Interaction of an Electromagnetic Wave with the Acoustic Field of a Traveling Point Source of Sound. Part I: Theory

It is well known that the passage of a sound wave through a fluid causes the permittivity of the fluid to vary in both time and space. As a result, an electromagnetic (EM) wave traveling in the fluid scatters in all directions. We consider here the interaction of a plane EM wave with the field of an acoustic point source traveling at a subsonic speed along a straight line. We look at the variation in permittivity as a small perturbation about its constant value, and we compute the backscattered far field of the first correction term to the EM plane wave. We find that it comprises two distinct waves: one due to the interaction with the part of the acoustic wavefronts traveling in the backscattering direction, and the other due to the part of the acoustic wavefronts traveling away from it. For each wave we define a backscattering cross section and we show that, for the right combination of parameters, a Bragg-type condition obtains and causes the cross section to form a sharp peak. The magnitude of this peak is further increased as Mach 1 is approached and as the direction of travel becomes coincident with the EM backscattering direction.