二維光子晶體負折射現象研究

Abstract

利用平面波展開法，我們系統地建立了一個等頻率面結構的模型來研究電磁波於二維光子晶體中之折射行為；而利用時域有限差分演算法，我們分別驗證了光子晶體稜鏡中的正折射、負折射、全內反射、及非偶合效應現象。我們也運用斯涅爾定律推算其量測之折射角並且在無窮和有限週期個案之間得到相當好的一致性。此外，更進一步實現一個具有等效負折射率的光子晶體厚板中藉由其平面聚焦電磁波的模擬，同時亦推論其負折射之成像機制並與傳統透鏡成像作一比較。 另外我們針對發表於Phys. Rev. B 65, 201104(2002)，「不具等效負折射率的光子晶體厚板中的全角度負折射」的理論提出批評並且給予一個全新的定義–準直穿透效應：電磁波垂直向前穿透光子晶體厚板，並且場被高度限制在厚板中央的一條類似通道的路徑上。

We have systematically established a model of equal frequency surface configuration to examine the refractive behaviors of the electromagnetic wave propagating through a two-dimensional photonic crystal by using the plane-wave expansion method. Positive refraction, negative refraction, total internal reflection, and uncoupling effect in photonic crystal prisms have been numerically demonstrated by utilizing the finite-difference time-domain method. Applying the Snell’s law, we got a well consistence of measuring refractive angles between the infinite case and the finite case. Besides, we have also performed that the flat surface can focus light by virtue of the negatively effective refraction index in a photonic crystal slab and deduced the imaging mechanism of photonic crystal slabs with negative refraction, which is different from the conventional lenses. In addition, we commented on the recent published paper “all-angle negative refraction in photonic crystals without negatively effective refraction index”, published in Phys. Rev. B 65, 201104(2002), and gave a new definition by using the “direct-tunneling effect” what the light is strongly confined in a channel-like around the center of slab and directly tunnels across the slab.