臺灣博碩士論文加值系統

在本論文中，我們使用耦合模態理論(Coupled mode theory; CMT)來解析布拉格光纖光柵(Fiber Bragg gratings; FBGs)，包含有uniform布拉格光纖光柵與apodized布拉格光纖光柵。而對於一個多模態的耦合模態理論，我們可以將之表示成變數為傳播距離的一階向量常微分方程式(Ordinary differential equations; ODEs)。
針對uniform布拉格光纖光柵，我們使用eigenvalue and eigenvector technique (EVVT)與Runge-Kutta method (RKM)來求解耦合模態理論。而對於uniform布拉格光纖光柵的耦合模態方程式(Coupled mode equations; CMEs)，我們在論文中提出了變數代換的技巧，並將原始的耦合模態方程式常數化成為新的微分方程式。由於EVVT可以求得線性微分方程的嚴格解，因此我們可以使用EVVT找到uniform FBGs的解析解，而同時RKM是常見使用來求解微分方程的數值方法，因此我們使用4階RKM來求解CMT。我們透過傳輸頻譜與反射頻譜，來比較EVVT與RKM，而結果顯示，兩個方法的結果皆相當的準確。
對於apodized布拉格光纖光柵，我們使用普遍使用的Gaussian-apodized布拉格光纖光柵。由於apodized布拉格光纖光柵的折射率分佈會隨著傳播距離變化，因此我們使用4階RKM與piecewise-uniform approach (PUA)來求解耦合模態方程式。我們在此並提供兩種離散技巧的PUA來分析光柵的折射率，同時我們也應用兩種PUA到EVVT以及傳輸矩陣中來分析Gaussian-apodized布拉格光纖光柵。而經由計算傳輸率與反射率來比較2種PUA與RKM數值方式。我們得到RKM可提供更快收斂且更為準確的數值結果。
我們還首次提出Chebyshe-apodized布拉格光纖光柵結構並分析其之特性。我們利用apodized布拉格光纖光柵的分析技巧分析Chebyshe-apodized布拉格光纖光柵，結果顯示在相同的FWHM之下，Chebyshev-apodized布拉格光纖光柵的旁波抑制效果優於Gaussian-apodized布拉格光纖光柵，而且不會降低其色散的特性。
我們在本論文中同時也分析uniform分佈型長週期光柵。我們提出長週期光柵的耦合模態理論以及耦合模態方程式，並提出EVVT與RKM兩種數值分法。在結果方面，我們對於不同參數的長週期光柵分析其傳輸頻譜特性。

In this dissertation, the coupled mode theory (CMT) is used to analyze fiber Bragg gratings (FBGs). The FBGs include uniform FBGs and apodized FBGs. The multi- mode CMT is expressed as the first-order vector ordinary differential equations (ODEs) with coefficients depending on the propagation distance.
For the uniform FBGs, the eigenvalue and eigenvector technique (EVVT) and the forth-order Runge-Kutta method (RKM) are used to solve the coupled mode theory. We show in this dissertation that by changing variables, the original coupled mode equations (CMEs) can be re-casted as constant coefficient ODEs. The EVVT is the rigorous method to solve the linear differential equations. Therefore, the analytical solution of the uniform FBGs can be obtained. On the other hand, the RKM is the most common used numerical method to solve the initial value problem of the ordinary differential equation. Therefore, the forth order RKM is applied to calculate the CMT in uniform FBGs as well. We compare the transmission and the reflection spectra obtained by EVVT with those by RKM. Both results agree within matching accuracy.
The coupled mode theory is used to analyze apodized Fiber Bragg gratings (FBGs) as well. Since the profile of gratings varies with the propagation distance, the coupled mode equations (CMEs) of apodized FBGs are solved by the fourth-order Runge-Kutta method (RKM) and piecewise-uniform approach (PUA). We present two discretization techniques of PUA to analyze the apodization profile of gratings. A uniform profile FBG can be expressed as a system of first-order ordinary differential equations with constant coefficients. The eigenvalue and eigenvector technique as well as the transfer matrix method is applied to analyze apodized FBGs by using PUAs. The transmission and reflection efficiencies calculated by two PUAs are compared with those computed by RKM. The results show that the order of the local truncation error of RKM is h-4, while both PUAs have the same order of the local truncation error of h-2. It is found that RKM, capable of providing fast-convergent and accurate numerical results is a preferred method in solving apodized FBG problems.
