Transformation of the three-dimensional beam propagation method to two dimensions for cylindrically symmetric structures based on the Hankel transform

Abstract

A new form of the beam propagation method is developed in cylindrical coordinates based on the Hankel transform which can be used to study the propagation in structures with azimuthal symmetry, usually excited by beams of circular symmetry like optical fibres, microlenses, etc. This method reduces the three-dimensional problems previously studied by the well known beam propagation method to two-dimensional problems, which reduces computation time by three orders of magnitude for the same number of calculation points in the direction of propagation and in the transverse plane. Also, the memory size required is greatly reduced.