A Study On The Focusing Properties And Spectrum Properties Of Beams

The focusing properties and spectral properties of light field are topics of current interest, which play important roles in the development of the modern optics theory and laser technologies.Firstly, a comprehensive review of the basic theories and analytical methods for the beam propagation and several beam models for the partially coherent beam are introduced, which include Gaussin Schell-model(GSM) beam, twisted Gaussian Schell-model beams, anisotropic Gaussian Schell-model beams, partially coherent modified Bessel-Gauss beams et al. The effect of the spherical aberration of lens on the focusing property of beam is also introduced. Based on the above theories and methods, the main tasks of this thesis are as follows:The propagation formula of flat-topped multi-Gaussian beams passing through ABCD optical system without aperture is derived by using Collins formula. Based on the second-order moment method, the analytic expressions for the beam width, M2 factor and Kurtosis parameter of flat-topped multi-Gaussian laser beams are also obtained. The waist width and their locations of the beams propagating in the free space and through a thin lens are also deduced. Based on the expressions for the axial light intensity of flat-topped multi-Gaussian laser beams by a lens with spherical aberration, the influence of Fresnel number N_w and spherical aberration coefficient kS₁ on the axial intensity distribution is discussed. It is shown that when the Fresnel number of Gaussian beams is small, the best focal positions corresponding with the positive and negative spherical aberration are at the left of the focus for the aberration-free case, but for large Fresnel number they are located at both sides of that of aberration-free respectively. For the lens with positive spherical aberration, no focal shift even the positive focal shift can be carried out by changing the value of Fresnel number of Gaussianbeams.Based on the propagation theory of partially coherent beam, the spectral shift and spectral switch of partially coherent modified Bessel-Gauss beams passing through an aperture lens are studied. Numerical results show that the spectral shift and spectral switch of partially coherent modified Bessel-Gauss beams are dependent upon truncation parameter, Fresnel number of beam and the spectral degree of coherence. The numbers of spectral switches increase with the increasing Fresnel number and truncation parameter, but decreases with the increasing spectral degree of coherence. When the truncation parameter increases to a certain value, the aperture effect can nearly be neglected, and the spectral switch disappears. For example, when the spectral degree of coherence equals to 0.5, and the truncation parameter is larger than 2, the spectral switch disappears and there is only the blue shift.The focusing of partially coherent modified Bessel-Gauss beam(MBGB) passing through a spherically aberrated lens is also studied. It is shown that, when the spectral degree of coherence is small, the best focal positions corresponding to positive and negative spherical aberrations are at the both sides of the focus for the aberration-free case. When the spectral degree of coherence is large, the best focal positions corresponding to positive and negative spherical aberrations are at the left of the focus for the aberration-free case. It is also found that as the Fresnel number of the lens increases, the best focal point moves toward the geometrical focus and finally approaches a constant. When the Fresnel number of Gaussian beams equals to 1, the best focal position for the aberration-free case gradually approaches 0.908 and is independent on the spectral degree of coherence. But for positive and negative spherical aberrations it depends upon the spectral degree of coherence.The light intensity on axis and the focal switch effect of Cosine Gaussianbeam focused by a thin lens without aperture are studied in detail by using Collins formula. It is shown that, if the beam parameter is larger than 1, the focal switch of Cosine Gaussian beam can occur. The relative transition height increases with the increase of the beam parameter. The normalized axial minimum intensity decreases with the increase of the beam parameter, and the normalized axial minimum intensity is zero, as the beam parameter is larger than 4.Based on the expression of the axial light intensity of Cosine-Gaussian beam by a lens with spherical aberration, the influences of the coefficient of the spherical aberration kS\ and Fresnel number of Gaussian beams Nw on the axial intensity distribution are discussed. The numerical results show that the lens with negative spherical aberration may be an approach for achieving flattened laser intensity distribution along the propagation axis. For the lens without spherical aberration, the maximum light intensity or the best focal point is on the left side of the geometrical focus. For the lens with positive spherical aberration, the best focal position can leap from the left of geometrical focus, zj\, to the right side of it, z/2, namely the focal switch occurs, by changing the value of Fresnel number of Gaussian beams Nw. With the more coefficient of the spherical aberration kS\ goes, the more relative transition height Az/=| zj\-Zfl\ is, but the less value of the critical Fresnel number (Nw)c. For example, when the coefficient of the spherical aberration increases from 0.3 to 0.5, the relative transition height Az/ goes from 0.146 to 0.246, but the critical Fresnel number decreases from 8.68 to 7.03.