G. H. Cocoletzi
Dept. of Phys., Ohio Univ., Athens, OH 45701
Theoretical studies are performed on the propagation of acoustic waves in multilayer systems using a transfer matrix approach similar to that developed for the studies of optical filters [L. I. Epstein, J. Opt. Soc. Am. 42, 806--810 (1952)] and metallic superlattices [E. L. Olazagasti et al. , Solid State Commun. 78, 9--12 (1991)]. The formalism presented here is used to calculate the reflectivity R of sound waves on multilayer structures. Comparisons are made with experimental results [B. G. Martin, J. Acoust. Soc. Am. 91, 1469--1473 (1992)] for a three-layer structure, in the normal incidence case. The calculated resonances are in good agreement with the experimental ones. For the same system, in the non-normal incidence of sound waves, the spectra of R suggests surface waves coupling. Finally, to show the usefulness of the theory, a Kronig--Penney type structure is studied, calculating the dispersion relation of the normal modes of an infinite system and the reflectivity for the semiinfinite case.