Propagation Properties And Spectral Changes Of Partially Coherent Beams

The propagation and transformation, the focusing properties and the spectral characteristics of the partially coherent light are main topics in the modern optics. The partially coherent light plays an important role in the development of modern optics theory and laser technologies. Starting from the propagation law of the partially coherent light and using typical models of partially coherent light, such as the modified Bessel-Gussian (MBG ) beam, J₀-correlated Schell-model (JSM) beam, the propagation properties, the focusing properties passing through a lens with spherical aberration and the spectrum properties through an aperture lens of partially coherent MBG beams are presented; the propagation and focal shift of JSM beams are discussed; the structure of the wavefront and transversal optical vortices in an interference field of two off-axis Gaussian beams are studied in this dissertation.The basic concepts and the theoretical methods of second-order coherent theory describing wave field such as the mutual coherent function and the complex degree of coherence in the space-time domain, the cross-spectral density function and the spectral degree of coherence in the space-frequency domain, the propagation equations and the theory of mode expansion are introduced. A comprehensive review of the basic analytical methods for the beam transformation including the matrix optics method, diffraction integral method and the criterion of the beam quality are presented. Several typical beam models for the partially coherent light are described: Gauss-Schell model beam, Bessel-Gaussian beam, MBG beam and JSM beam.Starting from the propagation law of partially coherent light, the analytical propagation equations of partially coherent MBG beams through a paraxial optical ABCD system are derived and illustrated with typical application examples. Furthermore, by using the intensity moments method and integral transformation technique, the important characteristic parameters, including the beam width, far-field divergence angle, m² factor and kurtosis parameter of partially coherent MBG beams, are expressed in a closed and simple form. As a result, some basic properties of MBG beams and the dependence of the M² factor and kurtosis parameter on the spectral degree of coherence and beam order are illustrated both analytically and numerically.Since 1986, Wolf shown that when the law of the scale law is not satisfied by the spectral degree of the partially coherent light sources, the spectrum of the light from the sources will change in the process of propagation. The mathematic-physics model which is most often used to study the changes of the spectrum is Gauss-Schell model. Based on the propagation theory of partially coherent light, the spectral shift and spectral switch of partially coherent modified Bessel-Gauss beams passing through an aperture lens are studied first time. Numerical results show that the spectral shift and spectral switch of partially coherent modified Bessel-Gauss beams are dependent upon the spectral degree of coherence, Fresnel number and truncation parameter. The number of spectral switches increases with increasing Fresnel number and truncation parameter, but decreases with increasing spectral degree of coherence. When the truncation parameter is larger than a certain value, the spectral switch disappears. For example, when the parameterξwhich specifies the spectral degree of coherence equals to 0.5, and the truncation parameter is larger than 2.2, the spectral switch disappears and there is only the blue shift.According to the propagation law of partially coherent light, the focusing of partially coherent MBG beam passing through a spherically aberration lens is studied. It is shown that, when the spectral degree of coherence is small, the real 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 real 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 real focal points move towards the geometrical focus and approaches a constant. When the Fresnel number of Gaussian beams equals to 1, the real focal position for the aberration-free case gradually approach 0.908 and is independent of the spectral degree of coherence. While the real focal positions corresponding to positive and negative spherical aberrations are dependent upon the spectral degree of coherence.JSM beams are a new type of beams. Palma et al studied the properties of the propagation of JSM in free space, Borghi et al discussed the generalization and the description of JSM beams by using the mode expansion theory. Based on the propagation law of partially coherent beams, the propagation equations of Jo-correlated Schell-model (JSM) beams through a paraxial optical ABCD system are derived and expressed in closed- form for the first time. The free-space propagation and focusing of JSM beams are regarded two special cases of our result. The focusing properties, in particular, the focal shift of JSM beams are studied, and illustrative numerical results are given. It is found that the focal shift of JSM beams, which is determined by an algebraic equation of the 3^rd order, increases with decreasing Fresnel number N and increasing parameterσ.In 2001, Ponomarenko introduced a new class of partially coherent beams with a separable phase, which can be expressed as an incoherent superposition of fully coherent Laguerre-Gauss modes. The new beams carry optical vortices and possess remarkable properties, for example, their spectral degree of coherence does not depend on the relative orientation of a pair of points at transversal plane. Since the strange properties from the phase singularities of beams, the dislocation of wave front and the optical vortices near the phase singularities can appear in this kind of beams, which may be used in atomic optics and biological optics, it has become one of the important research area of modern optics—singular optics. The structure of the wavefront and transversal optical vortices in an interference field of two off-axis Gaussian beams is studied in this dissertation. It is shown that the positions of phase saddles and vortices depend on the off-axis parameter, beam width, phase and relative amplitude of beams. The saddle can be located inside and outside vortices. For a certain value of the governing parameter, the saddle point coincides with the vortex. For off-axis beams, the collisions of the saddle point and vortex on both sides in the XZ cross-section do not occur at the same governing parameterη. Moreover, the x value corresponding to the collisions of saddle points is not equal to the x value corresponding to the collisions of vortices.