Abstract

Homogeneous and inhomogeneous equations of electromagnetic wave propagation in a 2D periodic medium are considered. The equations are obtained within the framework of the method of the generalized scattering matrix. It is shown that these equations derived in the initial form are weakly localized and need taking into account the interaction of the periodic medium particles, which are distant at large distances. It is found that the main problem in constructing the algorithm of the numerical solution of the propagation equations is the determination of the discrete Fourier transform of the coupling matrix. This transform is equivalent to the summation of double slowly convergent series. The localizing transformation of the propagation equations is suggested. It is shown that the localized propagation equations take into account only the interaction of particles located in a limited spatial region. The algorithms of calculation of the parameters of the localizing transformation and the discrete Fourier transform of the coupling matrix are considered. It is shown that the application of the localizing transformation considerably improves the convergence of series for the coupling matrix. The results obtained with the help of the suggested method and known method of calculation of the double discrete Fourier transform are compared.

中文翻译：

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周期介质中电磁波传播方程的定位

摘要

考虑了二维周期介质中电磁波传播的齐次和非齐次方程。这些方程是在广义散射矩阵方法的框架内获得的。结果表明，这些以初始形式导出的方程是弱局部化的，需要考虑远距离的周期性介质粒子的相互作用。发现构建传播方程数值解算法的主要问题是耦合矩阵的离散傅立叶变换的确定。这种变换等价于双重缓慢收敛级数的求和。建议对传播方程进行局部化变换。结果表明，局部传播方程只考虑了位于有限空间区域内的粒子的相互作用。考虑了耦合矩阵的定位变换和离散傅立叶变换参数的计算算法。结果表明，局部化变换的应用大大提高了耦合矩阵级数的收敛性。将在建议的方法和已知的双离散傅立叶变换计算方法的帮助下获得的结果进行比较。结果表明，局部化变换的应用大大提高了耦合矩阵级数的收敛性。将在建议的方法和已知的双离散傅立叶变换计算方法的帮助下获得的结果进行比较。结果表明，局部化变换的应用大大提高了耦合矩阵级数的收敛性。将在建议的方法和已知的双离散傅立叶变换计算方法的帮助下获得的结果进行比较。