Abstract

The solution of the paraxial wave equation by means of the split-operator fast-Fourier transform method, also known as the beam-propagation method (BPM), is now a firmly established approach for solving a variety of integrated-optics problems. One shortcoming of the paraxial equation is, however, that it is restricted to slowly varying index profiles. This means that application of the method to rib waveguide devices, which are characterized by large refractive-index discontinuities, will in general not be accurate. We need instead to apply the full Helmholtz equation, which after extraction of a carrier wave can be expressed as To generate the solution to this equation by marching requires application of a square root operator at each propagation step.¹

© 1991 Optical Society of America