Transient Analysis of Dispersive, Periodic Structures for Oblique Plane Wave Incidence Using Laguerre Marching-on-in-Degree (MoD)

Transient analysis of dispersive, periodic structures in the case of obliquely incident plane wave is presented in this work. The Laguerre marching-on-in-degree (MoD) is used for the development of an unconditionally stable algorithm. Due to the unconditional stability, Courant-Freidrich-Levy (CFL) temporal discretization limit can be circumvented resulting in less simulation time compared to the conventional dispersive finite difference time domain (FDTD). This is particularly advantageous for multiscale, dispersive structures. The uniaxial perfectly matched layer (UPML) is implemented in the Laguerre domain. By virtue of the Laguerre decomposition, the presented method can simulate general dispersive media compared to conventional dispersive FDTD which can simulate only standard dispersion models such as Debye, Lorentz and Drude. The formulations are validated by estimating the transmission spectra of an infinite double pole Debye slab and comparing the results with analytical results. Further confirmation is obtained by estimating the transmission spectra of zeroth order Floquet mode of a 1D periodic array of dispersive, square cylinders and comparing the results with periodic method of moments solution.