Abstract:
A number of acoustic reflection and refraction effects, normally associated with ray theory, are used here as tests of a normal mode model in the high-frequency limit, where the modes become dense in the complex wave-number plane. The ray effects, which are associated with saddle points or branch line integrals in the wave-number integration method, do not appear as characteristics of any single mode in the modal solution. Rather, they emerge as collective effects from the coherent addition of large numbers of modes. The effects demonstrated include beam splitting at the Brewster angle for a fluid--fluid interface and at the Rayleigh angle for a fluid--solid interface, beam displacement near the critical angle for total reflection, and beam spreading due to a fluid--solid lateral wave. Gaussian beams are modeled efficiently using the ORCA normal mode model, by assigning complex values to the source coordinates. This technique extends, in a full mode solution, methods that have previously been implemented for Gaussian beams propagating in free space [Deschamps, Electr. Lett. 7, 684 (1971)] and reflecting from single interfaces [Ra et al., J. Appl. Math. 24, 396 (1973)]. [Work supported by the U.S. Navy Office of Naval Research.]