| Recently, many new model sources for non-Gaussian correlated partially coherent beams have been developed based on the studies of traditional partially coherent beams. The unique optical characteristics including self-focusing, self-shifting, self-shaping and self-splitting are induced by the special correlation form. Generally, the new partially coherent beams are proposed on the basis of scalar theory which ignores the polarization propery of light beams. In 2003, Wolf pointed out in his unified theory of coherence and polarization that the coherence and polarization are closely related. Only when the studies are generalized from scalar fields to vector fields can many features of the fluctuating electromagnetic fields be fully investigated. The remarkable characteristics of the special correlated partially coherent beams indicate that such beams carry potential for practical application involving lasing detection, laser confinement fusion, optical shaping, and atmosphere optical communications. Besides, an important application is the optical trapping. The technology using light pressure to trap particle is the so-called optical tweezer. Different structures of optical tweezer can be used to trap, rotate, transport or pull, and lift particles. Moreover, due to the ability in subcontacted and nondestructive manipulation on small particles, the optical tweezer has become a powerful tool in trapping living cells, neutral atoms and molecule, quantum dot and different types of dielectric particles. On the other hand, the Airy beams have attracted immense interest for its unique features, such as nondiftracting, transversely accelerating and self-healing. In this dissertation, firstly, by using vector theory, we study the statistical properties of two kinds of non-Gaussian correlated partically coherent beams propagating in fractional Fourier transform optical system and turbulent atmosphere. Then, the trapping features of two other special correlated partially coherent beams on Rayleigh particles are investgated by using scalar theory and Rayleigh approximation theory. Finally, the propagation properties of the Airy vortex beams in chiral medium are considered.In Chapter 1, the background of the research is introduced in fives parts:conventional partially coherent beams; non-Gaussian correlated partically coherent beams; partially coherent electromagnetic beams; the development of optical trapping; the origin and development of the Airy beams. Then the fundamental method and the theoretical basis used in our dissertation are given:matrix optics and the theory of the diffraction integral; the theory of coherence and polarization of light; the method of calculating the radiation forces.In Chapter 2, firstly, we extend scalar rectangular Gaussian Schell-model (RGSM) beams to electromagnetic domain. The analytical expression for the elements of the cross-spectral density matrix of the RGSM beam propagating in ABCD optical system is obtained. Particularly, according to the derived expression the evolutions of the spectral density, the spectral degree of polarization, and the spectral degree of coherence of the RGSM propogating through fractional Fourier transform (FRFT) optical system are calculated. The transverse spectral density, the tranverse degree of polarization and the degree of coherence in different FRFT planes, and such statistical optical properties for selected values of the summation index in conventional Fourier plane are analyzed in detail. Secondly, we generalize a class of random source for circular optical frame to electromagnetic domain. The analytical formulas for the propagation of the electromagnetic source for circular frames combinations through atmospheric turbulence are derived. As two examples, the statistic properties of a single circular frame and two nested ones are comparatively studied in free space and in non-kolmogorov’s atmospheric turbulence. The impacts, arising from the parameters of the atmospheric turbulence and source parameter, on the statistical characteristics are discussed.In Chapter 3, firstly, the optical trapping of the focused multi-Gaussian Schell model (MGSM) beams on Rayleigh particles are studied. The analytical expressions for the intensity distribution and the radiation forces induced by the MGSM beams in the focal plane, and the radiation force maximum in the real focal plane are derived. The dependences of the trapping stability and the trapping range on the summation index and the coherence width of the beam are analyzed. The conditions for stable trapping are discussed. The low limit of coherence for stable trapping and the range of radius for high-index particles are both determined. Secondly, the optical trapping of the focused generalized multi-Gaussian Schell model (GMGSM) beams on two types of Rayleigh particle are investigated. The radiation forces induced by GMGSM beam on the high-index and low-index particles at the focus and at different positions away from the focus in the focal plane are analyzed. In addition, the effect of the summation index and the coherence width of the beam on the trapping stability and the trapping range are analyzed. Both the ranges of the radius of two types of particles for stable capturing are determined.In Chapter 4, analytical expression for the propagation of the Airy vortex beams through ABCD optical system is obtained. As an example the propagation properties of the beam in chiral medium are studied. The impacts, arising from vortex on the changes of the intensity and phase of the left circularly polarized (LCP) and the right circularly polarized (RCP) Airy vortex beam are analyzed. The propagation properties of the Airy vortex beam and the Airy beam in free space and in chiral medium are comparatively studied. The intensity distributions of the LCP Airy vortex and the RCP Airy vortex beams in near and far fields for different values of chiral parameters are discussed.In Chapter 5, the main conclusions and innovations are outlined, and the plans for future work are also discussed. |
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