On the acoustic-electromagnetic analogy

Abstract

We investigate the analogy between electromagnetic and acoustic waves, considering the kinematics and the energy balance of wave propagation. It is shown that the propagation of the TEM mode (transverse electric and magnetic) is completely analogous, from the mathematical point of view, to the propagation of viscoelastic SH waves in the plane of symmetry of a monoclinic medium. The viscoelastic model corresponding to the electromagnetic equations is the 3D Maxwell constitutive law. The analogy identifies particle velocity with magnetic field, stresses with electric field, compliance with permittivity, inverse of the viscosity with conductivity, and density with permeability. Therefore, it is possible to compute simultaneously the phase velocity, the slowness, the attenuation, the quality factor and the energy velocity of both wave phenomena. The dissipation effects due to anisotropic viscosity and conductivity are verified by numerical experiments performed with spectral time-domain techniques, which have been chosen because accuracy is very important when there are physical dispersion and anisotropic dissipation. An analytical solution is found for elastic anisotropic media, and extended to the viscoelastic and electromagnetic cases by using the correspondence principle. Finally, two corresponding examples are worked out numerically, and an electromagnetic problem is solved with a computer code originally designed for solving viscoelastic wave propagation.