In this dissertation, we also present the property of FBGs with Chebyshev apodization profile. The Chebyshev-apodized FBGs is first proposed and analyzed. We use the same analysis theory of apodized FBGs to analyze the Chebyshev-apodized FBGs. We compare the sidelobe suppression of reflection spectrum and dispersion of Chebyshev-apodized FBGs with Gaussian-apodized FBGs at the same full width half maximum (FWHM). The results show that the sidelobe suppression of Chebyshev- apodized FBGs is better than Gaussian-apodized FBGs, and the dispersion of Chebyshev- apodized FBGs is similar to that of Gaussian-apodized FBGs.
The long period gratings (LPGs) with uniform profile are analyzed in this dissertation. We present the CMT and CMEs of LPGs. The characteristic of transmission spectrum for LPGs with varies parameters are also discussed.

中文摘要I
ABSTRACT III
謝誌 V
List of Contents VI
List of Tables VIII
List of Figures IX
Chapter 1 Introduction 1
1-1 Overview 1
1-2 Background and Motivation 2
1-2-1 Uniform Fiber Bragg Gratings 2
1-2-2 Apodized Fiber Bragg Gratings 4
1-2-3 Long Period Braggs 6
1-3 Organization of the Dissertation 7
Chapter 2 Uniform Fiber Bragg Gratings 11
2-1 Coupled Mode Theory 11
2-2 Coupled Mode Equations 13
2-3 Coupled Mode Equations with Constant Coefficient 15
2-3-1 Symmetric From of CMEs 16
2-3-2 Asymmetric From of CMEs 19
2-4 Eigenvalue and Eigenvector Technique for Uniform FBGs 23
2-5 Runge-Kutta Method for Uniform FBGs 24
2-6 Transmission and Reflection Coefficients 26
Chapter 3 Apodized Fiber Bragg Gratings 29
3-1 Gaussian-Apodized Fiber Bragg Gratings 29
3-2 Coupled Mode Equations 29
3-3 Piecewise-Uniform Approach for Apodized Fiber Bragg Gratings 32
3-4 Runge-Kutta Method 34
Chapter 4 Results and Discussion of Uniform and Apodized Fiber Bragg Gratings 37
4-1 Uniform Fiber Bragg Gratings 37
4-2 Apodized Fiber Bragg Gratings 40
Chapter 5 Chebyshev-apodized Fiber Bragg Gratings 54
5-1 Introduction of Chebyshev-apodized Fiber Bragg Gratings 54
5-2 Simulation Results of Chebyshev-apodized Fiber Bragg Gratings 56
5-3 Chebyshev-apodized Fiber Bragg Gratings with Varies Grating Period 58
5-4 Comparison of Chebyshev apodization FBGs with Gaussian apodization FBGs 59
Chapter 6 Long Period Gratings 68
6-1 Coupled Mode Theory and Equations 68
6-2 Coupled Mode Equations with Constant Coefficients 69
6-3 Numerical Method 70
6-3-1 Eigenvalue and Eigenvector Technique 70
6-3-2 Runge-Kutta Method 71
6-3-3 Transmission Coefficient 72
6-4 Simulated Results of Gain Flattening Filter of an Erbium-doped Fiber Amplifier 73
6-5 Simulated Results of LPGs with Varies Parameters 74
Chapter 7 Conclusions and Future Work 80
REFFERENCES 83
List of Tables
Table 4-1. The comparison of transmission efficiency calculated by EVVT and RKM with various step numbers at wavelength of 1539.98nm 52
Table 4-2. The comparison of transmission efficiency calculated by PUA1 and RKM with various step numbers at wavelength of 1539.92nm 52
Table 4-3. The propagation constant βν and FBG parameters κν,δν at λ=1539.92nm. The unit is given in MKS system (M-1) 53
Table 5-1. Bandwidths and shape factors of Chebyshev-apodized with SLL=60dB, 80dB and 100dB 67
Table 5-2. Bandwidths and sidelobes of Chebyshev-apodized with Gaussian- apodized FBGs 67
List of Figures
Figure 1-1. The structure of typical optical fibers. The central region is the core, which is surrounded by the cladding. The cladding is also surrounded by a protective jacket 9
Figure 1-2. The refractive index profile of typical optical fibers. The core region has a higher refractive index than the surrounding cladding material. Within the core, the refractive index profile can be uniform or graded, while the cladding index is typically uniform 9
Figure 1-3. Diagram of a fiber Bragg grating. Z indicates the position of the grating, L is the grating length and Λ is the grating period (Λ<1μm) 10
Figure 1-4. Diagram of a long period gratings. Z indicates the position of the grating, L is the grating length and Λ is the grating period (Λ>100μm) 10
Figure 2-1. The illustration of the fiber gratings of the induced index change of the uniform grating structure 28
