Abstract

The normal modes of an arbitrary, lossey, plane-stratified waveguide symmetric about the propagation plane (i.e. supporting only TE or TM waves) are found from an expansion of its Green’s function. The radiating modes are the transversely bounded fields which results from the scattering of one or two plane waves by the waveguide. Their orthogonality relations are put in a simple form, involving a reflection-like scattering coefficient. A degeneracy occurs in lossless waveguides allowing one to write the orthogonal radiating normal modes under a great variety of forms; some of them lead to symmetric fields in symmetric waveguides. In the lossy case, these degenerate fields split into the “true” normal modes and “improper” modes. The latter may be viewed as analytic continuations of the true modes, they diverge at infinity but they may be useful in some asymptotic evaulations.

© 1979 Optical Society of America

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