Conformal mapping: limitations for waveguide bend analysis

Simulation of constant radius curves using the finite difference-beam propagation method (FD-BPM) is investigated. Two methods of modelling the curve are compared: conformal mapping and modelling in cylindrical coordinates. Modelling by conformal transformation is shown to have some practical implementation problems and has an inherent error when used in conjunction with FD-BPM. The use of cylindrical coordinates proves a superior method in terms of accuracy and practicality, where it is possible to retain uniform sampling and easy interfacing with rectangular coordinates. This leads us to propose a new curvilinear co-ordinate system for the accurate modelling of arbitrarily curved waveguides.