Figure 3-1. Diagram of the induced index change of Gaussian-apodized grating structure with the fringe visibility m set to one 36
Figure 4-1. The transmission spectrum of uniform FBGs using EVVT and RKM. The step number of RKM is 1000 45
Figure 4-2. The reflection spectrum of uniform FBGs using EVVT and RKM. The step number of RKM is 1000 45
Figure 4-3. The difference of the transmission efficiencies between the EVVT and RKM1 46
Figure 4-4. The difference of the reflection efficiencies between the EVVT and RKM1 46
Figure 4-5. The error of transmissivity by RKM1 and RKM2 as a function of step number at wavelength of 1541.69nm 47
Figure 4-6. The error of reflectivity by RKM1 and RKM2 as a function of step number at wavelength of 1541.69nm 47
Figure 4-7. The transmission spectrum of Gaussian-apodized gratings. The solid line is calculated by PUA1, the dash line is calculated by RKM 48
Figure 4-8. The reflection spectrum of Gaussian-apodized gratings. The solid line is calculated by PUA, the dash line is calculated by RKM 48
Figure 4-9. The transmission spectrum of Gaussian-apodized gratings calculated by RKM with the fundamental core mode and with a total of 25 modes (one fundamental mode and 24 cladding modes) 49
Figure 4-10. The reflection spectrum of Gaussian-apodized gratings calculated by RKM with the fundamental core mode and with a total of 25 modes (one fundamental mode and 24 cladding modes) 49
Figure 4-11. The difference of the transmission efficiencies between the PUA1 and RKM 50
Figure 4-12. The difference of the reflection efficiencies between the PUA1 and RKM 50
Figure 4-13. The error of transmissivity by RKM, PUA1 and PUA2 as a function of step numbers at wavelength of 1539.92nm 51
Figure 4-14. The error of reflectivity by RKM, PUA1 and PUA2 as a function of step numbers at wavelength of 1539.92nm 51
Figure 5-1. The envelop shape of Chebyshev-apodized profile with 40 sections uniform gratings 62
Figure 5-2. Index change of a Chebyshev profile with 40section uniform gratings. Chebyshev-apodized with zero-dc index change 62
Figure 5-3. The reflection spectrum of fiber Bragg gratings with uniform structure (solid line), Gaussian-apodized structure (thick dashed line) and Chebyshev-apodized structure (thin dashed line) 63
Figure 5-4. The group delay of fiber Bragg gratings with uniform structure (solid line), Gaussian-apodized structure (thick dashed line) and Chebyshev-apodized structure (thin dashed line) 63
Figure 5-5. The reflection spectrum of Chebyshev-apodized structure with SLL=60 (solid line), SLL=80(thick dashed line) and SLL=100(think dashed line) 64
Figure 5-6. The grating period of each section of Chebyshev-apodized structure with chirped gratings 64
Figure 5-7. The reflection spectrum of Chebyshev-apodized with zero-dc index change and Chebyshev-apodized with chirped gratings 65
Figure 5-8. Reflection spectra of the Chebyshev-apodized (solid line) and Gaussian -apodized fiber Bragg gratings (thick dash line is FWHM equals 7mm and thin dash line is FWHM equals 10mm) 65
Figure 5-9. Dispersion spectra of the Chebyshev-apodized (real line) and Gaussian -apodized fiber Bragg gratings (thick dash line is FWHM equals 7mm and thin dash line is FWHM equals 10mm) 66
Figure 6-1. Transmission spectra for the LPG measured during the HF acid etching process where the data lines are offset by 5dB 76
Figure 6-2. The transmission spectrum of LPG1, LPG2 and LPG3 76
Figure 6-3. The flattened gain spectrum of erbium-doped fiber amplifiers 77
Figure 6-4. The transmission spectrum of a long-period fiber grating 77
Figure 6-5. The transmission spectrum with various core radii 78
Figure 6-6. The transmission spectrum with various core indices 78
Figure 6-7. The transmission spectrum with various cladding radii 79

[1]A. Carballar, M. A. Muriel, and J. Azana “Fiber Grating Filter for WDM Systems An Improved Design,” IEEE Photonics Technology Letters, Vol. 11, No. 6, Jun. 1999
[2]A. Khajehpour and S. A. Mirtaheri, “Analysis of pyramid EM wave absorber by FDTD method and comparing with capacitance and homogenization methods,” Progress In Electromagnetics Research Letters, Vol. 3, pp. 123-131, 2008.
