Optical amplifiers are used to compensate for attenuation losses in optical fibers over long transmission distances. The three main types of optical amplifiers are semiconductor optical amplifiers, fiber Raman amplifiers, and rare earth doped fiber amplifiers. Rare earth doped fiber amplifiers like erbium doped fiber amplifiers are particularly useful as they can provide wide bandwidth amplification in the 1.5 micron wavelength region with high efficiency. They have advantages such as high power transfer efficiency, wide gain bandwidth, and polarization independence. However, they also produce amplified spontaneous emission noise and have saturation effects at high powers.
An Overview of EDFA Gain Flattening by Using Hybrid AmplifierIJEEE
Data communication systems are increasingly engrossing optical fiber communication system as the transmission paths for the information, the information is in the form of light pulses sending from one place to another through the optical fiber. Several types of optical amplifiers have been developed in optical fiber communication system to amplify the optical signals. The erbium doped fiber amplifier is one of the optical fiber amplifiers which are used for long distance communication. The most significant points in any optical amplifier design are gain and noise figure. They are connected to one another. The other optical amplifier, Raman amplifier has wide gain bandwidth. The EDFA gain spectrum has variations over 1536 to 1552 nm, therefore the gain flattening is a research issue in recent years with the development of high capacity DWDM. The gain variation becomes a problem as the number of channels increases. The gain of EDFA depends on large number of device parameters such as, Erbium ion concentration, amplifier length, core radius, pump power. Raman amplifiers can be combined with EDFAs to expand the optical gain flattened bandwidth. This paper focuses on different methods used for the gain flattening.
Optical Fiber Communication Part 3 Optical Digital ReceiverMadhumita Tamhane
Current generated by photodetector is very weak and is adversely effected by random noises associated with photo detection process. When amplified, this signal further gets corrupted by amplifiers. Noise considerations are thus important in designing optical receivers.
Most meaningful criteria for measuring performance of a digital communication system is average error probability, and in analog system, it is peak signal to rms noise ratio. ...
An Overview of EDFA Gain Flattening by Using Hybrid AmplifierIJEEE
Data communication systems are increasingly engrossing optical fiber communication system as the transmission paths for the information, the information is in the form of light pulses sending from one place to another through the optical fiber. Several types of optical amplifiers have been developed in optical fiber communication system to amplify the optical signals. The erbium doped fiber amplifier is one of the optical fiber amplifiers which are used for long distance communication. The most significant points in any optical amplifier design are gain and noise figure. They are connected to one another. The other optical amplifier, Raman amplifier has wide gain bandwidth. The EDFA gain spectrum has variations over 1536 to 1552 nm, therefore the gain flattening is a research issue in recent years with the development of high capacity DWDM. The gain variation becomes a problem as the number of channels increases. The gain of EDFA depends on large number of device parameters such as, Erbium ion concentration, amplifier length, core radius, pump power. Raman amplifiers can be combined with EDFAs to expand the optical gain flattened bandwidth. This paper focuses on different methods used for the gain flattening.
Optical Fiber Communication Part 3 Optical Digital ReceiverMadhumita Tamhane
Current generated by photodetector is very weak and is adversely effected by random noises associated with photo detection process. When amplified, this signal further gets corrupted by amplifiers. Noise considerations are thus important in designing optical receivers.
Most meaningful criteria for measuring performance of a digital communication system is average error probability, and in analog system, it is peak signal to rms noise ratio. ...
Gain and noise figure analysis of erbium doped fiber amplifierseSAT Journals
Abstract Erbium doped fiber amplifier (EDFA) performance is dependent on several factors such as fiber length, pump power, Er3+
concentration. This paper involves the simulation of an EDFA using Optisystem and analyzes the gain and noise figure of EDFA
in the Conventional band in terms of pump power and fiber length. The gain increases initially with the pump power when the
length is fixed and then it decreases. The gain also increases with the length when pump power is fixed and decreases after
reaching a maximum. Whereas the noise figure increases with length and decreases with pump power.
Key Words: EDFA, pump power, gain, noise figure
50W single-mode linearly polarized high peak power pulsed fiber lasernufchas
We demonstrate 50W single-mode linearly polarized high peak power pulsed fiber laser with tunable ns–µs pulse durations and kHz–MHz repetition rates capable to address a wide range of applications: frequency conversion, LIDAR and others.
