本研究計畫的目標是在理論上探討電磁波在光子晶體中的種種傳播特性，特別是關於光子晶體負折射與異常折射（例如「超稜鏡效應」 Superprism effect）的物理機制。以期有效利用這些特性去設計未來可使用於奈米結構的特殊元件。我們的研究重點將包括： 1. 比較均勻（Homogeneous）均向性（Isotropic）左手介質、均勻非均向性左手介質、光子晶體於負折射工作區的等效介質（根據計算出的Band structure dispersion relation 而建立），以及光子晶體本身在空氣---介質界面的反射與穿透特性，以找出那些左手介質的特性是光子晶介質所無法模擬的，又有那些光子晶體在負折射工作區的特性是左手介質無法模擬的，而其原因為何。預期除吸收性造成的差異外，部分帶隙效應（Partial gap effect）與顆粒性（Granularity）將是此兩種介質的最主要差異。 2. 研究如何改進幾何光學方法以對光子晶體介質的透射與反射特性做更完善的描述。研究光子於光子晶體中的「等效質量」（Effective mass）對電磁波傳播特性與色散特性的影響，以及如何將這些影響反映在幾何光學式的描述中。 3. 利用以上研究所獲得的知識與經驗設計可用於奈米至微米尺度的新式光學元件，以及適用於一般日常生活尺度的微波元件。 The aim of this project is to study theoretically the electromagnetic propagation properties in a photonic crystal medium in its negative-refraction or anomalous-refraction working frequency range. We expect that a complete understanding of these properties would help us to design useful new nano-scale photonic devices. We will focus our attention on the following items. 1. The comparison of propagation properties, especially the refraction and reflection properties, between photonic crystals, the effective media constructed from the photonic band structure (i.e. the dispersion relation) of photonic crystal, and the left-handed material media. We will try to find which characteristics can appear in one of these media but cannot appear in the other two, and why. We expect that the absorption effect, the partial band gap effect, and the granularity are the main causes of their different propagation properties. 2. We will try to construct a geometric-optics type theory for the effective media of the photonic crystals to have a better description of them. In this theory we will take into account the effective mass of photon to get a simple enough but qualitatively correct understanding of the propagation (refraction and reflection) properties in these media. 3. We will try to use the knowledge gained from the simulations to design useful nano-optics devices. Since Maxwell』s equations are linear, most of these devices can also be constructed in different scales. For example, some of them might be useful as microwave devices. 研究期間：9408 ~ 9507
