A modified imaginary distance BPM for directly computing arbitrary vector modes of 3-D optical waveguides

A method for the direct calculation of arbitrary vector modes of three-dimensional optical waveguides is presented. The proposed mode-solving scheme, based on a modified imaginary distance beam propagation method, provides an easy to implement explicit algorithm. A finite-difference discretization is used in the transverse plane and a Chebyshev approximation in the propagation direction. Approximate values of the propagation constants of the modes to be calculated are required and it is demonstrated that this data can be obtained in an efficient way by using the least squares Prony method.