Propagation in Curved Waveguides

Abstract

Asymptotic approximations to the waves guided by a curved, elastic waveguide, whose curvature is small and changes slowly over a wavelength are discussed using the JWKB method. The antiplane shear problem is treated. The asymptotic method is carefully explained and a brief comparison with similar and contrasting asymptotic approaches made. The conclusions reached are: (1) Provided the caustic is outside the guide, the presence of the curvature affects the mode shape and modulates the amplitude, but leaves the dispersion relation almost unchanged from that of a guide having no curvature. (2) A caustic can often form inside the guide. Its presence alters the modes, the modulated amplitude and the dispersion rather dramatically. The region of guided propagation becomes that between the caustic and the upper concave surface, though the lower convex surface continues to influence the propagation, and the wavenumber becomes dependent on the curvature.