse Pedestal and Dynamic Chirp Formation on Pico second Pulses After Propagation Through an SOA by A. M. Clarke, M. J. Connelly, P. Anandarajah, L. P. Barry, and D. Reid4. SOA-Based WDM Metro Ring Networks With Link Control Technologies by T. Rogowski, S. Faralli, G. Bolognini, F. Di Pasquale, Member, IEEE, R. Di Muro, and B. Nayar, Member, IEEE5. Optical Amplifiers by Bala Ramasamy and Robert Stacey6. Optical Fibre Communication by Gard Kaiser, international edition, 19917. Nonlinear Fibre Optics, Third Edition, by Govind P. Agrawal, The Institute of Optics, University of Rochester8. Optical Fibre communication, by J. M. Senior, 19859. Wideband Semiconductor Optical Amplifier Steady-State Numerical Model, byMichael J. Connelly, Member, IEEE10. Semiconductor Optical Amplifiers– High Power Operation, by Boris Stefanov, Leo Spiekman David Piehler Alphion Corporation,IEEE 802.3av Task Force Meeting, Orlando, 13-15 March 2007.11. Fast and Efficient Dynamic WDM Semiconductor Optical Amplifier Model, Walid Mathlouthi, Pascal Lemieux, Massimiliano Salsi, Armando Vannucci, Member, IEEE, Alberto Bononi, and Leslie A. Rusch, Senior Member, IEEE. 95