The attached narrated power point presentation attempts to explain the various digital communication techniques as applied to optical communications. The material will be useful for KTU final year B tech students who prepare for the subject EC 405, Optical Communications.
Light sources based on optical-scale acceleratorsGil Travish
Presented at the 2010 Future Light Sources Workshop, SLAC, Palo Alto, CA. Gives an overview of optical-scale particle accelerator structures as would be used in x-ray light sources.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Gain and noise figure analysis of erbium doped fiber amplifierseSAT Journals
Abstract Erbium doped fiber amplifier (EDFA) performance is dependent on several factors such as fiber length, pump power, Er3+
concentration. This paper involves the simulation of an EDFA using Optisystem and analyzes the gain and noise figure of EDFA
in the Conventional band in terms of pump power and fiber length. The gain increases initially with the pump power when the
length is fixed and then it decreases. The gain also increases with the length when pump power is fixed and decreases after
reaching a maximum. Whereas the noise figure increases with length and decreases with pump power.
Key Words: EDFA, pump power, gain, noise figure
50W single-mode linearly polarized high peak power pulsed fiber lasernufchas
We demonstrate 50W single-mode linearly polarized high peak power pulsed fiber laser with tunable ns–µs pulse durations and kHz–MHz repetition rates capable to address a wide range of applications: frequency conversion, LIDAR and others.
The attached narrated power point presentation attempts to explain the various digital communication techniques as applied to optical communications. The material will be useful for KTU final year B tech students who prepare for the subject EC 405, Optical Communications.
Light sources based on optical-scale acceleratorsGil Travish
Presented at the 2010 Future Light Sources Workshop, SLAC, Palo Alto, CA. Gives an overview of optical-scale particle accelerator structures as would be used in x-ray light sources.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The attached narrated power point presentation describes the principle of working, various configurations, advantages, disadvantages and applications of Erbium Doped Fiber Amplifiers. The material will be useful to KTU final year B tech students who prepare for the subject EC 405, Optical Communications.
The attached narrated power point presentation attempts to explain the methods for amplification of light, It throws light into the different types of optical amplifiers such as semiconductor optical amplifiers and fiber amplifiers. The material will be useful for KTU final year B Tech students who prepare for the subject EC 405, Optical Communications.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
EDFA play important role in optical communication networks, It provides high output power, high gain, wide frequency bandwidth, low power input, and low noise. This article will share some knowledge about EDFA.
The scope of this paper is to analyze the performance of HG_EDFA (High Gain Erbium Doped Fiber Amplifier) and LN_EYCDFA (Less ASE Noise erbium-ytterbium co-doped fiber amplifier) using single pumping with the wavelength of 980nm by the various parameters like Gain, forward output signal power and forward and backward ASE (Amplified spontaneous Emission) noise power. This Paper describes the simulation models of HG_EDFA is connected with an input of (DMLaser1) direct modulated laser source and the performance was analyzed with the parameters were measured and the values are tabulated and plotted and compared with LN_EYCDFA. The simulation model consists of input source 1mw with wavelength (1550nm), pumping CW Laser source with wavelength 980nm and Filter. The resulting models were accurately represents Gain and optimized output signal power. Simulation results shows that by choosing careful fiber length 20m and pump power 1mw in single pumping gives ASE noise 0.0025mw in HG_EDFA and 12X10-14mw in LN_EYCDFA.
In this paper, we utilized optimized C-band and L-band amplifiers to constitute a broadband CA-L erbium-doped amplifier with a parallel structure. This amplifier has a simple configuration, high-flattened gain and low noise. Meanwhile, we have realized an amplification bandwidth of over 70 nm(1 524—1 602 nm)without any broadband gain flattening component. The C-band average gain is over 30 dB and L-band gain variation is less than 2 dB.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
2. OPTICAL AMPLIFIERS
· In order to transmit signals over long distances (>100 km) it is necessary to
compensate for attenuation losses within the fiber.
· Initially this was accomplished with an optoelectronic module consisting of an
optical receiver, a regeneration and equalization system, and an optical
transmitter to send the data.
· Although functional this arrangement is limited by the optical to electrical and
electrical to optical conversions.
