寬帶隙二維光子晶體之合成

Abstract

光子晶體為一週期性排列之介質，在其介質常數對比很大的情況下，產生了某些電磁波無法在晶體中傳播的頻帶間隙。由於光子晶體具有如此特殊的性質，它在未來積體光路的應用方面有極大潛能。因此，如何合成具有大頻帶間隙的光子晶體結構是個重要的課題。 在本論文中，我們將分別利用牛頓迭代法及模擬退火法兩種方式來合成具有大頻帶間隙的光子晶體結構。基於平面波展開法，牛頓迭代法是一種逆向反求大頻帶間隙光子晶體結構的方法，但其合成之光子晶體的介質常數為連續分佈，甚難實際製作。不同於牛頓迭代法，模擬退火法可事先設定介質常數的數種可能數值，再以蒙地卡羅的方式來求得最佳解，故其合成之介質常數為離散分佈，較易於製作。在本論文中，我們進行數值模擬驗證此二法確實可以合成具有大頻帶間隙的光子晶體結構。

Photonic crystals are periodic structures that possess some photonic band gaps (PBG’s), i.e., ranges of frequencies where the electromagnetic wave is forbidden to propagate in the crystal. For a photonic crystal, the larger the PBG, the greater the bandwidth for preventing the optical wave from propagation. Most important applications of photonic crystals are based on this property. Therefore, how to enlarge PBG’s would be an important research topic. In this thesis, both Newton’s iteration method and simulated annealing (SA) approach are used to synthesize photonic crystals for large PBG’s. Based on the plane wave expansion method, Newton’s iteration method is an inversion approach to synthesize photonic crystals for large PBG’s. However, the synthesized dielectric constant is continuously distributed and is hard to realize. Unlike Newton’s iteration method, SA is a Monte Carlo approach for searching a global minimum. The synthesized dielectric constant can be in a discrete form which is easy to realize. In this thesis, numerical simulations are conducted to verify the feasibility of synthesizing photonic crystals for large PBG.