摘要
本論文使用數值方法分析光波模態在各種光纖光柵中的耦合現象。理論分析係基於模態耦合理論，吾人採矩陣法以解決多模態耦合之問題，這包括: 均勻短週期光柵、均勻長週期光柵、非均勻且參數快速變化的長週期光柵。利用串接矩陣的方法能有效計算非均勻光柵的特性。藉特殊設計的數值法則，吾人亦探討一混合短週期與長週期之光柵的耦合理論，此種結構能藉調整長週期光柵折射指數之變化量以控制不同波長的光波反射量。易言之，此種混合光柵能調變Bragg 波長與其他波長間的光波反射量。吾人亦對模態耦合的物理意義加以解釋。

Abstract
Mode coupling in various optical fiber gratings is numerically investigated in this thesis. The analysis is based on the coupled-mode theory. For easy programming, we use the matrix method to solve the problems of multimode couplings in uniform short- period gratings, uniform long-period gratings, and nonuniform long-period gratings with fast-varying parameters. The cascade of matrices can be utilized to calculate the characteristics of nonuniform gratings. In this thesis, we also investigate the problem of the mixed short- and long-period grating by using a specially designed numerical algorithm. It is found that the reflectivity at different wavelengths can be controlled by adjusting the index change in the core region of the long-period grating. In other words, we can directly modulate the reflectivity between the Bragg wavelength and some other wavelengths. The physical meaning of this kind of mode coupling is also explained.

Contents
Chapter 1 Introduction-------------------------------1
Chapter 2 Theoretical formulations-------------------4
2.1 Fiber modes------------------------------------4
2.2 Coupled-mode theory----------------------------9
2.2.1 Uniform short-period gratings---------------14
2.2.2 Uniform long-period gratings----------------17
2.2.3 Long-period gratings with fast-varying parameters
--------------------------------------------------19
2.2.4 Mixed short- and long-period fiber gratings-20
Chapter 3 Numerical algorithms----------------------25
3.1 Uniform short-period gratings-----------------25
3.2 Uniform long-period gratings------------------30
3.3 Long-period gratings with fast-varying parameters
--------------------------------------------------33
3.4 Mixed short- and long-period fiber gratings---36
Chapter 4 Numerical results-------------------------41
4.1 Fiber modes-----------------------------------41
4.2 Short-period fiber gratings-------------------43
4.3 Long-period fiber gratings--------------------44
4.3 Mixed short- and long-period fiber gratings---46
Chapter 5 Conclusions-------------------------------61
Appendix--------------------------------------------64
References------------------------------------------69

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