Comparative analysis of spectral methods in half-bounded domains; implementation of predefined exponential and Laguerre basis sets to study planar dielectric and plasmonic waveguides

Abstract

Two types of basis sets are used to analyze half bounded domains within the frame of multi-domain spectral method, namely the predefined exponential and physical Laguerre basis sets. Different planar waveguides are used for comparisons and the comparisons demonstrate the superiority of the predefined exponential basis set. The physical Laguerre basis set suffers from the slow convergence and its high sensitivity to scaling. Also, a narrow range of exponentially decaying rates can be calculated simultaneously. On the other hand, the predefined exponential basis set can handle wide spectrum of decaying range simultaneously with a small number of bases. It results in accuracies comparable to the machine accuracy with about 20 bases in most of the presented analyses.