負折射率於二維光子晶體之有限差分時域分析

A FDTD Study on Negative Refraction in Two-Dimensional Photonic Crystals

施維周(Wei-Chou Shih)

指導教授 ： 楊照彥

國立臺灣大學/工學院/應用力學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.02025

摘要

光子晶體的研究在最近為相當熱門的一個領域，許多關於光子晶體的研究以及應用之文獻及實驗如雨後春筍般的被提出。
近年來，負折射現象開始被廣泛的討論，原因在於負折射現象顛覆了傳統觀念中的光學理論，如果能夠實現此現象，將可以產生出許多與過去認知中所完全不同的光學行為。依據文獻表示，負折射現象是利用左手介質來達成負折射率，使得光產生與在右手介質中相反的行進方向。然而有另外一派學者提出利用光子晶體內的物理機制來產生負折射效應，而不需要使用左手物質。
本論文的主題是研究二維光子晶體中的負折射效應。在文中將會重建並且探討近年來關於如何利用光子晶體來產生負折射效應以及完美透鏡現象(The Perfect Lens)，並且模擬在不同光子晶體的厚度、不同的波源條件下所產生的效應。
文中利用平面波展開法(PWE)求出光子晶體結構的能隙結構圖，並使用時域有限差分法(FDTD)來模擬電磁波於光子晶體中傳遞的情形，並且以不同的光子晶體介電質常數及不同的結構(正方晶格與三角晶格)以及不同的入射波源條件及不同模型來驗證二維光子晶體的負折射效應。

關鍵字

光子晶體 ； 負折射 ； 有限差分時域法 ； 完美透鏡

並列摘要

The researches about photonic crystals have been increased rapidly. A lot of the researches and articles about applications of photonic crystals have been presented.
In the recent years, the negative refraction effect had been discussed extensively. The reason is that the phenomenon of negative refraction subverts the conventional optical theories. If this effect can be realized, it will lead to many dramatic phenomena. According to the documents about this topic, the negative refraction is realized by the left-handed materials whose permittivity and permeability are all negative. And the light propagation will be totally different. However, there are another group of researches assert that the physical properties of photonic crystals can also obtain the results of negative refraction, and the left-handed materials are needless.
The main purpose of this thesis is to discuss the phenomenon of negative refraction inside the two-dimensional photonic crystals. In this article, we rebuild the models of photonic crystals to validate the negative refraction inside the photonic crystals and the effect of “The Perfect Lens.”
In this thesis, the plane wave expansion (PWE) method is used to obtain the band structure of the photonic crystals and we use the finite-difference time-domain method (FDTD) to simulate the propagation of electromagnetic wave in the photonic crystals. We construct some models with different incident waves, dielectric constants, and different structures (square lattice and triangular lattice) to validate the negative refraction in two-dimensional photonic crystals.

並列關鍵字

photonic crystal ； negative refraction ； FDTD method ； The Perfect Lens

參考文獻

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