[3]A. M. vegsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-Period fiber Gratings as band-Rejection Filters,” J. Lightwave Technol., Vol. 14, pp. 58-65, 1996.
[4]A. Rostami and A. Yazdanpanah Goharrizi, “A new method for classification and identification of complex fiber Bragg grating using the genetic algorithm,” Progress In Electromagnetics Research, Vol. 75, 1105-1115, 2007.
[5]A. Yariv , Optical Electronics in Modern Communications, Oxford, 5th ed., 1996.
[6]Ashish M. Vengsarlar, Paul J. Lemaire, G. Jacobovitz-Veselka, Vikram Bhatia, and J. B. Judlkins, “Long-period fiber gratings as gain-flattening and Laser stabilizing devices,” in Proc. IOOC`95, June 1995, PD1-2.
[7]Ashish M. Vengsarlar, Paul J. Lemaire, Justin B. Judkins, Vikram Bhatia, T. Erdogan, and John E. Sipe, “Long-period fiber gratings as band-rejection filters,” Journal of Lightwave Technology, Vol. 14, No. 1, pp.58-65, 1996.
[8]Ashish. M. Vengsarlar, J. R. Pedrazzani, J. B. Judkins, P. J. Lemaire, N. S. Bergano, and C. R. Davison, “Long-period fibre-grating-based gain equalizers,” Opt. Lett., 21(5), pp. 336-338, 1996.
[9]Ashish. M. Vengsarlar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe and T. Erdogan, “Long-period fibre gratings as band-rejection Filters,” OFC’95, Vol. 8, PD4-2, 1995.
[10]B. E. A. Saleh and M. C. Teich, Fundamental of Photonics, John Wiley & Son, New York, 1991.
[11]Chih Cheng Chou, Jiun-Jie Liau, Chung-En Chou, Nai-Hsiang Sun, and Wen-Fung Liu, “Numerical Modeling of the Gain Flattening Filter of an EDFA Based on Etching LPGs Technology,” OECC/COIN 2004, 13P-81, Yokohama, Japan, 2004
[12]Chung En Chou, Nai Hsiang Sun, and Wen Fung Liu, “Gain flattening filter of an EDFA based on etching LPGs technology,” J. of Optical Engineering, Feb. 2004.
[13]D. V. Prokopovich, A. V. Popov, and A. V. Vinogradov, “Analytical and numerical aspects of Bragg fiber design,” Progress Electromagnetics Research B, Vol. 6, pp. 361-379, 2008.
[14]D. V. Prokopovich, A. V. Popov, and A. V. Vinogradov, “Analytical and numerical aspects of Bragg fiber design,” Progress In Electromagnetics Research B, Vol. 6, pp. 361-379, 2008.
[15]E. A. Hashish, “Forward and inverse scattering from an inhomogeneous dielectric slab,” Journal of Electromagnetic Waves and Applications, Vol. 17, 719-736, 2003.
