Brillouin precursors in Debye media

TL;DR

This paper provides an analytical study of Brillouin precursors in Debye media, revealing their dependence on medium properties and incident wave characteristics, with validation against experiments in water at radio frequencies.

Contribution

It offers explicit analytical expressions for Brillouin precursors in Debye media, clarifying their shape, amplitude, and dependence on medium and incident wave properties.

Findings

Precursors are visible at specific propagation distances where the impulse response is Gaussian.

Derived analytical expressions match experimental and numerical data in water at radio frequencies.

The shape and amplitude law of the precursor depend only on the incident wave's integral properties.

Abstract

We theoretically study the formation of Brillouin precursors in Debye media. We point out that the precursors are visible only at propagation distances such that the impulse response of the medium is essentially determined by the frequency dependence of its absorption and is practically Gaussian. By simple convolution, we then obtain explicit analytical expressions of the transmitted waves generated by reference incident waves, distinguishing precursor and main signal by a simple examination of the long-time behavior of the overall signal. These expressions are in good agreement with the signals obtained in numerical or real experiments performed on water in the radio-frequency domain and explain in particular some observed shapes of the precursor. Results are obtained for other remarkable incident waves. In addition, we show quite generally that the shape of the Brillouin precursor appearing alone at sufficiently large propagation distance and the law giving its amplitude as a function of this distance do not depend on the precise form of the incident wave but only on its integral properties. The incidence of a static conductivity of the medium is also examined and explicit analytical results are again given in the limit of weak and strong conductivities.