以時域有限差分法分析光子晶體波導之光學特性

Abstract

在本研究中，我們模擬二維光子晶體的模型並且分析了它的波導與光學特性。首先，我們採用平面波展開法計算二維正方晶格的能帶結構，並且探討其晶格參數對於能隙的影響。其次，我們採用時域有限差分法（finite-difference time-domain, FDTD）來動態分析光子晶體在電磁波傳播下的光學特性與過程。在我們的模擬中，我們分別改變了光子晶體波導的物理參數，例如：波長、光子晶體層數和介電圓柱尺寸。此外，我們探討二維光子晶體中的線缺陷對於直線或彎曲波導的特性與應用，並定量分析電磁波傳播時的穿透率頻譜。

In this research, we simulate a two-dimensional photonic crystal model and analyze its waveguide properties. Firstly, we employ the plane-wave expansion method to calculate the band structure of a 2D square lattice and investigate how the lattice parameters affect the energy gap. Secondly, We employ the finite-difference time-domain (FDTD) simulation technique to analyze the optical characteristics of the photonic crystal waveguides. In our simulation, we vary the physical parameters of the photonic crystal waveguides such as wavelength, the number of layers in the photonic crystal, and the size of the dielectric cylinders. Furthermore, we explore the properties and application of straight or curved waveguides with line defects in a two-dimensional photonic crystal and analyze the energy variation of electromagnetic wave propagation.