一維線性與非線性光波導陣列中的光束傳播特性

Abstract

在這篇論文中，我們提出一個將離散薛丁格方程式寫成矩陣的形式，利用轉移矩陣法分析能量在光波導陣列中基本光學特性、傳遞特性、色散關係式、電場分佈以及光的行進走向。在本文裡所分析的光波導陣列結構分為兩種:第一種為兩相異均質光波導陣列之間的邊界特性，另一種為一無限均質光波導陣列結構裡內嵌入有限結構的線性光波導陣列以及折射率會隨電場改變的非線性光波導陣列。前者是以離散斯涅爾定律為理論基礎，模擬其斜向入射(無繞射情形下的角度)時的場形，後者則著重於研究內嵌入的波導根數多寡對能量傳遞所造成的影響，並以解析解印證之，最後我們在非線性波導陣列中加入一非對稱因子，引入非互易系統，讓非線性波導陣列結構可應用在聲、光整流器。

The main purpose of this study is to propose a discrete Schrodinger equation which is expressed in the form of a matrix in order to analyze the properties of electric field coupling and other fundamental optical properties in the optical waveguide arrays, such as the light propagation, the dispersion relation, and the electric field distribution. In this thesis, we discuss two kinds of situations in the waveguide arrays: The first one is bound state at the edge of two homogeneous waveguide arrays, and the second one is the finite linear or nonlinear optical waveguide arrays embedded in an infinite arrays structure. Based on the theory of discrete Snell's law, the former study simulate the light propagation is and simulate the light propagation. The later focuses on the influence of the energy transport, which is caused by the increasing number of waveguides in the infinite arrays. Furthermore, we add the asymmetry factor in a nonlinear waveguide array, which introduces the non-reciprocal property, and it allows nonlinear waveguide arrays structure to be applied to sound and light rectifiers.