Vectorial EM Signal Reconstruction in Stochastic, Inhomogeneous Media and Optimal Observation Times

In this talk, we consider the problem of reconstructing electromagnetic (EM) wave fields from sensor time series data in inhomogeneous/stratified and stochastic media. The propagation of EM waves in inhomogeneous media has been studied in many contexts using scalar equations such as the wave, Helmholtz, and paraxial equations. Vectorial effects of propagation such as depolarization can be incorporated into the governing equations by retaining the gradient of the refractive index, giving the Maxwell vector wave equation. Stochastic media have been modeled in many ways including using random distributions of scatterers and random indexes of refraction. Here, we study the problem of vectorial EM propagation through an inhomogeneous medium with a stochastic current density and the effect on EM signal reconstruction in the context of the ionosphere. Closed-form expressions of the mean-squared reconstruction error can be obtained in special cases which can be used to obtain optimal observation times for sensor time series.