In this paper, we introduce a new technique that relates the split of polarization states through various scattering
mechanisms. We use the finite-difference time domain (FDTD) method in our computations since, by its nature, FDTD
can model an ultrawide band source and can separate the various scattering mechanisms by exploiting causality. The key
idea is that, once a non-monochromatic wave is incident upon a scattering object, the various spectral components will
be differently depolarized upon scattering depending upon the shape and material composition of the object. In the case
studied here, all of the impinging spectral components are co-polarized (whereas arbitrary polarization distributions are
permitted more generally). Fundamentally, we are exploring a concept similar to the split or quantization of energy states
in quantum mechanics. We first introduce the concept of the quantization of polarization states, and then we explain the
formulation of the "State Space Matrix" in relationship to the polarization gaps. Once the technique is introduced, we
demonstrate its potential applications to realistic problems such as materials detection.
A backscattered signal is coherently or incoherently polarized depending on the nature of the scattering surface and the
bandwidth of the incident signal. In various applications, and more realistic scenarios, multi spectra or Ultra Wide Band
(UWB) have certain advantages over narrow band signals especially in target detection or resolution. Under these
circumstances, we investigate the depolarizing effects of wide band signals to understand the relationship of coherency
or incoherency with various scattering mechanisms such as reflection/transmission or diffraction. In other words, these
major scattering mechanisms may depolarize a signal incoherently in one instance while coherently in another. In this
paper we present results showing that the coherency or incoherency of a signal is highly dependent on the nature of the
scatterer in relationship to the bandwidth of the incident signal. We use the Finite Difference Time Domain (FDTD)
methodology to analyze signals scattering off various homogenous or inhomogeneous surfaces.
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