ON THE CLASSIFICATION OF DISCRETE MODES IN LOSSY PLANAR WAVE-GUIDES -THE MODAL-ANALYSIS REVISITED

In integrated-optical components such as integrated optical detectors or semiconductor light amplifiers, multilayer dielectric waveguiding s tructures 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 mode s are only considered in connection with their possible excitation wit h a current line-source. Starting from the lossless situation, the ana lysis is extended to the lossy case and the details of the classificat ion problem are investigated numerically. It was found that the validi ty 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 o f causality has been lost. To test this hypothesis, wave propagation i s investigated along lossy waveguides in the time-Laplace-transform do main and using Lerch's causality theorem. It surprisingly turns out th at in the time-laplace-transform domain, the discrete part of the long itudinal spectrum does not exist, so that the test of the hypothesis i s not conclusive. The classification problem of guided modes in strong ly lossy waveguides is still an open problem.