Fiber Fiber
OE OE
Rx Tx
Electronic Amp Optical
Equalization Signal
Optical Regeneration Out
Signal
In
· Several types of optical amplifiers have since been demonstrated to replace the
OE – electronic regeneration systems.
· These systems eliminate the need for E-O and O-E conversions.
· This is one of the main reasons for the success of today’s optical
communications systems.
2
3. OPTICAL AMPLIFIERS
The general form of an optical amplifier:
PUMP
Power
Amplified
Fiber Weak
Signal Fiber
Signal
Optical AMP Medium
Optical
Signal
Optical Out
Signal
In
Some types of OAs that have been demonstrated include:
· Semiconductor optical amplifiers (SOAs)
· Fiber Raman and Brillouin amplifiers
· Rare earth doped fiber amplifiers (erbium – EDFA 1500 nm, praseodymium –
PDFA 1300 nm)
The most practical optical amplifiers to date include the SOA and EDFA types.
New pumping methods and materials are also improving the performance of
Raman amplifiers.
3
4. Characteristics of SOA types:
· Polarization dependent – require polarization maintaining fiber
· Relatively high gain ~20 dB
· Output saturation power 5-10 dBm
· Large BW
· Can operate at 800, 1300, and 1500 nm wavelength regions.
· Compact and easily integrated with other devices
· Can be integrated into arrays
· High noise figure and cross-talk levels due to nonlinear phenomenon such as 4-
wave mixing.
This last feature restricts the use of SOAs.
· Semiconductor Optical Amplifier (SOA) – similar to a laser cavity. Used as a
discrete amplifiers. They can be integrated into arrays of amplifying
switching and gating devices. Finding application in all optical 3R-
regeneration systems.
Electrical
Drive Current
AR AR
Weak Optical Amplified Optical
Signal In Signal
Semiconductor Cavity
· Limited in operation below 10 Gb/s. (Higher rates are possible with lower
gain.)
4
5. Rare Earth Doped Fiber Amplifier Characteristics:
Rare earth doped fiber amplifiers are finding increasing importance in optical
communications systems. Perhaps the most important version is erbium doped
fiber amplifiers (EDFAs) due to their ability to amplify signals at the low loss 1.55
mm wavelength range.
Characteristics of EDFAs (advantages):
· High power transfer efficiency from pump to signal power (> 50%).
· Wide spectral band amplification with relative flat gain (>20 dB) – useful for
WDM applications.
· Saturation output > 1 mW (10 to 25 dBm).
· Gain-time constant long (>100 msec) to overcome patterning effects and inter-
modulation distortions ( low noise).
· Large dynamic range.
· Low noise figure.
· Polarization independent.
· Suitable for long-haul applications.
Disadvantages of EDFAs:
· Relatively large devices (km lengths of fiber) – not easily integrated with other
devices.
· ASE – amplified spontaneous emission. There is always some output even with
no signal input due to some excitation of ions in the fiber – spontaneous noise.
· Cross-talk effects.
· Gain saturation effects.
5
6. · An energy level diagram for Er doped silica is shown below.
4I (11/2) 0.98 um
4I (13/2) 1.53 um
Pump 1.48 um
Bands
Emission
Wavelengths
4I (15/2)
· Pumping is primarily done optically with the primary pump wavelengths at 1.48
mm and 0.98 mm. As indicated atoms pumped to the 4I (11/2) 0.98 mm band
decays to the primary emission transition band. Pumping with 1.48 mm light is
directly to the upper transition levels of the emission band.
· Semiconductor lasers have been developed for both pump wavelengths.
· 10-20 mW of absorbed pump power at these wavelengths can produce 30-40
dB of amplifier gain.
· Pump Efficiencies of 11 dB/mW achieved at 980 nm.
· Pumping can also be performed at 820 and 670 nm with GaAlAs laser diodes.
Pump efficiencies are lower but these lasers can be made with high output
power.
6
7. Typical Absorption/Gain Spectrum for Erbium Doped Fiber:
10
6
(X 10^(-25)m^2)
Cross Section
Loss/Gain
(dB/m)
Absorption 4
5
2
Gain
0
1.51 1.53 1.55
Wavelength (um)
· Since the gain spectrum of erbium resembles a 3-level atom it is possible to
model the gain properties using this approach.
