Analyzing numerically study the effect of add a spacer layer in gires tournois

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Analyzing numerically study the effect of add a spacer layer in gires tournois

  1. 1. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME85ANALYZING NUMERICALLY STUDY THE EFFECT OF ADD ASPACER LAYER IN GIRES-TOURNOIS INTERFEROMETER DESIGNGaillan H. Abdullah 1, Elham Jasim Mohammad 21Physics Directorate, Technology Materials Chemistry/Ministry of Science, Iraq2Physics Department, Collage of Sciences/Al-Mustansiriyah University, IraqABSTRACTWe demonstrated Gires-Tournoise interferometer (GTI) design as an optical standing-wave cavity to generate chromatic dispersion. In this research we design three structures withdifferent spacers to study the impact on the pulse width and reflectivity using two types ofdielectric materials TiO2/SiO2 as the high and low refractive index.Keywords: Gires-Tournoise, Group Delay Dispersion, Optical Filter, Round Trip.I. INTRODUCTIONOptical filters have been widely applied to optical communication systems and fibersensing fields. With the rapid development of optical communication, many techniques havebeen proposed for optical filters, such as birefringence, optical-electric thin-films, arraywaveguide gratings, ring resonators, fiber gratings, Michelson and Mach-Zehnderinterferometers, and Gires-Tournois interferometer (GTI) [1].Gires-Tournois interferometers are generally used to compensate highly chirpedpicosecond or femtosecond pulses the way they exist, especially in narrow gain band-widthlasers like Nd: YAG. Large amounts of intracavity negative GDD are essential in ultrashortpulse lasers, in order to compensate for the gain bandwidth and self-phase modulation (SPM)due to nonlinear elements [2]. In comparison to a prism pair sequence, the GTI is easily threeorders of magnitude more dispersive but also linear over a much smaller bandwidth. Theamount of available group delay dispersion can be further increased by reecting theintracavity pulse several times of the surface of the GTI, because the introduced dispersion isproportional to the number of bounces from the surface. Several schemes of GTI have beenproposed introducing these large amounts of group delay dispersion (GDD) [3]. In large gainINTERNATIONAL JOURNAL OF ADVANCED RESEARCH INENGINEERING AND TECHNOLOGY (IJARET)ISSN 0976 - 6480 (Print)ISSN 0976 - 6499 (Online)Volume 4, Issue 2 March – April 2013, pp. 85-91© IAEME: www.iaeme.com/ijaret.aspJournal Impact Factor (2013): 5.8376 (Calculated by GISI)www.jifactor.comIJARET© I A E M E
  2. 2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME86bandwidth lasers like Ti:sapphire and Cr:LiSAF the GTI are used to tune the laser in thepicosecond regime. This is done by changing the pulse angle of incidence upon the GTI,which thereby correctly compensates a narrow bandwidth of intracavity dispersion [4]. Sofar, these devices have been used in a much ex-perimental manner, by simply maintaining theround trip time inside the GTI much below the pulse duration and adjusting the number ofreactions from its surface in order to minimize the pulse duration. Here we calculate thebandwidth over which the dispersion of a GTI is linear. We are therefore capable ofdesigning a GTI, which introduces constant GDD over the whole gain bandwidth (FWHM),meanwhile keeping the losses low by minimizing the number of reactions needed [4,5].II. GTI THEORY AND PRINCIPLE OF OPERATIONA Gires-Tournois interferometer consists of two parallel surfaces, the second of whichis 100 % reflective as show in Figure 1. Therefore, the two quantities which characterize theGTI are the reflection coefficient r of the first surface and the distance ݀ between them [6].Figure 1: Schematic setup of a gires–tournois interferometer [7]The round trip time inside the GTI for an angle of incidence ߠ is then given by [4]:‫ݐ‬଴ ൌଶ௡ௗ௖ට1 െ௦௜௡మఏ௡మ (1)Where c is the speed of light and ݊ the refractive index of the medium between themirrors. If the pulse duration is longer than t0, the fields of successive reflections of the samepulse do temporally overlap and the pulse envelope may be reshaped. This puts an upper limitto the distance between the reecting surfaces. But, as the distance d becomes shorter, theGDD becomes smaller too, as can be seen from the equation below [4]:‫ܦܦܩ‬ ൌ 2ߨௗ்ௗఠൌ െ2ߨௗమ‫׎‬ௗఠమ ൌ 2ߨ‫ݐ‬ଶଶ ൫௥మିଵ൯ଶ௥ ୱ୧୬ ఠ௧బሺଵା௥మିଶ௥ ୡ୭ୱ ఠ௧బሻమ (2)where, T = group delay , ߱=angular frequency, ‫=׎‬ phase and r= reflectivity.In order to obtain constant negative GDD over finite bandwidth, ω > 0, the phasehas to be adjusted such that the GDD is a minimum. This phase is a function of r, as seen inabove equation. In order to obtain high values of negative dispersion and large bandwidth
