Leaky axisymmetric modes in infinite clad rods

A detailed computational study is presented for the radial-axial modes-both leaky and nonleaky--in an infinitely clad isotropic rods. The complex phase velocities of leaky modes are located using an application of the argument principle. Particle orbits are determined, and leaky modes are shown to have an asymptotic leakage angle away from the interface. By using the homotopic methods of varying densities and elastic constants, clad-rod modes are compared with those in a bare rod. The topology of the clad-rod mode dispersion diagram differs qualitatively from that of a bare rod, even when the cladding has negligible density, with no velocity cutoffs and with wave mode knitting. Comparison is also given with modes occurring in a cladding without a rod present (a tunnel) and for a planar interface. Most leaky modes can be correlated with rod modes; only a limited number of tunnel modes exist. Energy flow contours within modes are also calculated. The local energy velocity, which generalizes group velocity, can vary considerably in the radial direction for bare rod modes. For leaky modes the contours are quite complex due to the cylindrical geometry, giving rise to apparent shift in wave position across the interface.