Two numerical techniques of the analysis of complex dielectric waveguides

Abstract

The scalar wave equation with a complex dielectric constant describes the propagation of light in a waveguide having parallel stratification with gain or loss. Unlike their passive and lossless counterparts, complex dielectric waveguides no longer have the self-adjoint (Hermitian) form when described by the wave equation. The lack of the self-adjoint property makes the standard methods for analysis of the wave equation inapplicable. This paper describes two numerical methods for solving the wave equation. The first technique described performs an integration in the direction of propagation by the beam propagation method (BPM) with adaptive step-size control. The second technique is an eigenmode analysis using a finite-difference formulation of the wave equation with the inverse power method used to determine the eigenmodes of interest. As examples of the techniques' applications to semiconductor laser structures are developed.