Polarimetry Of Random Fields

On temporal, spatial and spectral scales which are small enough, all fields are fully polarized. In the optical regime, however, instantaneous fields can rarely be examined, and, instead, only average quantities are accessible. The study of polarimetry is concerned with both the description of electromagnetic fields and the characterization of media a field has interacted with. The polarimetric information is conventionally presented in terms of second order field correlations which are averaged over the ensemble of field realizations. Motivated by the deficiencies of classical polarimetry in dealing with specific practical situations, this dissertation expands the traditional polarimetric approaches to include higher order field correlations and the description of fields fluctuating in three dimensions. In relation to characterization of depolarizing media, a number of fourth-order correlations are introduced in this dissertation. Measurements of full polarization distributions, and the subsequent evaluation of Stokes vector element correlations and Complex Degree of Mutual Polarization demonstrate the use of these quantities for material discrimination and characterization. Recent advancements in detection capabilities allow access to fields near their sources and close to material boundaries, where a unique direction of propagation is not evident. Similarly, there exist classical situations such as overlapping beams, focusing, or diffusive scattering in which there is no unique transverse direction. In this dissertation, the correlation matrix formalism is expanded to describe three dimensional electromagnetic fields, providing a definition for the degree of polarization of such a field. It is also shown that, because of the dimensionality of the problem, a second parameter is necessary to fully describe the polarimetric properties of three dimensional fields. Measurements of second-order correlations of a three dimensional field are demonstrated, allowing the determination of both the degree of polarization and the state of polarization. These new theoretical concepts and innovative experimental approaches introduced in thiss dissertation are expected to impact scientific areas as diverse as near field optics, remote sensing, high energy laser physics, fluorescence microscopy, and imaging