Special Laser Beams And Its Diffraction Characteristics

Since the first laser was invented in the1960s, lasers have found wide applications indifferent areas. With the expansion of applications and the development of laser technology,the ordinary laser beam with a Gaussian distribution can not meet the applicationrequirements. Therefore developing the specific shape of the distribution of the laser beamis urgent. Special laser beams have very important applications in the particle trapping,atom optics, beam shaping, and laser processing. It is of practical importance to study thepropagation and diffraction properties of these special laser beams. Based on the researchfoundation of our group, the propagation properties of Lorentz, Lorentz Gaussian beamand vector hollow beam are studied in this paper. The Lorenz and Lorentz, Gaussian beamare extended to partially coherent fields, and the effect of initial spatial coherence on thepropagation and diffraction properties of such beams is studied numerically and analyzedin detail.The structure of this paper is organized as follows:First, Lorentz and Lorentz-Gaussian beam, vector hollow beam, the two special laserbeam profiles are described, and the development of propagation theory of laser beam areintroduced.Secondly, we used complex Gauss expansion to expand Lorentz and Lorentz-Gaussbeam model, and then we study the propagation of Lorentz and Lorentz-Gauss beamsthrough an apertured fractional Fourier transform optical system. We derive the theoreticalmodels for the Lorentz and Lorentz-Gauss beams passing through apertured fractionalFourier transform system. Through numerical comparison, we find that as the aperture sizedecreases, the diffraction phenomenon of the beam at the output pane is more obvious.These phenomena are helpful for us to study the special laser beam diffractioncharacteristic. The Lorenz and Lorentz, Gaussian beam are extended to partially coherent fields, and we study the partially coherent Lorentz and Lorentz-Gauss beam theory modeland the propagation properties of a partially coherent Lorentz and Lorentz-Guass beampassing through apertured aligned and misaligned ABCD optical systems. The two systemsare compared. We study the diffraction characteristics of the partially coherent Lorentz andLorentz-Gauss beams passing through apertured aligned and misalignment optical systems.Thirdly, we carry out research on another special laser beam named vector beam. Weestablished the theoretical models for vector circular and elliptical dark hollow beam. Withthe help of the Collins integral formula, we derived the formula for vector dark hollowbeam passing through paraxial ABCD optical system. We studied the diffractioncharacteristics of vector circular and elliptical dark hollow beam passing through paraxialABCD optical system. Through numerical calculation, we analyze the dependence of thedegree of polarization and the intensity of the vector circular and elliptic dark hollowGauss beam on the propagation distance. At the same time, the degree of polarization andthe spectral degree of the two beams are derived, and it is found that the polarization andthe spectral degree change as the propagation distance varies. Our results are helpful forthe application of dark hollow beam. The obtained diffraction features also provide aconvenient way for studying the properties of vector dark hollow beam.At last, a summary of the whole text is given. Based on the current research ondiffraction characteristics of these two laser beams in this thesis and the foundation of ourresearch group, we can study the nonparaxial propagation of these two special laser beamsin future.