應用光柵繞射於濾波器之設計

Applications of Grating Diffraction on Design of Optical Filters

林子敬(Zih-Jing Lin)

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(2012年)

https://doi.org/10.6342/NTU.2012.10855

摘要

本論文主要目的在於探討光柵之繞射特性如何應用於濾波器上。首先討論光柵的繞射狀況，並利用嚴格耦合波分析法來分析。接著藉由光柵的次波長結構特性，利用等效介質理論將光柵等效成均勻之波導結構。在波導模型的假設下，對結構作模態分析，並找出波導特徵方程式以預測導波模態共振之位置。
　　對於兩種不同狀況的光柵結構，進行結構參數的變化來討論其濾波特性。透過數值分析可以發現，光柵的結構對稱性與否，將會影響導波模態共振的簡併態效果。從改變結構參數的結果顯示，當光柵厚度提高時，內部所能容納的通道數也會變多。而且藉由調整光柵的調變強度以及填充因子，也能對於濾波之半峰全寬作控制。本文成功利用嚴格耦合波分析法對光柵內的繞射情況做分析，並找出電磁場之場形圖做探討，對於光柵應用於濾波器元件的設計具有相當大的助益。

關鍵字

光柵 ； 繞射效率 ； 等效介質理論 ； 導波模態共振 ； 濾波器

並列摘要

The main purpose of this thesis is to represent the characteristics of diffraction efficiency of grating in filters. The diffraction efficiency of the gratings is investigated by using rigorous coupled wave analysis. With the sub-wavelength scale of the structure, the grating can be treated as a homogeneous waveguide layer. In this model, the modes and the eigen-equations of the waveguide layer will be found to predict the locations of the guided mode resonance.
　　With two different types of gratings, the characteristics of the grating filters can be found by changing the parameters of the structure. According to the results of numerical calculations, the symmetry of the structures will affect the degeneracy of the guided mode resonance. When the grating depth is increasing, the number of channels of grating will increase too. The full width half maximum of resonant wavelength also can be controlled by tuning the modulation and filling factors. The EM fields in grating filter is successfully analyzed by using rigorous coupled wave analysis which have a great benefit for the design of the filter components with grating.

並列關鍵字

grating ； diffraction efficiency ； effective media theory ； guided mode resonance ； filters

參考文獻

[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,

[6] Lord Rayleigh, “On the Dynamical Theory of Gratings,” Proc. Roy. Soc. (London)

[7] A. Hessel and A. A. Oliner, “A new theory of Wood’s anomalies on optical