| Coherence and polarization are two important characteristics of optical beam. In1994, James first demonstrated that the degree of polarization of partially coherent optical beam would been varying when the beam propagating in free space. Since then, the coherence and polarization have been consider correlative. The2×2matrix of cross spectral density has been used to describe random electromagnetic beams(REMBs) in spatio-frequency domain by E. Wolf. The unified theory of coherence and polarization has been built. Then the research of REMBs has attracted people’s widespread attention. The partially coherent and partially polarized beam has been widely applied in nonlinear optics, free-space optical communications, inertial confinement fusion by laser, and optical imaging. This thesis focuses on the studies on the propagation property of REMBs in optical resonator and the analysis of the affecting of REMBs’coherence, polarization and spectrum by resonator parameter. Furthermore, the condition of spatio-temporal coupling of random electromagnetic pulsed beams(REMPBs) has been studied in spatio-temporal domain. The affecting of polarized characteristic of pulsed beams by the spatio-temporal coupling is analyzed. The contents of this thesis are as follows:In Chapter1, the history of light propagation and transformation theory, the background of the research on partially coherent light and the progresses in polarized light theory are reviewed. The purpose, main content and originality of this paper are presented.In Chapter2, the basic theory of light propagation, such as theory optical diffraction, matrix optics, the tensor method of partially coherent optics and theory of polarized optics, are introduced.In Chapter3, The interaction of an electromagnetic Gaussian Schell-model (EGSM) beam with a Gaussian cavity is analyzed. In particular, the evolution of the degree of polarization of the EGSM beam is investigated. The results show that the behavior of the degree of polarization depends on both the statistical properties of the source that generate the EGSM beam and on the parameters of the cavity.In Chapter4, On the basis of the unified theory of coherence and polarization we investigate the behavior of the state of polarization of a stochastic electromagnetic beam in the Gaussian cavity. Both formulations in terms of Stokes parameters and in terms of polarization ellipse are given. We show that the state of polarization stabilizes, except in the case of a lossless cavity, after several passages between the mirrors and might exhibit monotonic or oscillatory behavior depending on the parameters of the resonator. We also find that an initially uniformly polarized beam remains non-uniformly polarized even for large number of passages between the mirrors of the cavity.In Chapter5, Evolution of the spectral shift of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in a Gaussian cavity is investigated in detail. It is shown that the spectral shift of the EGSM beam in a Gaussian cavity is mainly determined by the degree of polarization of the initial beam and the parameters of the cavity. The blue shift occurs at the on-axis point, while the red shift can occur at the off-axis points. The condition under which the relative spectral shift is independent of the degree of polarization of the initial beam is analyzed.In Chapter6, Matrix optics is applied to a class of random, in time and space, electromagnetic pulsed beam-like (REMPB) radiation interacting with linear optical elements. A6x6order matrix describing transformation of a six-dimensional state vector including four spatial and two temporal positions within the field is used to derive conditions for spatio-temporal coupling. An example is included which deals with a spatio-temporal coupling in a typical REMPB on reflection from a reflecting grating. Electromagnetic nature of such interaction is explored via considering dependence of the degree of polarization of the reflected REMPB on its source and on the structure of the grating. |
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