Classification of Discrete Modes in Lossy Planar Waveguides: The Modal AnalysisRevisited

摘要

In integrated-optical components like integrated optical detectors or semi-conductor 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. In this paper, we review 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, we extend the analysis to the lossy case and investigate numerically the details of the classification problem. We found that the validity of a unique classification is always limited. For that reason we investigate, 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 we investigate wave propagation along lossy waveguides in the time-Laplace-transform domain and use Lerch's causality theorem.