· Several different wavelength bands have been designated for wavelength
division multiplexing and EDFAs have been designed to operate in these bands.
· The divisions have been designated as*:
S-Band 1480-1520 nm
C-Band 1521-1560 nm
L-Band 1561-1620 nm
(* Note some variability in these values is common.)
7
8. General EDFA Amplifier Configuration:
980 or 1480 pump laser
Amplified Output
Isolator Signal
EDFA
Weak Input
Signal Coupler Narrow Band
Filter
Basic Amplifier Characteristics
Optical Gain
· Rare earth doped optical amplifiers work much like a laser.
· The primary difference is that they do not have a resonator.
· Amplification occurs primarily through the stimulated emission process.
· The medium is pumped until a population inversion state is achieved. Pump
powers are typically several 20-250 mW. An isolator is used to reduce
reflections at the input to the amplifier. A narrow band optical filter is used to
reduce transmission of amplified spontaneous emission frequency components.
· The resultant optical gain depends both on the optical frequency and the local
beam intensity within the amplifier section.
· For basic discussion consider a two-level homogeneously broadened medium.
8
9. · The gain coefficient can be expressed as:
go
g (w ) =
1 + (w - w o ) 2 T22 + P / Ps ,
go is the peak gain, w is the optical frequency of the incident signal,
wo is the transition frequency, P is the optical power of the incident signal,
T2 is the dipole relaxation time, and Ps is the saturation power.
· Typically T2 is small < 1 ps, and the saturation power Ps depends on gain
medium parameters such as the fluorescence time and the transition cross
section.
9
10. _____________________________________________________________
Gain Spectrum and BW:
· When not saturated (i.e. P/Ps <<1) the gain coefficient g(w) becomes:
go
g (w ) = .
1 + (w - w o ) 2 T22
· Gain is maximum when w = wo (i.e. the gain coefficient is at resonance).
· At non-resonant frequencies the gain follows the homogeneously broadened
characteristics of a two level atom (i.e. Lorentzian profile).
· The gain BW for this spectrum is typically expressed as the (Full Width at Half
Maximum) FWHM
Dw g = 2 T2 .
Dw g
Dn g =
2p
with T2 ; 0.1 ps
Dn g ; 3THz
· Large Spectral BW amplifiers are preferred for fiber optic systems to make
them less sensitive to dispersed transmitted signals and useful for WDM
systems.
EDFA Gain Spectrum:
· The gain spectrum of erbium ions alone is homogeneously broadened and the
BW is determined by the dipole relaxation time T2.
· However when placed in a glass host the spectrum is influenced both by the
silica and any other dopants. This can result in inhomogeneous broadening
contributions.
· The combined homogeneous and inhomogeneous BW of EDFAs: ~ 30 nm.
10
11. Amplification factor:
· Define as:
G = Pout/Pin
Pout is the amplifier output power and Pin the input power of a CW input signal.
Pump
P N2 P
in Gain out
Medium
N1
z=0 z=L
· From the previous discussion of the laser the gain in optical power per length of
gain medium (z) with gain g is
dP
= gP .
dz
· Integrating over a length z of amplifier medium gives the resultant optical
power
P( z ) = P(0) exp( gz ) .
11
12. The amplification factor after a length L of OAM (optical amplifier medium) is
G (w ) = exp[g (w ) L]
Both g(w) and G(w) are a maximum when the frequency is at resonance w = w o
and decrease when the frequency is detuned from resonance.
However the amplifier factor(G) decreases much faster than the gain coefficient(g).
· The amplifier BW DnA is defined as the FWHM of G(w)
0.5
æ ln 2 ö
ç ln(G / 2) ÷
Dn A = Dn g ç ÷
è o ø
where Dng is the gain BW, and Go = exp(goL).
· The amplifier BW is smaller than the gain BW. The difference depends on the
amplifier gain characteristics.
If Go = 10, Dn A = 0.656 Dn g
12
13. Gain Saturation:
· Since g(w) depends on the incident optical power when P » PS, G will start to
decrease with an increase in optical power P.
· Assume that the incident frequency is tuned for peak gain (w = wo)
dP go P
= .
dz 1 + P / Ps
· With the conditions P(0) = Pinc and P(L) = Pout = GPinc the large signal
amplifier gain becomes
æ G - 1 Pout ö
G = Go expç -
ç ÷.
