An Electromagnetic Interrogation Technique Utilizing Pressure-dependent Polarization

Abstract

This dissertation focuses on an interrogation technique that uses traveling acoustic wavefronts as a virtual reflector for an oncoming electromagnetic wave. Electromagnetic interrogation techniques in general have the potential for wide applicability in practical problems and this technique in particular enjoys that potential.

We begin by developing a viable model for pressure-dependent orientational (Debye) polarization. We then incorporate it into a one-dimensional Maxwell system to describe the electromagnetic/acoustic interaction.

This system may be generalized to include a wider class of electromagnetic behavior; we establish well-posedness, enhanced regularity, and convergence results for this general system.

Under the framework provided by the mathematical theory, we obtain computational results for sample forward and inverse problems relating to the interrogation technique. Our numerical algorithms for the forward problem involve finite difference approximations in time and finite element approximations with piecewise linear basis elements in space. Solving the inverse problem entails least squares minimization using a gradient-free Nelder Mead optimization routine.

Finally, as a first step in developing a model in which the pressure wave may be modulated by the electromagnetic wave (unlike the one-way coupling in the model presented here), we consider the system describing an acoustic wave propagating through a layered medium. We derive a weak formulation for this system and present computational findings.