Solving a spectral problem for large-area photonic crystal surface-emitting lasers

Abstract

We present algorithms for constructing and resolving spectral problems for novel photonic crystal surface-emitting lasers with large emission areas, given by first-order PDEs with two spatial dimensions. These algorithms include methods to overcome computer-arithmetic-related challenges when dealing with huge and small numbers. We show that the finite difference schemes, constructed using relatively coarse numerical meshes enable accurate estimation of several major, optical modes, which are essential in practical applications.