Transfer matrix theory of the propagation of leaky waves in periodic or inhomogeneous media

Abstract

A general transfer matrix approach for the propagation of guided waves in the presence of inhomogeneities or “scatterers” is presented that particularly addresses the problem of coupling with radiation modes leading to a leakage of the guided wave in the bulk at each scattering. From symmetry and conservation laws, the general form of the transfer matrix is obtained in terms of four independent real parameters. For one‐dimensional periodic lattices of identical scatterers, the leakage vanishes at the band edges: This coherent effect stems from the complete destructive interference between the radiations of the different scatterers at these particular points. The competition between Anderson localization and coherent leakage in the presence of disorder is discussed. Experimental results on the propagation of one‐dimensional surface acoustic waves in quasiperiodic and random systems of parallel grooves are presented. Spectral and temporal properties of localization in such systems are well put in evidence in this model experimental system. [Work supported by DRET.]