[16]E. M. Dianov, V. I. Karpov, A. S. Kurkov, O. I. Medvedkov, A. M. Prokhorov, V. N. Protopopov, S. A. Vasiliev, “Gain spectrum flattening of erbium-doped fiber amplifier using long-period fiber grating,” in Photosensitivity and Quadratic Nonlinearity in Glass Waveguides: Fundamental and Applications, 1995 OSA Tech. Dig. Series, Vol.22, paper SaB3.
[17]F. A. Molinet, “Plane wave diffraction by a strongly elongated object illuminated in the paraxial direction,” Progress In Electromagnetics Research B, Vol. 6, pp. 135-151, 2008.
[18]G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron., Vol. 34, pp. 1390-1402, Aug. 1998.
[19]G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Optics Letters, Vol. 14, pp. 823-825, 1989.
[20]H. J. Patrick, A. D. Kersey, and F. Bucholtz, “Analysis of the response of long period fiber gratings to the external index of refraction,” Journal of Lightwave Technology, Vol. 16, pp. 1606-1612, Sept. 1998.
[21]H. Ke, J. Peng, and C. Fan, “Design of Long-Period Fiber Gratings With Fast-Varying Parameters,” IEEE J. Quantum Electron., vol. 13, pp. 1194-1196, Nov. 2001.
[22]H. Singh and M. Zippin, “Apodized fiber Bragg gratings for DWDM applications using uniform phase mask,” in ECOC’98, Madrid, Spain, pp. 189-190, Sept.1998.
[23]H. T. Hattori, “Fractal-like square lattices of air holes,” Progress In Electromagnetics Research Letters, Vol. 4, pp. 9-16, 2008.
[24]H. W. Chang and M. H. Sheng, “Errata for the paper ‘entitled dielectric waveguide devices based on coupled transverse-mode integral equation-Mathematical and numerical formulations,” Progress In Electromagnetics Research C, Vol. 8, pp. 195-197, 2009.
[25]H. W. Chang and M. H. Sheng, “Field analysis of dielectric waveguide devices based on coupled transverse-mode integral equation-Mathematical and numerical formulations,” Progress In Electromagnetics Research, Vol. 78, pp. 329-347, 2008.
[26]H. W. Chang and W. C. Cheng, “Analysis of dielectric waveguide termination with tilted facets by analytic continuity method,” Journal of Electromagnetic Waves and Applications, Vol. 21, pp. 1621-1630, 2007.
[27]H. W. Chang, Y. H. Wu, S. M. Lu, W. C. Cheng, and M.-H. Sheng, “Field analysis of dielectric waveguide devices based on coupled transverse-mode integral equation– Numerical investigation,” Progress In Electromagnetics Research, Vol. 97, pp. 159-176, 2009
[28]Hadjicostas, J. K. Buter, G. A. Evans, N. W. Carlson, and R. Amantea, “A numerical investigation of wave interactions in dielectric waveguides with periodic surface corrugations,” IEEE J. Quantum Electron. Vol. 26, pp. 893-902, 1990.
[29]J. A. M. Rojas, J. Alpuente, P. Lopez-Espi, and P. Garcia, “Accurate model of electromagnetic wave propagation unidimensional photonic crystals with defects,” Journal of Electromagnetic Waves and Applications, Vol. 21, No. 8, pp. 1037-1051, 2007.
[30]J. Alberk, K. O. Hill, B. Malo, S. Theriault, F. Bilodeau, D. C. Johnson, and L. E. Erickson, “Apodization of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett., vol. 31, pp. 222-223, Feb. 1995.
[31]J. E. Sipe, L. Poladian, and C. M. De Sterke, “Propagation through nonuniform grating structures,” J. Opt. Soc. Amer. A, vol. 11, pp. 1307-1320, Apr. 1994.
[32]J. J. Liau, N. H. Sun, R. Y. Ro, P. J. Chiang, and S. C. Lin, “Numerical approaches for solving coupled mode theory – Part I: Uniform fiber Bragg gratings,” Progress In Electromagnetics Research Symposium, 2A6-3, Hangzhou, China, 2008.
[33]J. J. Liau, N. H. Sun, S. C. Lin, R. Y. Ro, J. S. Chiang, C. L. Pan, and H.-W. Chang, “A new look at numerical analysis of uniform fiber Bragg gratings using coupled mode theory,” Progress In Electromagnetics Research, Vol. 93, pp. 385-401, 2009.
