Fundamental study on photonic crystal optical waveguides

本文用数值方法分析了空气中圆形介质棒二维光子晶体在正方形阵列上构成的几种光波导的特性。求解方法是基于多维波数字滤波器原理的时域有限差分法（FD-TD）；该方法易于实现，且比传统的Yee算法精度更高。首先，我们研究了光子晶体光波导中本征模的传播，并利用普罗尼方法计算了本征模的传播常数。结果表明，该波导中的电场和磁场强度在光子晶体晶格常数周期内振荡。在此基础上，我们分析了基于共振隧道、定向耦合器和多路/解路复用的锐弯波导等基本光子晶体光波导器件，并对其传输和反射特性进行了评价。这些结果表明，光子晶体光波导是构建尺寸为波长数量级的高密度集成光电路的候选基本元件。

We have analyzed the characteristics of several kinds of optical waveguides constructed by two-dimensional photonic crystal of circular dielectric rods in air on a square array numerically. The method of solution is finite-difference time-domain (FD-TD) method based on the principles of multidimensional wave digital filters; this method can easily be implemented and is more accurate than the conventional one, the Yee algorithm.First, we have examined the eigen mode propagation in the photonic crystal optical waveguide and computed its propagation constant using the Prony's method. As a result we have shown that electric and magnetic field intensities in this waveguide oscillate in the period of lattice constant of photonic crystal. Next, we have checked the dispersion relation of this waveguide, and confirm the performance of a single mode propagation, Next, we have analyzed the elementary photonic crystal optical waveguide devices such as a sharp bent waveguide using resonant tunneling, directional coupler, and multiplexer/demultiplexer and evaluated transmission and reflection characteristics of those waveguides. From these results we can conclude that the photonic crystal optical waveguide is a candidate of basic elements for constructing high density integrated optical circuits whose size is on the order of the wavelength of light.