COMPARISON OF FINITE-DIFFERENCE AND FOURIER-TRANSFORM SOLUTIONS OF THE PARABOLIC WAVE-EQUATION WITH EMPHASIS ON INTEGRATED-OPTICS APPLICATIONS

The solution of the scalar wave equation in the parabolic approximation is considered through the finite-difference and the Fourier-transform (i.e., beam propagation method) techniques. Examples are taken from the field of integrated optics and include propagation in straight, tapered, Y-branched, and coupled waveguides. A comparison of numerical results obtained by the two methods is presented, and a comparison with other analytical or numerical methods is also given. In the numerous cases studied it is shown that the finite-difference method yields a large, order-of-magnitude range improvement in accuracy or computational speed when compared with the Fourier-transform method.