Guided waves in nonuniform media

Abstract

A waveguide is characterized by three parameters. These are the waveguide cross section A(z), the medium's inertia (density) μ(z), and its elasticity σ(z). The coordinate system is defined by the positions of the guided wave's (constant z) isophase surfaces. The one‐dimensional wave‐guide equations for generalized effort e and flow φ can be written ζ = (σ/μ) [ζ″ + 2(ln Rζ)′ζ′] where ζ is either e or φ, a dot denotes ∂/∂t and a prime ∂/∂z. In the approximation that the wavefronts are parallel, Re = (A>/μ)1/2 and Rφ = (σ/A)1/2. For non parallel wavefronts greater accuracy can be gained by redefining the R's in terms of the M and N functions of Weibel's waveguide equations. The equation for each aspect (e,φ) leads to its own locally defined phase and group velocities vpζand vgζ. However, the local wave impedance Zw, and the rate of energy transport vw are defined via both aspects jointly. In general, vpζ,vgζ,vw, and Zw depend on all three parameter functions. If all three functions are constant, we find the ...