÷
è G PS ø
· This expression shows how the amplifier gain decreases when Pout » Ps.
Output saturation power º the optical power at which G is reduced to Go/2 (3 dB)
out Go ln 2
Psat = Ps .
Go - 2
· Typically Go =1000 (30 dB),
s
Pout » (ln 2) Ps » 0.69 Ps .
13
14. Amplifier Noise:
· Spontaneous emission in the amplifier will degrade the SNR by adding to the
noise during the amplification process.
· SNR degradation is quantified through the amplifier noise figure Fn
(SNR )in
Fn =
(SNR )out
where the SNR is based on the electrical power after converting the optical signal
to an electrical current. Therefore Fn is referenced to the detection process and
depends on parameters such as detector bandwidth (Be) and thermal and shot noise.
· Consider a simple case with an ideal detector with performance limited by shot
noise.
· The amplifier has an amplification factor G (Pout = G Pin).
· SNR of the input signal:
(RPin )2
2
I Pin
SNRin = = = ,
s s2 2q( RPin )Be 2hnBe
s s2 = 2q (RPin )Be .
· The spontaneous emission contribution is amplified along with the signal. The
Spectral density of the spontaneous emission induced noise is nearly constant
(white noise) and can be expressed as:
S sp (n ) = (G - 1)n sp hn
· Spontaneous emission population inversion factor nsp is given by:
N2
n sp = .
N 2 - N1
N2 and N1 are the population densities for the excited and ground states of the
amplifying medium.
14
15. · Alternatively can express the spontaneous emission power within the receiver
bandwidth Be as:
Psp = 2 S sp Be
· Spontaneous emission adds fluctuations to the amplified power and is converted
to current fluctuations at the detector output.
· Major contribution to receiver noise results from coherent interference (beating)
between the spontaneous emission with the signal. This results in a noise
current given by
DI = 2 R(GPin Psp )1/ 2 cos q
· The variance in the photocurrent after the signal is passed through the amplifier
is
s 2 » 4( RGPin ) × (RS sp )Be
where cos2 q is replaced with its average value of ½. (Note that this relation
assumes several idealizations on the detection process i.e. other noise sources are
negligible.)
· The SNR of the amplified signal becomes
(RGPin )2 GPin
SNRout = »
s2 4 S sp Be
and the amplifier noise figure is
Fn = 2n sp (G - 1) / G » 2n sp .
· For most amplifiers Fn > 3 dB and can be 6-8 dB.
15
16. · Characteristic plot of gain and noise figure for an erbium doped fiber
amplifier pumped ~30 mW at 980 nm.
40 40
30 30
Noise Figure
Gain (dB)
20 20
10 10
0 0
1510 1520 1530 1540
Wavelength (nm)
16
17. EDFA Gain Equalization
10
Unflattened
EDFA Gain
Loss/Gain
(dB/m)
5
Flattened
EDFA Gain
0
1.51 1.53 1.55 1.56
Wavelength (um)
· Gain equalization can be accomplished in several ways:
a. Thin film filters
b. Long period fiber gratings
c. Chirped fiber Bragg gratings
17
18. Raman Scattering, Stimulated Raman Scattering, and Raman Amplifiers:
· Raman scattering is an elastic scattering mechanism. Does not require a
population inversion.
· A photon with energy hn1 traveling through a material can excite a
vibrational transition of the material forming an optical phonon with energy
hnp and a photon with slightly reduced energy hn2 given by
n 2 = n1 -n p
Energy
hn
2
hn1
hnp
· Molecule is raised to a new vibrational state and the energy of the photon
is reduced.
· There is a large difference between the photon and phonon energies.
· Raman scattering is weak effect. It occurs through a slight modulation of
the refractive index through molecular vibrations of the material.
· Can derive the effect through a discussion of polarizability of a material.
18
19. · The electric field induces a dipole moment of the molecule
p = qx
or
p =aE
where a is the complex polarizability of the molecule.
x
o
+q -q
E
· The bulk polarizability of a material is expressed as
P = eo c ( ) E
1
with c (1) the linear susceptibility of the material.
