Study On Propagation Properties And Phase Singularities Of Dark-hollow Beams

The theoretical model, propagation, transformation and other issues of the hollow beam have been important research subjects in the laser optics field. As is well-known, the distribution of the initial light field of the hollow beam has the characteristic of phase singularities. Therefore, the hollow beam has aroused people's widespread interest. But the diffraction transmission, transformation, and the singularity optical effect of the hollow beam in complex optical systems (such as misaligned lens system, Diffraction grating lens system, etc.) has not yet been thoroughly studied. This paper is committed to the subject and organized as follows:firstly, the basic concepts of the hollow beams, theories and research methods are introduce, followed by researching and analyzing of the diffraction transmission, as well as the spatial distribution and evolution of their interactions of the phase singularities in the complex optical systems diffraction field. The main contents of this paper are:The basic concepts, characteristics and expressions of the hollow beam and the singular optics are introduced in the first and second chapters. Firstly, the realization and application of the hollow beam are summed up. Secondly, the basic theory and research methods to study the beam's propagation are concluded. The advantages and disadvantages of various research methods as well as the scope of these applications are analyzed. Finally, we present a comparative analysis of the diffraction integral in the theory of the Huygens-Fresnel principle, Kirchhoff diffraction integral formula, Collins formula, Rayleigh-Sommerfeld diffraction integral formula and the angular spectrum theory.The propagation characteristics and the singularity effect of a hollow beam are studied in the third, forth and fifth chapters. In the third chapter, we study and analyze the diffraction of the typical non-uniform hollow beam-the hollow Gaussian beams diffracted by the two-dimensional sinusoidal phase grating. By using the Collins formula, we deduced the electric field equation, intensity and phase distribution function when hollow Gaussian beams pass through a diffraction grating lens system. We also calculate some effects produced by various optical parameters on the spatial distribution of light intensity in the diffraction field by numerical simulation, and then analysis the impact caused by the system parameters changing on the position of the phase vortex center and the number of vortex. In the fourth and fifth chapters, we discuss the complex optical system's matrix which composed of misaligned lens system matrix, transformation matrix. We numerical calculate the diffraction propagation and its singularity optical effect of two hollow beams (Hollow Gaussian beam and elliptical hollow beam) in this complex system by using the misaligned system Collins diffraction integral formula. The diffraction equation of electric field, the beam characteristics and surface distribution are obtained when the two hollow beams pass through the complex misaligned optical system. The propagation characteristics are discussed when these two hollow beams pass through a hard-edged circular collimator aperture and the misaligned 4f lens system. The results show that the order of hollow Gaussian beams, waist and misaligned lens system 4f dislocation displacement have a great influence on the diffraction field intensity distribution, and elliptical Gaussian beam centrifugal coefficient and light intensity of the diffraction field phase distribution also have a certain influence on it.The paper's summary is concluded in Chapter VI.