近年來元件的設計與製造成本皆變得越來越複雜，透過使用數值方法與分析設計線性與非線性光學元件將可以降低大量成本浪費。本文採用基因演算法實現線性與非線性光學元件之最佳化設計，透過基因演算法對所求逆向設計問題的最佳解搜尋能力，我們希望達到全面性最佳化的光學元件設計。對於線性光學元件設計，我們利用Layer-Peeling Algorithm驗證單一與多通道矩形布拉格光柵濾波器(Rectangle FBG Filter)。其中，多通道布拉格光柵是在折射率上使用Sinc取樣函數產生並以基因演算法優化每個通道中的相位值達到多通道最佳化設計。而對於非線性晶體的準相位匹配(Quasi-Phase-Matching, QPM)元件，我們使用基因演算法分析並考慮實際製程限制條件，設計一具有雙穿透波長的準相位匹配元件。

Recently, the design and fabrication of optical devices become more and more complex. Through numerical simulation and analysis for linear and nonlinear optical devices, we can reduce the fabrication cost dramatically. In this work we use genetic algorithm (GA) realize the optimization for linear and nonlinear optical devices. With the ability for finding a global optimal solution by the GA method, we hope to solve the problems of inverse design in optical devices optimization. For the linear optical devices, we use Layer-Peeling algorithm both for designing single and multi-channels optical fiber Bragg gratings with rectangle reflection filters. Especially for multi-channel fiber Bragg gratings, first we use a Sinc function as the sampling functions in the index modulation profiles. Then GA method is used to optimize the relative phases in each channels. And for the nonlinear optical devices, we use GA method to synthesize quantum-phase-matching (QPM) devices with the considerations of constrained conditions in practical fabrications. A QPM device with two Gaussian profiles in the transmission spectrum is demonstrated.

[1] Andrew Chipperfield, Peter Fleming, Hartmut Pohlheim, and Carlos Fonseca, Genetic Algorithm Toolbox for Use with MATLAB®, Version 1.2. User’s Guide, 1994
[2] Randy L.Haupt and Sue Ellen Haupt, Practical Genetic Algorithms, 2nd edition, WILEY, 2004
[3] Johannes Skaar and Knut Magne Risvik, “A Genetic Algorithm for the Inverse Problem in Synthesis of Fiber Gratings,” IEEE Journal of Lightwave Technology, Vol. 16, pp. 1928-1932, 1998
[4] G. Cormier, R. Boudreau, and S. Theriault, “Real-Coded Genetic Algorithm for Bragg Grating Parameter Synthesis,” Journal of the Optical Society of America B, Vol. 18, pp. 1771–1776, 2001
[5] Cheng-Ling Lee and Yinchieh Lai, “Evolutionary Programming Synthesis of Optimal Long-Period Fiber Grating Filters for EDFA Gain Flattening,” IEEE Photonics Technology Letters, Vol. 14, pp.1557–1559, 2002
[6] Cheng-Ling Lee and Yinchieh Lai, “Optimal Narrowband Dispersion Less Fiber Bragg Grating Filters with Short Grating Length and Smooth Dispersion Profile,” Journal of Optical Communications, Vol. 235, pp.99–106, 2004
[7] Cheng-Ling Lee and Yinchieh Lai, “Long-Period Fiber Grating Filter Synthesis Using Evolutionary Programming,” Fiber Int. Opt., Vol. 23, pp. 249–261, 2004
[8] Steven Manos and Leon Poladian, “Multi-Objective and Constrained Design of Fiber Bragg Gratings Using Evolutionary Algorithms,” Optics Express, Vol. 13, pp. 7350-7364, 2005
[9] John H. Holland, Adaption in Natural and Artificial Systems, The M.I.T. Press, Cambridge, 1992
[10] Eva Peral, JosC Capmany, and Javier Marti, ”Iterative Solution of the
Gel'Fand-Levitan-Marchenko Coupled Equations and Application to Synthesis
of Fiber Gratings,” IEEE Journal of Quantum Electronics, Vol. 32, pp. 2078-2084, 1996
