Fourier modal expansion techniques are very well suited for electromagnetic (EM) scattering in planar periodic stratified media. These techniques expand the transverse EM fields in Bloch modes in each strata unit-cell, but do not rigorously enforce EM boundary conditions at interior material interfaces which gives rise to slow convergence of the polarized S-matrix values with increasing Fourier series truncation order. We present a normal vector (NV) Fourier modal scattering approach that uses the gradient of the real permittivity in the unit-cell to generate a local NV resulting in anisotropic eigenmodes of Maxwell's equations that satisfy interior boundary conditions. The convergence of this expansion method is examine numerically for our analytic NV derived from planar primitive geometry elements for various example structures. The Fourier modal NV method is then derived for the planar cavity boundary value problem and the cavity eigenmodes and density of states is determined from the analytic continuation of the secular determinant. A complete scattering method for highly dispersive materials and sub-wavelength structures has been presented that is adaptable to planar EM cavity problems using fluctuation electrodynamics formalism.

傅立叶模态扩展技术非常适合于平面周期性分层介质中的电磁（EM）散射。这些技术在每个地层单位晶胞中以Bloch模式扩展了横向EM场，但并未在内部材料界面上严格执行EM边界条件，这会导致傅立叶级数截断顺序的增加使极化S矩阵值缓慢收敛。我们提出了一种法向矢量（NV）傅里叶模态散射方法，该方法使用晶胞中实际介电常数的梯度来生成局部NV，从而产生满足内部边界条件的Maxwell方程的各向异性本征模。对于从各种示例结构的平面原始几何元素派生的我们的分析NV，将对该扩展方法的收敛性进行数值检验。然后针对平面腔边界值问题推导傅里叶模态NV方法，并根据世俗行列式的解析连续性确定腔本征模和状态密度。提出了一种适用于高色散材料和亚波长结构的完整散射方法，该方法适用于使用波动电动力学形式主义的平面EM腔问题。