An analytic decomposition approach to modeling evanescent transient plane waves with an illustrative application to acoustics at a fluid–fluid interface

Abstract

This work introduces an analytic decomposition approach for transient plane waves, broadly applicable to their interaction with layered media in linear physics. The time-domain signal, assumed to be analytic, is extended into the complex plane and then analytically decomposed into two parts, in a manner reminiscent of the Wiener–Hopf technique. The method directly provides the Hilbert transform of the signal and the expressions of the complex fields without resorting to Fourier transforms or the calculation of singular integrals. It applies to a wide class of functions capable of simulating most realistic signals, such as multi-frequency oscillatory signals of limited duration, and is particularly relevant whenever certain fields become evanescent. An illustrative application to acoustics at a fluid–fluid interface offers deeper physical insight than previously available, particularly regarding the processes that generate precursor and successor phenomena in the reflected and transmitted fields, taking advantage of both the simplicity and the effectiveness of the method.