Application of multigrid method to lightwave propagation in two‐dimensional optical waveguide

Abstract

SUMMARYThe multigrid method widely used in computational fluid dynamics is applied to the problem of propagation of an optical wave in an optical waveguide. This method is a technique for accelerating the convergence speed of the relaxation method. The electromagnetic field components contain various frequency components. Higher-frequency components contain local effects of the shape. On the other hand, the lower-frequency components contain more global aspects. By using this phenomenon, the discretized equations are made to reduce errors corresponding to the grid size. As a numerical example, linear and nonlinear directional couplers are treated and the effects of the number of levels and the number of iterations in the multigrid method are studied.

Application of Multigrid Moment Method to Scattering of a Gaussian Beam by a Dielectric Cylinder

“…Three-level scheme (ν = 3) of the multigrid method is applied, since the residual norm doesn't improve much better for this problem when the number of level increases. For the optical waveguide, the number of level affects the residual norm (23) . The computer used is Pentium 4 with 512 M Bytes of memory and a CPU speed of 2GHz.…”

Application of four-point MEGMSOR method for the solution of 2D Helmholtz equations

“…PDEs provide an important instrument for solving numerous scientific problems, such as BVPs. Their historical development is sturdily connected to the solution of BVPs in potential theory and had a significance impact on the development such as time harmonic acoustic and electromagnetic fields, optical waveguide, acoustic wave scattering, noise reduction in silencer, water wave propagation, radar scattering and lightwave propagation problems (Yokota and Sugio, [10]; Nabavi et al, [24]; Kassim et al, [25]). Thus, in this paper, numerical solutions for Helmholtz equations given in the form Eq.…”

QSMSOR iterative method for the solution of 2D homogeneous Helmholtz equations

“…Many problems in engineering and science involve Helmholtz equation, occur in real time application. On the other hand, the applications of Helmholtz equation are encountered in many fields such as time harmonic acoustic and electromagnetic fields, optical waveguide, acoustic wave scattering, noise reduction in silencer, water wave propagation, radar scattering and lightwave propagation problems (Muthuvalu et al, 2014a; Nabavi et al, 2007;Kassim et al, 2006;Yokota and Sugio, 2002). There is a high important in improving the performance of the methods for solving Helmholtz equation.…”