The Finite-Difference Vector Beam Propagation Method: Analysis and Assessment

The newly developed finite-difference vector beam propagation method (FD-VBPM) is analyzed and assessed for the application to two-dimensional waveguide structures. The general formulations for the FD-VBPM are derived from the vector wave equations for the electric fields. The stability criteria, the numerical dissipation and dispersion of the finite-difference schemes are analyzed by applying the von Neumann method. Important issues regarding to the implementation such as the choice of reference refractive index, the application of numerical boundary conditions, and the use of numerical solution schemes, are discussed. The FD-VBPM is assessed by calculating the attenuation coefficients and the percentage errors of the propagation constants of the TE and TM modes of a step-index slab waveguide. Several salient features of the FD-VBPM are illustrated.