Investigation of the Pade approximant-based wide-angle beam propagation method for accurate modeling of waveguiding circuits

An analytical and numerical study of the accuracy of the beam propagation method that includes approximate treatments of wide-angle propagation based on Pade rational functions is presented. The investigation identifies the error terms associated with a sequence of higher order operators and the range of validity of different approximant operators is studied through examination of two-dimensional (2-D) waveguide structures. An analytical model for the general error in Pade-based wide-angle schemes is developed and compared with numerical simulations of simple waveguiding devices for which the exact solution is known. Guidelines for determining the range of error pertinent to the Pade operator are established.