The Studies On Propagation And Tight Focusing Properties Of Partially Coherent Beams With Special Correlation Functions

Laser beams have important practical applications in laser communications, optical image and optical trapping due to their strong direction, single color, high coherence and high energy, etc. However, in some practical applications, partially coherent beams have been revealed to exhibit unique advantages over the fully coherent beams. Hence, more and more attentions have been paid to the study of partially coherent beams. Over the past decades, most of the studies on partially coherent fields are restricted on considering fields with the conventional Gaussian-Schell model correlation functions whose degrees of coherence have position-independent Gaussian profiles. However, the spatial correlation structure of partially coherent beams is not only limited to the form of Gaussian distribution function. One can regulate the spatial correlation structure of partially coherent beams by some methods to make them having a special correlatin function. A variety of partially coherent beams with non-conventional correlation functions have been theoretically introduced and experimentally generated since the sufficient conditions for devising the genuine correlation function of scalar and vector partially coherent beams were discussed by Gori. Of particular interest, it has been shown that those partially coherent beams with special correlation functions exhibit some extraordinary propagation characteristics and focusing properties. Recently, more and more attention is being paid to partially coherent beams with non-conventional correlation functions propagating in various mediums. This dissertation is focus on the study of propagation properties of partially coherent beams with special correlation functions in turbulent atmosphere and uniaxial crystals. In addition, we study the tight focusing properties and radiation forces on small particles of such partially coherent beams through a high numerical-aperture (NA) focusing system. The primary research contents are as the followings:In Chapter 1, we introduce the background and basic theory of partially coherent beams, and then introduce the basic theory, research status and research significance of partially coherent beams with special correlation functions. At last, we give a brief overview of the main research contents of our thesis.In Chapter 2, based on the extended Huygens-Fresnel principle and second-order moments of the Wigner distribution function, we have theoretically derived the analytical expressions of the relative root-mean-square (rms) angular width and the propagation factor of cosine-Gaussian-correlated Schell-model (CGSM) beams propagating in non-Kolmogorov turbulence. We have concretely analyzed the effect of different beam parameters and turbulence parameters on the spreading properties of the relative rms angular width and normalized propagation factor. Presented results are generally compared to the analogous ones obtained for the case of a conventional Gaussian Schell model (GSM) beam. We tend to find suitable ways to overcome or reduce the destructive effect of the atmospheric turbulence and improve the propagation performance of laser beams.In Chapter 3, based on paraxial vector propagation theory, we have derived the analytical expressions for an orthogonal cosine-Gaussian Schell-model (OCGSM) beam propagating in uniaxial crystals orthogonal to the optical axis. We have numerically analyzed the propagation properties, such as the normalized spectral density, the spectral degree of coherence and the effective beam width of an OCGSM in uniaxial crystals, the case for the conventional partially coherent beams is also shown for comparison. At last, we have analyzed the influence of different beam parameters and the ratio of the extraordinary refractive index to the ordinary refractive index on the the propagation properties of the OCGSM beam in uniaxial crystals.In Chapter 4, based on the Richards-Wolf vectorial diffraction theory, the tight focusing properties, including the intensity distribution, the degree of polarization, and the degree of coherence, of the Laguerre-Gaussian-correlated Schell-model (LGSM) beams through a high-numerical-aperture (NA) focusing system are investigated in detail. We have compared the difference of the tight focusing properties between the partially coherent beam with a special correlation function and the conventional partially coherent beam. At last, we have discussed the effect of different beam parameters on the tight focusing properties.In Chapter 5, we have theoretically studied the tight focusing properties and the radiation forces on a metallic Rayleigh particle of a radially polarized narrow-width annular beam through a high-numerical-aperture (NA) objective. A novel optical-trap method for improving the trapping capability has been proposed. A circular blocking mask is placed subtly in front of an aplanatic objective lens to generate a radially polarized narrow-width annular beam. It is shown that a. sub-wavelength focal spot with a quite long depth of focus can be formed in the vicinity of the focus. In the aspect of trapping particles, one can largely enhance the transverse trap stiffness and broaden the longitudinal trap range by choosing a suitable width of the annular beam.In Chapter 6, we have derived the analytical expressions of partially coherent dark hollow beams (DHBs) through a paraxial ABCD optical system in a tensor form. The focusing properties of coherent and partially coherent DHBs and its radiation forces on a Ralyleigh particle are numerically investigated. In addition, the effect of different beam parameters (i.e., the spatial coherence, the waist width, the beam order and the hollow parameter) on the radiation forces and the trap stiffness are discussed in detail. Finally, the stability conditions for effective trapping particles are also analyzed.In Chapter 7, we summarize the work which has been done and draw up a plan for the future work.