Optical wave guide analysis using higher order compact FDM in combination with Newton Krylov Subspace methods

In this paper we accomplish a comprehensive study of three different numerical solution techniques based on semi vectorial Higher Order(4th order) Compact(HOC)Finite Difference Method (FDM) for rib-structured optical wave guide modeling. We have used iterative schemes using the Successive Over Relaxation (SOR), the Steepest Descent (SD), and the Conjugate Gradient (CG) algorithms - the last two belong to the famous Newton-Krylov Subspace category. We started with the simplest type - the SOR scheme. But higher divergence factor and run time error pose a serious problem so far as its applicability in our wave-guide modeling is concerned. So here we have studied also SD and CG schemes. Their performances are evaluated and compared in terms of CPU time for various grid sizes. Here CG scheme proves to be the most effective one showing least computational time, assuring convergence while producing similar simulation results. Corresponding surface and contour plots of the electric field profiles for GaAs and GeSi material systems determined by our scheme when compared to the 2nd order central difference scheme, show same qualitative behavior and so verify its acceptability and applicability as well.