繞射光柵中波導模態共振特性

Guided-Mode Resonances in Diffraction Gratings

蔡文崎(Wen-Chi Tsai)

指導教授 ： 薛文証

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.10566

摘要

本論文主要目的在於研究繞射光柵中波導模態共振現象。本文首先簡單介紹光柵的歷史及背景，接著由於本文所分析的結構為光柵波導結構，其原理是利用光柵耦合的效果將入射光耦合至波導中，並且當耦合波符合波導模態時即會產生波導模態共振，因此本文利用均勻波導理論來預測出波導模態共振的位置。
探討光柵的繞射特性我們使用嚴格耦合波分析法，分別推導TE及TM兩種極化下的耦合波方程，並且透過數值求解耦合波方程。我們可以藉由改變結構參數了解該結構參數對繞射特性之影響，包含改變波導厚度、光柵之調變強度與填充因子會影響共振位置及頻寬，此外還包含光柵週期、入射角度以及各區域折射率等等也會對光柵繞射產生影響。本文利用嚴格耦合波分析法對光柵繞射特性進行分析之結果相信對於在設計光學元件時有非常大的幫助。

關鍵字

光柵 ； 繞射效率 ； 波導模態共振 ； 嚴謹耦合波分析法

並列摘要

The main purpose of this thesis is to investigate the phenomena of guided-mode resonance in diffraction gratings. At first, the principle and history of optical grating is introduced briefly. The structure analyzed in this study is the waveguide grating structure. The basic physics is to couple incident light into waveguide with the effect of grating coupling. When the coupled-wave match the guided mode, guided-mode resonance occurs. Therefore, in this study the uniform waveguide theory is selected to predict the existence of the guided-mode resonance.
The properties of diffraction from grating are discussed with rigorous coupled -wave analysis (RCWA). The coupled wavefunction under TE and TM mode polarization is derived by RCWA respectively and solved by numerical methods. The influence of structure parameters on the properties of diffraction can be studied by changing the structure parameters. For instance, changing the thickness of waveguide, intensity modulation of grating and filling factor will affect the position of resonance and bandwidth. Moreover, the period of grating, incident angle and the refraction index of different region also influence the diffraction of grating. Such analysis on the properties of diffraction from gratings with RCWA in this study is useful for the design of optical devices.

並列關鍵字

grating ； diffraction efficiency ； guided-mode resonance ； RCWA

參考文獻

[1] D. C. Flanders, H. Kogelnik, R. V. Schmidt and C. V. Shank, “Grating filters for

thin film optical waveguides,” Appl. Phys. Lett. 24, 194-196 (1974).

[2] E. Hecht, Optics, 4th Edition, Addison Wesley Longman, Inc., New York, (2002).

[3] S. S. Wang, R. Magnusson, J. S. Bagby and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470-1475 (1990).

[4] C. Palmer, Diffraction Grating Handbook, 5th Edition, Thermo RGL, New York, (2002).