[11] Ricardo Feced, Michalis N. Zervas, and Miguel A. Muriel, “An Efficient
Inverse Scattering Algorithm for the Design of Nonuniform Fiber Bragg
Gratings,” IEEE Journal of Quantum Electronics, Vol. 35, pp. 1105-1115,
1999
[12] Gabriel Cormier, Roger Boudreau and Sylvain The´riault, “Real-Coded
Genetic Algorithm for Bragg Grating Parameter Synthesis,” Journal of the Optical Society of America B, Vol. 18, 2001
[13] Turan Erdogan, “Fiber Grating Spectra,” IEEE Journal of Lightwave
Technology, Vol. 15, pp. 1277-1294, 1997
[14] Amnon Yariv, “Coupled-Mode Theory for Guided-Wave Optics,” IEEE
Journal of Quantum Electronics, Vol. 9, pp.919-933, 1973
[15]H. A. Haus, W. P. Huang, S. Kawakami, AND N. A. Whitaker, “Coupled-Mode Theory of Optical Waveguides,” IEEE Journal of Lightwave Technology, Vol. 5, pp.16-23, 1987
[16] H. Kogelnik, “Theory of Optical Waveguides,” Guided-Wave Optoelectronics, Springer Series in Electronics and Photonics 26, pp.7-88, 1990
[17] Johannes Skaar, Ligang Wang, and Turan Erdogen, “On the Synthesis of Fiber Bragg Gratings by Layer Peeling,” IEEE Journal of Quantum Electronics, Vol. 37, pp. 165-173, 2001
[18] Hongpu Li and Yunlong Sheng, “Direct Design of Multichannel Fiber Bragg Grating With Discrete Layer-Peeling Algorithm,” IEEE Photonics Technology Letters, Vol. 15, pp. 1252-1254, 2003
[19] Morten Ibsen, Michael K. Durkin, Martin J. Cole, and Richard I. Laming, ”Sinc-Sampled Fiber Bragg Gratings for Identical Multiple Wavelength Operation,” IEEE Photonics Technology Letters, Vol. 10, pp.842-844,1998
[20] Alexander V. Buryak, Kazimir Y. Kolossovski, and Dmitrii Yu. Stepanov, ”Optimization of Refractive Index Sampling for Multichannel Fiber Bragg Gratings,” IEEE Journal of Quantum Electronics, Vol. 39, pp.91-98, 2003
[21] Hongpu Li, Yunlong Sheng, Yao Li, and Joshua E. Rothenberg, “Phased-Only Sampled Fiber Bragg Gratings for High-Channel-Count Chromatic Dispersion Compensation,” IEEE Journal of Lightwave
Technology, Vol. 21, pp. 2074-2083, 2003
[22] A. V. Buryak and D.Y. Stepanov, “Novel multi-channel grating devices,” in Proc. Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, Optical Society of America, Vol. 60, 2001
[23] H. Ishii, H. Tanobe, F. Kano, Y. Tohmori, Y. Kondo, and Y. Yoshikuni, “Quasicontinuous Wavelength Tuning in Super-Structure-Grating (SSG) DBR Lasers,” IEEE Journal of Quantum Electronics, Vol. 32, pp. 433–441, 1996
[24] D. T. Reid, “Engineered Quasi-Phase-Matching for Second-Harmonic Generation,” Journal of Optics A: Pure Applied Optics, Vol. 5, pp. 97–102, 2003
[25] Amnon Yariv, Quantum Electronics, 3rd edition, Wiley, 1989
[26] Dieter H. Jundt, “Temperature-Dependent Sellmeier Equation for The Index of Refraction, in Congruent Lithium Niobate,” Optics Letters, Vol. 22, pp. 1553-1555, 1997
[27] G. J. Edwards and M. Lawrence, “A Temperature-Dependent Dispersion for Congruently Grown Lithium Niobate,” Optical and Quantum Electronics, Vol. 16, pp. 373-374, 1984
[28] D. F. Nelson and R. M. Mikulyak, “Refractive Indices of Congruently Melting Lithium Niobate,” Journal of Applied Physics, Vol. 45, pp. 3688-3689, 1974
[29] R. S. Weis and T. K. Gaylord, “Lithium Niobate: Summary of Physical and Crystal Structure,” Applied Physics A, Vol. 37, pp. 191- 203, 1985