Visualizations of wave dynamics in a wedge waveguide with non-penetrable boundaries: Normal-, adiabatic-, and intrinsic-mode representations

Many natural or man-made guiding environments are characterized by physical parameters that render the wave equation non-separable in any of the standard coordinate systems. In particular, in the absence of transverse-longitudinal separability, it is not possible to define discrete or continuous normal modes (NM) that individually satisfy the transverse boundary conditions and that propagate longitudinally without coupling to other modes. When transverse-longitudinal separability is only weakly perturbed, one may define local (adiabatic) modes that adapt smoothly, without inter-mode coupling, to the slowly changing conditions. Adiabatic modes (AM) fail in cutoff regions, and can be made uniform there by intrinsic modes (IM), which are synthesized by a spectral continuum of adiabatic modes. These concepts have been elucidated and validated previously by investigating the wave dynamics in a simple test environment: a wedge waveguide with non-penetrable boundaries, viewed either in coordinate-separable cylindrical coordinates that yield exact field solutions in terms of normal mode, or in non-separable rectangular coordinates that yield approximate field solutions in terms of adiabatic modes and intrinsic modes. The present article is intended as a tutorial to enhance the utility and understanding of these analytical formulations through visualizations of the dynamic interaction between the various wave species, implemented through an educational MATLABtrade package. The visualizations for the full range of ray, mode, and hybrid options, parameterized in the spectral wavenumber domain, has been explored by us previously for the inherently separable canonical environment of a line-source-excited parallel-plate waveguide. In our present investigation of the wedge waveguide, we shall not attempt to mimic the variety of options because of the substantial complications and subtleties inherent in their rectilinearly weakly-non-separable implementation. For our purposes here, a single specific option suffices to address the normal-mode, adiabatic-mode, and intrinsic-mode phenomenologies. Throughout this article, the intended audience is expected to be familiar with asymptotic methods for the evaluation of integrals.