[34]J. J. Liau, N. H. Sun, S. C. Lin, R. Y. Ro, J. S. Chiang, C. L. Pan, and H. W. Chang, “A New Look at Numerical Analysis of Uniform Fiber Bragg Gratings Using Coupled Mode Theory,” Progress in Electromagnetics Research, Vol. 93, pp. 385-401, 2009.
[35]J. L. Rebola and A. V. T. Cartaxo, “Performance optimization of gaussian apodized fiber Bragg grating filter in WDM systems,” IEEE Journal of Lightwave Technology, Vol. 20, pp. 1537-1544, 2002.
[36]João L. Rebola, Adolfo V. T. Cartaxo, "Performance optimization of Gaussian apodized fiber Bragg grating filters in WDM systems," J. Lightwave Technol, Vol. 20, no. 8, Aug. 2002.
[37]K. C. Chang, V. Shah, and T. Tamir, “Scattering and guiding of waves by dielectric gratings with arbitrary profiles,” J. Opt. Soc. Amer., Vol. 70, pp. 804-813, 1980.
[38]K. Ennser, M. N. Zervas, and R. I. Laming, “Optimization of apodized linearly chirped fiber gratings for optical communications,” IEEE J. Quantum Electron., Vol. 34, pp. 770-778, 1998.
[39]K. Mizuno, Y. Nishi, Y. Mimura, Y. Lida, H. Matsuura, D. Yoon, O. Aso, T. Yamamoto, T. Toratani, Y. Ono, A. Yo, “Development of Etalon-type gain-flattening filter,” Furukawa Review, No. 19, pp. 53-58, 2000.
[40]K. O. Hill and Gerald Meltz, “Fiber Bragg Grating Technology Fundamentals and Overview,” J. Lightwave Technol., vol.15, No. 8, pp. 1263-1276, 1997.
[41]K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication,” Appl. Phys. Lett., vol.32, pp. 647-649, 1978.
[42]K. Watanabe and K. Kuto, “Numerical analysis of optical waveguides based on periodic Fourier transform,” Progress In Electromagnetics Research, Vol. 64, pp. 1-21, 2006.
[43]K. Watanabe, “Fast converging and widely applicable formulation of the differential theory for anisotropic gratings,” Progress In Electromagnetics Research, Vol. 48, pp. 279-299, 2004.
[44]K. Watanabe, “Fast converging and widely applicable formulation of the differential theory for anisotropic gratings,” Progress In Electromagnetics Research, Vol. 48, pp. 279-299, 2004.
[45]M. He, J. Jiang, J. Han, and T. Liu, “An experiment research on extend the range of fiber Bragg grating sensor for strain measurement based on CWDM,” Progress In Electromagnetics Research Letters, Vol. 6, pp. 115-121, 2009.
[46]M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fiber/phase mask-scanning beam technique for enhanced flex-ibility in producing fiber gratings with uniform phase-mask,” Electron. Lett., vol. 31, pp. 1488-1490, Aug. 1995.
[47]M. J. Moghimi, H. Ghafoori Fard, and A. Rostami, “Analysis and design of all-optical switching in apodized and chirped Bragg gratings,” Progress In Electromagnetics Research B, Vol. 8, pp. 87-102, 2008.
[48]M. J. Moghimi, H. Ghafoori-Fard, and A. Rostami, “Analysis and design of all-optical switching in apodized and chirped Bragg gratings," Progress In Electromagnetics Research B, Vol. 8, pp. 87-102, 2008.
[49]M. J. N. Lima, A. L. J. Teixeira, and J. R. F. Da Rocha, “Optimization of apodized fiber grating filters for WDM systems,” Proc. of IEEE LEOS Annual Meeting, ThZ2, 876-877, San Francisco, USA, 1999.
[50]M. Rochette, M. Guy, S. LaRochelle, J. Lauzon, “Gain equalization of EDFA’s with Bragg gratings,” Photonics Technology Letters, Vol. 11, N0. 5, May 1999.
