Focusing Properties Of Beams: Focal Shift, Focal Switch And Phase Shift

Beam focusing is a useful way for achieving higher power density and smaller beam width, and is an interesting subject in the field of high-power-laser technology. Recently, a lot of literatures have studied focusing properties of beams particularly. Further studies of beam focusing are of great significance for lasers application and design of optical system. The present thesis is devoted to studying focused intensity distribution, focal shift, focal switch and phase shift in Laugerre-Gaussian beams, Hermite-Gaussian beams and Sinh-Gaussian beams passing through different optical systems. The main results achieved in this thesis can be summarized as follows:1. Starting from the generalized Huygens-Fresnel diffraction integral (Collins formula), the propagation expressions of Laguerre-Gaussian beams and Hermite-Gaussian beams passing through an un-aperture lens optical system are derived. The focused intensity distribution and focal shift are analyzed in detailed by numerical calculations.2. Focal switch in Laguerre-Gaussian beams and Hermite-Gaussian beams is studied by using the propagation expression of Laguerre-Gaussian beams and Hermite-Gaussian beams passing through an aperture-lens separated optical system. Emergence of focal switch is analyzed, and conditions for its emergence are obtained. Influences of truncated parameter and Fresnel number on focal shift are analyzed. The reason for emergence of focal switch is explained starting from the propagation formula. As compared with the results for focal switch in the previous literatures, the results achieved in this paper are original.3. Phase shift in Laugerre-Gaussian beams passing through apetured ABCD optical system is studied. Our study has extended the concept of phase shift in Gaussian beam to high order Gaussian beams. Relations between physical parameters such as truncated parameter, Fresnelnumber and phase shift are analyzed. It is found that phase shift is eliminated when certain conditions are satisfied. Influence of phase to intensity distribution is analyzed, which can be used to controlled intensity distribution.4. Based on the generalized Huygens-Fresnel diffraction integral, the propagation expression of Hermite-Gaussian beams passing through apertured thin lens optical system is derived. Focused intensity distribution and focal shift in different mode Hermite-Gaussian beams are analyzed in detailed. Focal shift in Hermite-Gaussian beams whose on-axis intensity vanishes is studied based on the encircle-power criterion (GH method), for which tradition treatment can't be used. For the case that on-axis' intensity exists but the maximum intensity is not located on axis, both the LW method and GH method can be used. The two methods are compared by numerical calculations.5. Using the propagation expression of elegant (complex-argument) Laugerre-Gaussian beams, the focused intensity distribution is studied. The focal shift in elegant (complex-argument) Laugerre-Gaussian beams is studied by two different treatments, and the results are analyzed and compared.6. Focused intensity distribution and focal shift in Sinh-Gaussian beams whose on-axis intensity is zero are studied based on the encircle-power criterion. Dependences of focused intensity distribution and focal shift upon relative physical parameters are analyzed. Condition for optimum focusing is obtained.