Subcell dispersive finite-difference time-domain schemes for infinite graphene-based structures

A systematic three-dimensional (3D) frequency-dependent finite-difference time-domain technique for the consistent and rigorous analysis of infinite graphene layers is developed in this study. The generalised formulation divides the overall geometry into unit cells and applies the appropriate Floquet periodic boundary conditions to their lateral surfaces. In this framework, the infinite graphene sheet is carefully manipulated by means of an efficient subcell discretisation concept along with a complex surface conductivity representation defined by quantum mechanical equations. This conductivity model is, subsequently, converted to its volume counterpart to allow realistic time-domain investigations, while the dispersive nature of graphene is described via an auxiliary differential equation algorithm. Furthermore, a set of linearly polarised normally incident wideband pulses or obliquely incident monochromatic waves excite the computational domain based on a properly modified total-field/scattered-field scheme. Numerical simulations, involving an assortment of multilayer arrangements, reveal the promising accuracy and stability of the proposed method through detailed comparisons with data from analytical closed-form expressions.