光子晶體雷射耦合波理論之研究

Abstract

本篇論文主旨在利用耦合波理論探討在四方晶格以及三角晶格結構下造成光子晶體雷射於橫向電場極化之分析。用來描述二維光學耦合的四方晶格模型是由八個布拉格衍射的耦合平面波組合而成的；而用來描述二維光學耦合的三角晶格模型是由六個布拉格衍射的耦合平面波組合而成的。根據光子晶體的布拉格理論，光子晶體必須滿足特定的布拉格繞射條件才能產生雷射。由於面射型光子晶體的特性，我們特別著重於在Γ點能帶的研究。共振頻率偏差和閾值增益的振盪模式在週期性圓孔晶格的情況下已經被探討。這些諧振模式的空間強度分佈也被計算。我們探討了耦合強度對於閾值增益和頻率偏差的影響。最後，我們考慮正方晶格和三角晶格面射型光子晶體雷射的輻射損失。這論文有助於我們了解正方晶格和三角晶格面射型光子晶體雷射的特性。

In this thesis, we investigated the coupled wave analysis for square lattice and triangular lattice of photonic crystal (PC) lasers with transverse electric polarization. A model for square lattice consisting of eight plane waves coupled by Bragg diffraction is used to describe two-dimensional optical coupling. A model for triangular lattice consisting of six plane waves coupled by Bragg diffraction is used to describe two-dimensional optical coupling. Based on the Bragg diffraction theory for PCs period structure, the lasing behavior could only be happened when the Bragg condition is satisfied. Our studies are especially focused on the band edge at Γ point because of the characteristic of surface emitting condition. The resonant frequency deviation and threshold gain for the modes of oscillation have been determined for the case of index periodicity with a lattice of circular holes. The spatial intensity distributions of these resonant modes have also been calculated. We have investigated that the influence of coupling strength is to the threshold gain and frequency deviation. Finally, we consider the radiation loss for square lattice and triangular lattice of PCSELs. This thesis helped us to understand the characteristics of PCSELs for square lattice and triangular lattice.