Adiabatic and intrinsic modes for wave propagation in guiding environments with longitudinal and transverse variation: formulation and canonical test

For an application of the present formalism to continuously refracting media, see ibid., vol.39, no.8, p.1137-42 (1991). Adiabatic modes (AMs) fail in cutoff regions and can be made uniform by intrinsic modes (IMs), which are synthesized by a spectral continuum of AMs. Extending previous studies, the AM-IM format is applied here to longitudinally varying guiding environments wherein transverse confinement is due to a transversely graded trapping index of refraction instead of, or in addition to, the presence of boundaries or interfaces. After the general formulation of the problem, which involves the choice of best coordinate system, the solution strategy is applied to a simple test case, a conventional wedge waveguide treated in (nonseparable) rectangular and in (separable) cylindrical coordinates, in order to assess the numerical accuracy of the AM-IM formalism, and of various approximate versions of it