Comprehensive theory of plane-wave expansion based eigenmode method for scattering-matrix analysis of photonic structures

Abstract

A plane-wave-based eigenmode method for scattering-matrix propagation of waves through layered photonic structures is presented. Mode matching using plane-wave-based eigenmode expansion requires a balance between the number of plane waves for the expansion of fields and the number of modes (number of eigensolutions) for mode matching. A matrix-free Fourier operator can handle the increase in the number of plane waves for large structures independently of the number of eigenmodes needed for the scattering-matrix analysis. A convergence analysis of the reflection and transmission of photonic crystal and photonic crystal defect structures as a function of the number of plane waves and the number of eigenmodes is carried out.