Modified Floquet Boundary Condition for Open Boundary Problems with N-Path Symmetry

Space-time modulated structures have attracted substantial attention in the meta-materials community in recent years. Most physical realizations of space-time modulated systems consist of discrete unit cells that can be independently modulated. While these physical structures are often analyzed as continuously modulated media, consideration of the spatial discretization yields a more accurate model. Additionally, a finite unit cell size enables phenomena which do not arise in the continuum limit. In this paper, a relation between the fields in each unit cell (pixel) of a free-space N-path system is derived. The relation is incorporated into a method of moments solver to compute the scattered field from a space-time modulated metasurface.