Method of Lines Framework for Analysis of Arbitrary-shaped Spatial Periodic Structures: A Generalized Formalism

Method of lines (MoL) is numerically described for analysis of spatial periodic structures based on discrete finite difference hybridization of each transverse plane of multilayer structure. The results show rigorous simulation of the three-dimensional (3D) arbitrary-shaped space grating with the best convergence and high stability for highly conductive metallic layers. We propose our method to be considered for analysis of stacked rotated grating (SRG). Also, we propose time-varying MOL using implementation of the multi-frequency finite difference frequency domain (FDFD) method upon our presented method, so that one can simulate spatiotemporal structures in the hybridization framework faster and much more accurately.