Studies On Optical Statistic Properties Of Partiallv Coherent Vortex Beams And Gaussian Schell-model Beams

Propagation of laser beams, a subject of fundamental importance in the laser physics and laser applications, has attracted increasing attention during the past decades. Compared to the totally coherent beams, partially coherent beams show unique advantages in some special aspects. Nowadays, the study of partially coherent beams has become a major branch of modern optics, due to its rich physical properties and potential applications. On the other hand, considerable interest has been exhibited in the investigations of phenomenon and nature of light in order to realize the control of light, therefore, it is vital to have a comprehensive understanding of properties of light. Exploring the optical statistic properties of partially coherent beams on propagation is of great theoretical and practical significance, providing us guidance for understanding the interaction of light and matter and the structure of matter. Based on the above background, in this thesis, we have studied the optical properties of the partially coherent vortex beams and Gaussian Schell-model beams on propagation,and discussed the influences arising from the parameters related to the beam source and the medium. The thesis is arranged as follows:In Chapter 1, the related background of the vortex beams and the theory of the partially coherent beams were introduced. We point out the motivations and the significances of our research by describing the research status and development trends of the partially coherent vortex beams and Gaussian Schell-model beams. Then we present the theoretical bases and the fundamental methods mentioned in this thesis,such as the extended diffraction integrals, the mutual coherent function, the cross-spectral density function for scalar beams and the cross-spectral density matrix for stochastic electromagnetic beams.In Chapter 2, based on the extended Huygens-Fresnel principle and the unified theory of coherence and polarization, we derived out the analytical expressions of the elements of the cross-spectral density matrix of stochastic electromagnetic vortex beams propagating in random and determinate media, respectively. On the basis of fractal model of biological tissue, numerical simulation was carried out to analyze the effects of the topological charge, the beam size, the coherence length and the propagation distance on the spectral density and spectral degree of polarization. Then we take a misaligned optical system with an aperture as example, the influences of the topological charge, the radius of the aperture and the displacement, on the spectral degree of polarization and the spectral degree of coherence are investigated in detail.It is tempting to find the method of modulating the optical statistic properties.In Chapter 3, the change of sign of the topological charge of vortex beams on propagation was studied, and the methods for measuring the topological charge of statistically stationary and non-stationary vortex beams were also proposed. First an analytical expression of the orbital angular momentum of a linearly polarized and totally coherent vortex beam traversing a tilted lens was derived. The influences stemming from the tilted angle of the lens and the separation between the beam and the lens are mainly focused on. Moreover, the possibility of reversing the sign of the topological charge was discussed, and a single slit experiment was carried out to verify the theoretical results. Then we suggest a method to access the measurement of the topological charge of statistically stationary vector vortex beams based on the spectral degree of cross-polarization. And the application scope of this method was also verified by adjusting the coherence length. Finally, the dynamics of the degree of polarization and the degree of cross-polarization for statistically nonstationary electromagnetic pulsed vortex beams in dispersive media are explored both in the space-time and space-frequency domains. The impacts arising from the second-order dispersion coefficient and the temporal coherence length are emphasized.In Chapter 4, the far-zone correlation between intensity fluctuations with polychromatic Gaussian Schell-model beams in free space is investigated by giving two illustrative examples with different source spectrum, where the effects of frequency and the observed angle are analyzed. Moreover, we have discussed the extreme case of critical angle at which no frequency shift occurs, and also proposed the so-called scaling law for correlation between intensity fluctuations. Next, the correlation between intensity fluctuations generated by Gaussian Schell-model beams with two varying wavelengths through turbulent atmosphere is investigated, compared with that generated by a single wavelength in free space. The influences arising from difference of two incident wavelengths and perturbation of atmosphere are mainly emphasized.In Chapter 5, the performances of the correlation image and the visibility with partially coherent elliptical Gaussian-Schell model beams have been studied by taking a soft circular aperture as example. In that case we have derived the condition under which the goal ghost image is achievable. The influences of the parameters related to beam size and coherence length in x direction and y direction on the ghost imaging and its visibility are assessed.Finally, Chapter 6 gives a summary of the main work and innovations of the thesis and prospects the next work content.