· Response of a to an incident harmonic electric field:
¶a
a ( x ) = ao + dx
¶x xo
dx is the displacement from the equilibrium molecular length xo
d x ( t ) = d xo e
± jw p t
19
20. p(t ) = a (t ) E (t )
æ ¶a ± jw p t ö jw t
= çao + d xo e ÷ Eo e 1
ç
è ¶x xo
÷
ø
¶a ( )
j w1 ±w p t
= a o Eo e jw1t + d xo Eo e
¶x xo
· There are two frequency components: a) w1 ; b) w1 ± w p
· The second component is nonlinear ® the output frequency is different
from the input frequency.
Stokes Anti-Stokes
Energy
Energy
hn2
hn1 hn1 hn
2
hnp hnp
· Scattered light with lower energy (n 2 < n 1 ) ® Stokes Scattering.
· Scattered light with higher energy (n 2 > n 1 ) ® Anti-Stokes Scattering.
· Stokes scattering typically dominates due to greater population of the ground
state relative to the vibrational state when the system is in thermal
equilibrium.
· At low illumination levels the Raman process results in low scattering levels.
· The molecules contributing to the process are vibrating independently and
the scattered light is non-directional. Spontaneous Raman Scattering.
20
21. · At higher intensity levels the generated photons begin to act in phase or
coherently – i.e. the molecules oscillate as an array of vibrating oscillators.
This gives rise to Stimulated Raman Scattering (SRS).
· SRS can be can be a problem but it can also be used as a signal amplification
process.
· On the negative side it contributes to dispersion and places an operational
limit on the amount of power that can be transmitted through a fiber.
· The Stokes wave is amplified as it propagates through the medium
dI 2
= Gr I 2 I1
dz
I2 is the intensity of the Stokes shifted light (w s = w1 - wvib ) ; I1 is the intensity
of the pump beam (w1); and Gr is the Raman gain term that includes material
factors such as ¶a / ¶x and varies as 1/l2.
· For I2 <<I1 and cases where the pump beam is not significantly depleted:
I 2 ( z ) = I 2 ( 0 ) eGr ×I1× z
21
22. Properties of Raman Amplifiers:
· The peak resonance in silica fibers occurs about 13 THz from the pump
wavelength. At 1550 nm this corresponds to a shift of about 100 nm.
Raman Gain Coefficient
l p = 1550 nm
0 13 24
Frequency Shift (THz)
· As indicated power is transferred from shorter wavelengths to longer
wavelengths.
· Coupling with the pump wavelength can be accomplished either in the
forward or counter propagating direction.
· Power is coupled from the pump only if the signal channel is sending a 1
bit.
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23. Pump Arrangement to Extend the Range for Stimulated Raman Amplification:
· An array of laser diodes can be used to provide the Raman pump. The beams
are combined and then coupled to the transmission fiber. The pump beams
can counter propagate to the direction of the signal beams.
14xx/1550 nm
Transmission Fiber WDM Coupler
Raman Pump
Block 1430 nm
1450 nm
Laser 14xx nm
Diode 1470 nm
Array 1490 nm Combiner
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24. Difficulties with Raman Amplifiers:
· The Pump and amplified signals are at different wavelengths. Therefore
the signal and the pump pulses will separate due to dispersion
(waveguide dispersion) after a certain propagation distance. The
difference in propagation time is given by:
d t = ( L / c ) l 2 d 2 n / d l 2 (d n / n )
L is the fiber length.
· A 1 psec pump pulse at 600 nm separates from a 1 psec Stokes pulse in ~
30 cm.
· A second problem is that the pump power decreases along the fiber
length due to linear absorption and scattering – Raman gain is greater at
the input end.
· A final problem results from amplifying spontaneous Raman photons.
This occurs when the pump power is increased to offset attenuation
losses and spontaneous Raman photons are coupled into the guided mode
all along the length of the fiber. This increases noise.
· Upper limit on the power into a communications signal from SRS
amplification can be defined as the point at which the Stokes power Pr
equals the signal power Psig.
2
16p wo
P=
Gr Leff
1 - e -a L
Leff =
a
Example:
l p = 1.55m m
wo » 5m m ® Amod e » 80 m m2
a linear » 0.2dB / km ® Leff » 20km ® 700 mW
Gr = 9 ´10-12 m / W
QUITE LARGE compared to normal optical signal powers (~1 mW).
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