Multipole Dirichlet-to-Neumann map method for photonic crystals with complex unit cells

Abstract

The periodicity of photonic crystals can be utilized to develop efficient numerical methods for analyzing light waves propagating in these structures. The Dirichlet-to-Neumann (DtN) operator of a unit cell maps the wave field on the boundary of the unit cell to its normal derivative, and it can be used to reduce the computation to the edges of the unit cells. For two-dimensional photonic crystals with complex unit cells, each containing a number of possibly different circular cylinders, we develop an efficient multipole method for constructing the DtN maps. The DtN maps are used to calculate the transmission and reflection spectra for finite photonic crystals with complex unit cells.