A Study On The Focusing Properties Of Beams In Astigmatic Optical System

Focusing properties of laser beams are an important researching content in laser optics, which play important roles in the practical application of laser technology. In practice there will be a variety of aberrations, so the investigation of focusing properties of the laser beams passing through an non-ideal optical system has practical interest. Based on the propagation theory of laser beams, the change of beam parameters, focal switch and beam shaping of laser beams after passing through an astigmatic lens are analysed in the present thesis.1. The analytical formula for the beam width of sin-Gaussian beams passing through an astigmatic lens is derived by using the second-order moment method. By numerical calculation, the beam parameters, such as the beam width and far-field divergence angle of sin-Gaussian beams passing through an astigmatic lens are studied. It is shown that the beam widths and far-field divergence angles in the x and y directions are not equal due to the astigmatism; by compared with the ideal astigmatism-free case, with the changes of astigmatic coefficient and decentered parameter the relative error of the beam width in the x direction is similar with the y direction along the propagation distance z, the relative errors of the beam widths in the x and y directions at the geometrical focal plane are equal, by choosing the proper astigmatic coefficient the relative error of the beam width in the x direction at the waist plane in the image space can be eliminated, whereas always exist in the y direction; the relative errors of the far-field divergence angles in the x and y directions are not equal and dependent on the astigmatic coefficient and the decentered parameter.2. The analytical expression for the axial irradiance distribution of cosine-squared Gaussian beams passing through an astigmatic lens is derived using the Collins formula. By numerical calculation and analysis of the results, the dependence of the relative focal shift on the astigmatic parameter is investigated at different positions of the beam's incidence plane for a particular beam parameter and Fresnel number; the range of the beam's incidence position of arising dual focal switchs is obtained under this condition and the physical interpretations of the focal switch due to the astigmatism are given. The following conclusions are obtained by futher analysis:by changing the optical system parameterδmulti-focal switchs can be produced; the numbers of focal switch and the critical value ofδfor arising focal switch are dependent on astigmatic parameter, Fresnel number and beam parameter; whether or not three times focal switch is produced, is determined by the astigmatic parameter and Fresnel number, the beam parameter decide the occurrence of the focal switch phenomena. By changing the Fresnel number the focal switch can also be produced under certain conditions.3. The focal switch of elegant cosh Gaussian beams focused by an astigmatic lens is studied in detail and the influence of parameters on the focal switch are investigated. The results of numerical calculations show that by changing the beam parameter b or Fresnel number, the focal switch can be produced, and especially the change of beam parameter a or astigmatic parameter will lead to dual focal switchs under certain conditions. When the optical system parameter take specific values, the once, twice or three times focal switch can be produced, meanwhile the numbers of the focal switch reduce with the increase of beam parameter a, increase with the increase of beam parameter b, Fresnel number or astigmatic parameter.4. Based on the propagation law of partially coherent light, the beam profiles of J0-correlated Schell-model (JSM) beams focused by an astigmatic lens are investigated. The results shown that flat-topped beams or bottle beams can be acquired by changing spatial coherent length for specific astigmatic parameter and Fresnel number. Furthermore, the vertical and horizontal sizes of the bottle beams reduce with the increase of the spatial coherence length or Fresnel number, increase with the increase of astigmatic parameter. The position of bottle beams is determined by astigmatic parameter.