Theoretical Study On The Evolution Properties And Fine Structure Of Polarization Parameters In Light Fields

Modern optical techniques make more and more frequent use of information extracted with the help of polarized light. Polarization parameters, like light intensities, phase and spectrum do, provide very important available freedoms including the degree of polarization (DP) and the state of polarization (SP) of polarized part in light. The knowledges of these parameters are fundamental prerequisite to make efficient use of them. It is thus of radical importance for developing polarization engineering techniques to theoretically scrutinize how these polariza-tion parameters behavior. In this thesis we theoretically study the the longitudinal evolution of the degree of polarization during processes like radiation from light sources and scattering from random medium and the spatial fine structure of SP in light fields.For evolution properties, our mainly concern is the mechanism that induces the change of DP. We first studied the angular distribution of DP in light scattered from a quasi-homogeneous random medium. Based on the generalization of scalar scattering to its vectorial counterpart using the method of angular spectrum, we analyzed the effect of spatial correlation of refractive index on the DP and pointed out that correlation effect predominantly contributes to the change of DP. Keeping in mind that there are similarities between scattering and radiation problems, our analysis naturally saturated to the fard fields radiated from partially coherent lights sources. We demonstrated that for radiation problems, there is another effect beyond the coherence ef-fect that induces the change of DP, and it is called cross-polarizaiton effect. This was proved by considering a group of light sources that have the same degrees of polarization, the same spatial degrees of coherence but with different degrees of cross-polarization to confirm that they gener-ate beams with different DP. These results clarified the question of what mechanisms are indeed responsible for the evolution of DP. Using the degree of cross-polarization as a tool, we also supposed a procedure for constructing a physically sound definition of the DP for three dimen-sional light fields. This could be achieved by first generalizing the degree of cross-polarization to the three dimensional case then using it at coincident points as the usual DP.As for the fine structure of SP, we concentrated mainly on the possible methods generat-ing a space-variant polarization distribution. For this task, we demonstrated that two kinds of birefringent devices, one of linear type and the other circular type could modulate SP in one dimension. Two beams of light each modulated this way could superpose to generate a two-dimensional distribution. It was found that the correlation properties between these two beams have an evident modulation on the distribution of poalrization parameters. A particular example of polarization distribution generated by superposing two modulated beam which contain phase vortices was studies. The embedded polarization singularities, namely, points where the polar-ization is circular and curves where the polarization is linear were analyzed in the framework of singular optics. These singularities were found to have topological stabilities under small per-turbations. Perturbations could drag and compress the streamlines of polarization major axis and induce the trasformation of the morphologies of these line from one type to another. The other arena where light fields could have fine structure is the focal region of a high numerical aperture system. We numericall simulated the energy, the phase and the polarization distribu-tions of some types of non-uniformly polarized incident light. A fast FFT numerical method was adopted to achieve fast computations. It was found that the shape and orientation of the focal spot, the energy ratio between the three components are all sensitive to the polarization distribution across the aperture. These results may shed lights on the possibility of intentionally controlling the focal spot with polarization engineering. The generation of polarization singu-larities which lie on curves in space and points in planes, was found sensitive to the existence of phase vortex in the aperture. The variations of these singularities were found to be able to take place in scales much smaller than the wavelength of light. All these numerical results agree well with theories.The researches and results presented in this thesis will be of value in a broader regime of applications using polarized light. In particular, they may be of help in giving prediction to possible results and analyzing emerged various phenomena in situations where complex manip-ulation of polarized light are needed. For situations multiple degrees of freedom of polarization parameters are engaged they may also find potential values.