二维光子晶体传输特性的时域精细积分法

PRECISE INTEGRATION TIME DOMAIN METHOD FOR THE TRANSMISSION PROPERTIES OF TWO-DIMENSIONAL PHOTONIC CRYSTALS

本文研究了二维光子晶体的时域精细积分法,并对其精度、效率、以及稳定性进行分析.从麦克斯韦方程的微分形式出发,利用Yee元胞将空间微分算子近似为差分算子,结合边界条件及激励源的表达式得到一组关于时间的常微分方程.对时间进行精细划分,使用精细积分算法求解常微分方程组.结合通解与激励源的特解得到光子晶体两端的反射场及透射场分布,进而通过傅里叶变换求得二维光子晶体的传输特性.数值算例表明,本文方法具有准确、稳定、高效的特点.

A precise integration time domain method was proposed to study the transmission properties of two-dimensional photonic crystals, and its accuracy, efficiency and stability were also analyzed. The Yee′s difference technique was employed to discrete the first order Maxwell equations in the spatial domain. Considering the boundary conditions and the expression of the excitation, the equations were transformed into a set of ordinary differential equations. Then the time step was precisely divided, and the ordinary differential equations were solved by using the high precision integration. The reflection and transmission field distributions of the photonic crystal were obtained by combining the general solution with the particular solution resulting from the excitation. Finally, the transmission properties of the photonic crystal were obtained by Fourier transformation. Practical calculations of the two-dimensional photonic crystals were carried out. The results show that the precise integration time domain method is more accurate, stable and efficient than the finite difference time domain method.