  3. 3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME87(for short pulse duration), one has to increase the reflectivity of the intermediate mirror in acontrolled manner. The commonly used round trip time (1) shows no dependency with theintermediate surface reflectivity. We know, that the higher the reflectivity, the longer thedelay time within the GTI. Therefore, as the reflectivity increases, the pulse, coming out ofthe GTI, gets stretched in time. Taking into account the reflectivity we derive an expressionfor the decay time of a pulse in a passive resonator, τ [4]:߬ ൌ ‫ݐ‬଴ . ቜ1 ൅ଵ୪୬ቀଵ௥మൗ ቁቝ (3)Where t0 is given by (1). By analyzing numerically various GTIs we found that thisexpression gives a very good estimate in the case of Fourier transform limited pulse width. Amore useful approximation is obtained by calculating the bandwidth, ∆νGTI, over which thegroup delay is linear. We therefore expand the group delay as a function of frequency aboutthe points of maximum GDD. At these points the second derivative of the group delay is zeroand we obtain [8]:ܶሺ߱ሻ ൌ ܶሺ߱଴ሻ ൅ௗ்ሺఠబሻௗఠ∆߱ ൅ௗయ்ሺఠబሻ଺ௗఠయ ∆߱ଷ(4)Linearity of the group delay is guaranteed as long as the third term in above equation issmaller than the second term [8]:ௗ்ሺఠబሻௗఠయ ൌௗ்ሺఠబሻௗఠ∆߱ (5)Where we have dropped the factor (6) in the denominator of the third term. Using the abovecriteria for linearity we obtain:∆νGTI ൌ 2∆ఠଶగൌଵగටௗ்ሺఠబሻௗఠቀௗయ்ሺఠబሻௗఠయ ቁିଵ(6)III. DESIGN AND DISCUSSIONSince in 1984~1987, whereas standard quarter-wave dielectric mirrors were shown tointroduce negligible dispersion at the center of their reflectivity bands [9-11], various specifichigh-reflectivity coatings (GTI, double-stack mirrors, etc.) with adjustable GDD (throughangle tuning) were devised and used for the precise control of intra-cavity dispersion infemtosecond dye lasers. The material used in all design is TiO2/SiO2 as the high and lowrefractive index. The design wavelength is 600nm and the spectral range 450–800nm.Figure 2 and Figure 3 show the reflectance and reflectance GDD, where H and L are quarterwave layers at 800nm with indices 2.35 and 1.45 which correspond to TiO2 and SiO2,respectively, and the refractive index of Glass is 1.51. The bandwidth of high reflectance(>70%) is 520~710 nm, and the reflectance GDD value is near zero. Table 1 shows the layerstructure for the first design.
  4. 4. International Journal of Advanced Research in Engineering and Technology (IJARET),6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, MarchFigure 2: RefFigure 3: Group delay disTable 1No MaterialsThicknesses1 TiO22 SiO23 TiO24 SiO25 TiO2Then we add a spacer 2H and a low reflectance streflectance and reflectance GDD of the stack are showing inshows Layer structure of the secondFigure 4: Reflection vs. wavelengthInternational Journal of Advanced Research in Engineering and Technology (IJARET),6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME88eflections vs. wavelength for the first designroup delay dispersion vs. wavelength for the first designTable 1: Layer structure of the first designThicknesses(nm)No. MaterialsThicknesses(nm )64.844 6 SiO2 101.303101.303 7 TiO2 64.84464.844 8 SiO2 101.303101.303 9 TiO2 64.84464.844 10 SiO2 101.844Then we add a spacer 2H and a low reflectance stack (LH) to the above designreflectance and reflectance GDD of the stack are showing in Figure 4 and Figuresecond design.eflection vs. wavelength for the second designInternational Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –April (2013), © IAEMEdesignThicknessesack (LH) to the above design, theFigure 4 and Figure 5. Table 2
  5. 5. International Journal of Advanced Research in Engineering and Technology (IJARET),6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, MarchFigure 5: Group delay disTable 2:No Materials Thicknesses1 TiO22 SiO23 TiO24 SiO25 TiO26 SiO27 TiO2The reflectance is broadingGDD has a high non-linear value in the bandwidth of 570~620nm.Finally, if the spacer 2H in Figurethird design shows in Table 3.Figure 6: Reflection vs. wavelength for thirdFigure 7: Group delay disInternational Journal of Advanced Research in Engineering and Technology (IJARET),6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME89roup delay dispersion vs. wavelength for the second designLayer structure for the second designThicknesses(nm)No. Materials Thicknesses(nm )64.844 8 SiO2 101.303101.303 9 TiO2 64.84464.844 10 SiO2 101.844101.303 11 TiO2 129.68964.844 12 SiO2 101.303101.303 13 TiO2 64.84464.844The reflectance is broading from 190nm to 230 nm (510~740nm), but the reflectancelinear value in the bandwidth of 570~620nm.Finally, if the spacer 2H in Figure 4 changed to 10H, then the Layer structure ofReflection vs. wavelength for third designroup delay dispersion vs. wavelength for the third designInternational Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –April (2013), © IAEMEdesignThicknessesbut the reflectanceLayer structure of thedesign
