On the classification of discrete modes in lossy planar waveguides: the modal analysis revisited

Abstract

In integrated-optical components such as integrated optical detectors or semiconductor light amplifiers, multilayer dielectric waveguiding structures occur in which some layers may be strongly lossy or may have gain. In such structures, the classification of the guided modes may become impossible. This paper reviews the modal analysis in which modes are only considered in connection with their possible excitation with a current line-source. Starting from the lossless situation, the analysis is extended to the lossy case and the details of the classification problem are investigated numerically. It was found that the validity of a unique classification is always limited. For that reason it is investigated, whether the classification problem might be due to the fact that in the time-harmonic formulation, the physical requirement of causality has been lost. To test this hypothesis, wave propagation is investigated along lossy waveguides in the timeLaplace-transform domain and using Lerch's causality theorem. It surprisingly turns out that in the time-Laplace-transform domain, the discrete part of the longitudinal spectrum does not exist, so that the test of the hypothesis is not conclusive. The classification problem of guided modes in strongly lossy waveguides is still an open problem.