Accurate solution of the paraxial wave equation using Richardson extrapolation

Abstract

Richardson extrapolation is used along with the midstep Euler finite difference method to solve the paraxial wave equation. Highly accurate solutions can be efficiently obtained using this combined approach. Numerical results are presented for wave propagation in a straight integrated optical waveguide and a Y-junction waveguide. Discretization errors in both the propagation and the transverse dimension can be systematically eliminated by using Richardson extrapolation. Accuracies on the order of 10/sup /spl minus/11/ or better are obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>