Acoustic and electromagnetic wave interaction: Analytical formulation for acousto-electromagnetic scattering behavior of a dielectric cylinder

An analytical solution for the bi-static electromagnetic (EM) scattering from an acoustically excited vibrating dielectric circular cylinder is presented. The incident acoustic wave causes a boundary deformation as well as a dielectric inhomogeneity within the dielectric cylinder. First, a perturbation method is developed to calculate the EM scattering from a slightly deformed and inhomogeneous dielectric cylinder. Then, assuming the vibration frequency is much smaller than the frequency of the incident EM wave, a closed form expression for the time-frequency response of the bi-static scattered field is obtained. The solution for acoustic scattering from an elastic cylinder is applied to give the displacement on the surface as well as the compression and dilation within the cylinder. Both the surface displacement and the variation in material density (dielectric constant fluctuation) within the cylinder contribute to the Doppler component of the EM scattered field. Results indicate that the Doppler frequencies correspond to the mechanical vibration frequencies of the cylinder and that the Doppler components only become sizeable near frequencies corresponding to the natural modes of free vibration in the cylinder. These resonances depend only on the object properties and are independent of the surrounding medium. Thus, utilizing the information in the Doppler spectrum scattered by an acoustically excited object vibrating at resonance could provide a means for buried object identification.