二維光子晶體特性探討與光學元件之設計

Abstract

本論文提出二維光子晶體的等效折射係數（Effective refractive index）之旋轉不變性以及光在具有缺陷(Defects)中的散射現象之探討。光子晶體對於光由空氣入射，於某些特殊的等頻率面(equal-frequency surface)，其等效折射係數具有旋轉不變性。此外，由於光子晶體於某些頻段中，其光學性質可以由各方向均一的等效折射係數來表示，因此於這些頻段中，可以由等效介質來討論缺陷的散射問題，並進一歨可設計出具週期性缺陷的光子晶體，其特別處可將原本不具光子晶體能隙(Photonic band gap)處，產生新的光子晶體能隙。 應用光子晶體設計的光學元件，則包括設計異質結構光子晶體Y型分歧波導(Heterostructure photonic crystal Y-branch waveguide)，以及利用超導體光子晶體的溫度變化而設計的馬赫任德干涉儀（Mach-Zehnder interferometer）。設計的異質結構光子晶體Y型分歧波導，可以增加波導的寬度，以利與其他光學元件如光纖的耦合，並可達到高傳輸效率。超導體光子晶體對溫度的敏感特性，可有效地改變入射光方向。利用超導體的溫度變化，可以設計具有開-關性質的光學元件。

This thesis discusses the invariance of the effective refractive index of the two-dimensional photonic crystal under the rotation operator on the equifrequency surface and the scattering phenomena by defects. The effective refractive index can be defined when light is incident from the free space into the photonic crystal. We find out only two solutions of the equifrequency surface possess invariant effective refractive index when the equifrequency surface is rotated by a symmetry operation. Besides, the photonic crystal can be represented homogeneously by the effective refractive index within a certain frequency band, the scattering phenomenon scattered by defects can be discussed by the effective medium with effective defects. Finally, a periodic-defects photonic crystal is proposed. Some photonic-crystal optical devices are designed, including the photonic crystal heterostructure Y-branch waveguide and the temperature modulation photonic crystal Mach-Zehnder interferometer composed of copper oxide high-temperature superconductor. The photonic crystal heterostructure Y-branch waveguide has a large width of the waveguide, which is benefit to couple to other optical device, such as the fiber, and reaches a high-efficiency transmission. The sensitive characteristics of the superconductor photonic crystal can change the propagation direction of light efficiently. The on-off optical device can be designed by using the temperature variation of the superconductor.