二维光子晶体的龙格库塔多分辨分析

Improved Multi-resolution Time Method in Two-dimension Photonic Crystal

二维光子晶体带隙特性分析过程中,由于传统时域多分辨率算法的时间微分离散阶数较低,所以易导致色散误差积累而使晶体结构内传播波形产生时域形变,大大降低了特性分析的准确性。针对这一现象,提出了可变精度龙格库塔多分辨率算法,算法通过高阶的时间迭代来减少晶体结构中数值波的传播变形,使频率特性分析不再受时间微分引起的波前失真的影响,并在时域和空域上同时具有任意高阶的收敛特性,以得到稳定而准确的带隙特性分析结果。通过具体算例的数值仿真,验证了改进策略在分析光子晶体传输特性时的有效性和可靠性。

In the characteristic analysis of two-dimensional photonic crystals, traditional multi-resolution timedomain method will lose its accuracy greatly and lead to a deformation of incident wave because of time domain error accumulation, which is caused by low-order approximate of time differential. With regard to this problem, the variable precision Runge-Kutta method is introduced in traditional multi-resolution time-domain method. The new algorithm reduces the numerical wave deformation in the crystal structure through high-order time iteration and frequency properties are no longer bounded by the error of time differential approximate. The stable and accurate bandgap characteristics and integrated time-domain numerical waveform in the crystal structure could be got. Through the examples of numerical simulation, the validity and reliability of improved strategy in two-dimensional photonic analysis is verified.