k-space TE/TM beam propagation method: derivation, assessment, and accurate correction for reflected fields and multiple reflections
An accurate k-space two-dimensional TE and TM beam propagation method is presented that has no step-size limitation, permits accurate correction for the reflected fields, and operates in lossy or lossless media. The algorithm is based on the matrix representation of operators and an eigenmode expansion, and it extends the TE/TM Fresnel coefficients of reflection and transmission to nonuniform surfaces. Methods that accurately correct for multiple reflections are presented, based on a sweep procedure or a matrix multireflection approach. The relation of the k-space TE/TM beam propagation method to standard fast-Fourier-transform-based beam propagation methods (FFTBPM's) is shown, the TE-FFTBPM is extended for nonparaxial situations, and a TM-FFTBPM is proposed. A waveguide index step serves as a numerical example.