[51]M. Tilsch, Hulse, C. A., Hendrix, K. D., and Sargen, R. B., “Design and demonstration of a thin film based gain equalization filter for c-band EDFAs,” NFOEC’99
[52]MJN Lima, ALJ Teixeira, JRF da Rocha, “Optimization of apodized fiber grating filters for WDM systems”, in Proc. of LEOS’ 99 - 12 th IEEE LEOS Annual Meeting, paper ThZ2, pp. 876-877, San Francisco, USA, 1999.
[53]N. Mohammad, W. Szyszkowski, W. J. Zhang, E. I. Haddad, J. Zou, W. Jamroz, and R. Kruzelecky, “Analysis and development of a tunable fiber Bragg grating filter base on axial tension/compression,” J. Lightwave Technol. Vol. 22, pp. 2001-2013, 2004.
[54]Nai Hsiang Sun, Jiun Jie Liau, Shih Chiang Lin, Jung Sheng Chiang and Wen Fung Liu, “Second-Order Fiber Bragg Gratings,” in OptoElectronics and Communications Conference, Hong Kong China, 2009, paper, WG6.
[55]O. Forslund and S. He, “Electromagnetic scattering from an inhomogeneous grating using a wave-splitting approach,” ProgressIn Electromagnetics Research, Vol. 19, pp. 147-171, 1998.
[56]P. St. J. Russell, “Bloch wave analysis of dispersion and pulse propagation in pure distributed feedback structures,” J. Mod. Opt. Vol. 38, pp. 1599-1619, 1993.
[57]R. Feced, M. N. Zervas, and M. A. Muriel, “An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings,” IEEE J. Quantum Electron., Vol. 35, pp. 1105-1115, 1999.
[58]R. Kashyap, R. Wyatt, and R. J. Campbell, “Wideband gain flattened erbium fibre amplifier using a photosensitive fibre blazed grating,” Electronics Letters, Vol.29, No. 2, pp. 154-156, January 21, 1993.
[59]R. L. Burden and J. D. Faires, Numerical Analysis, Brooks/Cole, Pacific Grove, CA, 2001.
[60]Ruyen Ro et al., “Design of two-track surface acoustic wave filters with width-controlled reflectors,” JJAP., vol. 43. pp. 688-694, 2004.
[61]T. Erdogan, ‘‘Fiber Grating Spectra,’’ J. Lightwave Technol, Vol. 15, pp 1277-1294, Aug. 1997.
[62]T. Erdogan, ’’Cladding-mode resonances in short- and long-period fiber grating filters,’’ J. Opt. Soc. Am A, Vol. 14, pp. 1760-1773, Aug. 1997.
[63]T. Erdogen and J. E. Sipe, “Tilted fiber phase gratings,” J. Opt. Soc. Am. A, Vol. 13, No. 2, pp. 296-313, 1996.
[64]Taha Masood, Steve Patterson, Nuditha V. Amarasinghe, Scott McWilliams, Duy Phan, Darren Lee, Zuhair A. Hilali, Xiong Zhang, Gary A. Evans, and Jerome K. Butler, “Single-frequency 1310-nm AlInGaAs-InP grating- outcoupled surface-emitting lasers,” IEEE Photon. Technol. Lett. Vol. 16, pp. 726-728, 2004.
[65]V. Singh, Y. Prajapati, and J. P. Saini, “Modal analysis and dispersion curves of a new unconventional Bragg waveguide using a very simple method,” Progress In Electromagnetics Research, Vol. 64, pp. 191-204, 2006.
[66]Vikram Bhatia, Mary K. Burford, Kent A. Murphy, Ashish M. Vengsarlar, “Long-period fiber grating sensors,” OFC’96, Technical Digest, Thp1, 1996.
[67]W. F. Liu, I. M. Liu, L. W. Chung, D. W. Huang, and C. C. Yang, “Acoustic-induced switching of the reflection wavelength in a fiber Bragg grating,” Opt. Lett., Vol. 25. pp. 1319-1321, Sep. 2000.
[68]W. Sha, X. L. Wu, Z. X. Huang, and M. S. Chen, “Waveguide simulation suing the high-order symplectic finite-difference time-domain scheme,” Progress In Electromagnetics Research B, Vol. 13, pp. 237-256, 2009.