  6. 6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME90Table 3: Layer structure of the third designNo. Materials Thicknesses(nm)No. Materials Thicknesses(nm )1 TiO2 64.844 7 TiO2 64.8442 SiO2 101.303 8 SiO2 101.3033 TiO2 64.844 9 TiO2 64.8444 SiO2 101.303 10 SiO2 101.8445 TiO2 64.844 11 TiO2 713.2896 SiO2 101.303 12 SiO2 101.303From Figure 6 and Figure 7, it is clearly seen that the values of the reflectance andreflectance GDD is becoming higher than the one in Figure 4. But the bandwidth of highreflectance is narrow and the non-linear reflectance GDD is worse than the one in Figure 5.IV. CONCLUSIONA Gires–Tournois interferometer is an optical standing-wave resonator designed forgenerating chromatic dispersion. The front mirror is partially reflective, whereas the backmirror has a high reflectivity. If no losses occur in the resonator, the power reflectivity isunity at all wavelengths, but the phase of the reflected light is frequency-dependent due to theresonance effect, causing chromatic dispersion. The phase change of reflected light and thedispersion (including group delay dispersion and higher-order dispersion) change periodicallywith optical frequency, if material dispersion is negligible. There is no second-orderdispersion exactly on-resonance or anti-resonance, and positive or negative dispersionbetween these points.Ideally, the GTI is operated near a maximum or minimum of the GDD, and the usablebandwidth is some fraction (e.g. one-tenth) of the free spectral range, which is inverselyproportional to the resonator length. In the time domain, this means that the pulse durationneeds to be well above the round-trip time of the GTI. The maximum magnitude of GDDscales with the square of the resonator length.From the above result, we can see that the layer structure can be easily adapted for any otherwavelength regime. We believe that this compensator of thin-film has more potential to bedeployed in ultrafast optics and optical communication.REFERENCES[1] Y. Zhang, W. Huang, X. Wang, H. Xu, Z. Cai, A novel super-high extinction ratiocomb-filter based on cascaded Mach-Zehnder Gires-Tournois interferometers withdispersion Compensation, OSA, 17(16), 2009, 13685-13699.[2] E. P. Ippen, Principles of Passive mode Locking, Appl. Phys B 58, 1994, 159.[3] J. Kuhl, J. Heppner, Compression of Femtosecond Optical Pulses with DielectricMultilayer Interferometers, IEEE J. Quant. Electron. QE- 22, 1986, 182.[4] J. D. Kafka, M. L. Watts, J-W. J. Pieterse, Picosecond and Femtosecond PulseGeneration in a Regeneratively Mode-Locked Ti:Sapphire Laser, IEEE J. Quant.Electron. QE-28, 1992, 2151.
  7. 7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME91[5] R. Szipıcs, Dispersive Properties of Dielectric Laser Mirrors and their Use inFemtosecond Pulse Lasers, doctoral diss., SZTE TTK Szeged, Department for Opticsand Quantumelectronics, Hungary, 2000.[6] L. Orsila, Interferometric Dielectric Reflectors for Dispersion Compensation in FiberLasers, Ms.C. thesis, Tampere University of Technology, Finland, 2003.[7] http://www.rp-photonics.com/gires_tournois_interferometers.html.[8] M. Ramaswamy, A.S. Gouveia-Neto, D.K. Negus, J.A. Izatt and J.G. Fujimoto, 2.3-pspulses from a Kerr-lens mode-locked lamp-pumped Nd-YLF laser with a microdotmirror, Optics Letters 18, 1993, 1825.[9] W. Dietel, E. Dbpel, K. Hehl, W. Rudolph, and E. Schmidt, Multilayer dielectric mirrorsgenerated chirp in femtosecond dye-ring lasers, Opt. Commun., 50, 1984, 179.[10] S. De Silvestri, P. Laporta, and O. Svelto, Analysis of quarter-wave dielectric-mirrordispersion in femtosecond dye-laser cavities, Opt. Lett., 9, 1984, 335.[11] W. H. Knox, N. M. Pearson, K D. Li, and Ch. A. Hirlimann, Interferometricmeasurements of femtosecond group delay in optical components, Opt. Lett., 13, 1988,574.[12] K. Karuna Kumari and Dr. P.V.Sridevi, “Performance Evaluation of Circular MicrostripPatch Antenna Array with Different Dielectric Substrate Materials”, Internationaljournal of Electronics and Communication Engineering &Technology (IJECET),Volume 4, Issue 1, 2013, pp. 236 – 249, ISSN Print: 0976-6464, ISSN Online: 0976-6472.[13] Ahmed Thabet and Youssef A. Mobarak, “Experimental Study for Dielectric Strength ofNew Nanocomposite Polyethylene Industrial Materials”, International Journal ofElectrical Engineering & Technology (IJEET), Volume 3, Issue 1, 2012, pp. 353 - 364,ISSN Print : 0976-6545, ISSN Online: 0976-6553.

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