Computational wavefunction dynamics in photonic graphene with symmetry breaking

This paper is devoted to the derivation and analysis of a simple pseudospectral computational method for a two-dimensional time-dependent Schrödinger equations with periodic coefficients, modeling electromagnetic waves propagating in photonic graphene with symmetry breaking. In particular, we are interested in the propagation of edge states along a wall, modeling a defect/heterogeneity in the optical set-up. Perfectly matched layers are here combined with the derived pseudospectral method in order to absorb wavefunctions in the direction orthogonal to the wall. We numerically and analytically exhibit the possible trapping of wavefunctions.