针对传统时域有限差分(FDTD)法的计算精度低、色散误差大的问题,将辛时域多分辨率(S-MRTD)算法引到光子晶体的数值模拟计算中。先将S-MRTD算法在时间和空间上分别引入辛传播子技术和小波尺度函数近似差分;再根据时间可逆约束条件和增长因子求解一组优化的辛算子,讨论传统FDTD法与S-MRTD算法的稳定性和数值色散性;最后基于S-MRTD算法对光子晶体的透射系数和反射系数等进行分析研究。通过数值计算和仿真结果验证了S-MRTD算法的可行性和精确性。S-MRTD算法的成功应用,为研究光子晶体的传输特性提供了高精确度和高效的全新数值计算方法。

In this study, the symplectic multi-resolution time-domain (S-MRTD) algorithm is introduced in numerical simulation calculations of photonic crystals to address the problems of low calculation accuracy and large dispersion error in the traditional finite-difference time-domain (FDTD) method. First, the symplectic sub-technology and approximate difference of wavelet scale function were introduced into the S-MRTD algorithm in time and space, respectively. Next, based on the time-reversible constraints and growth factors, a set of optimized symplectic operators was solved. Further, the stability and numerical dispersion of the traditional FDTD method and S-MRTD algorithm were discussed. Finally, based on the S-MRTD algorithm, the transmission and reflection coefficients of photonic crystals were analyzed. Numerical calculation and simulation results verify the feasibility and accuracy of the S-MRTD algorithm. The successful application of the S-MRTD algorithm facilitates a new numerical calculation technique with high accuracy and efficiency for elucidating the transmission characteristics of photonic crystals.