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.