Sharif Digital Repository

The Fourier modal method is one of the most important methods in the analysis of flat periodic structures (gratings). Using this method, the problem of wave propagation in the periodic medium leads to an eigenproblem, in which eigenvalues represent the propagation constants and eigenvector or eigenfunctions determine the filed distribution of the modes. On the other side, considering all the generalizations and modifications reported so far, the Fourier modal method still faces two fundamental problems. First, for problems involving large dielectric constants or high contrasts, the matrix form of the eigenproblem (the modal matrix) can be large, dense, and require a high computational cost.... 

Over the past few years, time-periodic and space-time-periodic media have garnered a considerable amount of attention, thanks to their exotic and unique interactions with electromagnetic phenomena. These media do not generally comport with Lorentz's reciprocity theorem, thus can be utilized in order to implement non-reciprocal amplification and frequency transformation. One class of such media, that have been the subject of less discussion and interest, are space-time periodic diffraction gratings.In this thesis, we aim to develop a series of semi-analytical methods in order to analyze such structures. Our focus will be on a subset of methods which make use of the modal expansion of fields...