Full-Vectorial Meshfree Spectral Method for Optical-Waveguide Analysis

A full-vectorial multidomain spectral method (MDSM) for optical modal analysis is developed and presented. The formulation is based on considering the coupling between the transverse magnetic (TM) field components as the other electromagnetic components can be calculated directly from them. The method is meshfree where Chebyshev polynomials are used to expand the components in the internal domains and tempered exponential sets are used for the external domains. Practically, the presented method is applicable to 3-D optical-waveguide structures that are invariant in one direction. The field profiles are expanded by 1-D preselected basis functions with variable expansion coefficients. The presented method is used to study different waveguide structures and exhibits superior performance in time and accuracy and highly agrees with the published results obtained by various methods. The presented method computations are very fast when compared with the conventional mesh-based methods. To have the same accuracy, the required number of unknowns in MDSM is orders of magnitude less than those needed by finite-difference and finite-element methods.