Study Of The Beam Characterization, Propagation And Spectrum Properties

The laser beam characterization and classification are topics refering to wide fields. It has not only the research sense of basic theories but also important practical values. Usually, the real laser beam is very complex. It could neither be completely described with a simple math-physics model nor be criticized its physics characteristics with a simple parameter. At the same time its transformation properties could not be expressed with a single formula. Only on the basis of research target and practical purpose could it be made to be similar and simple. According to the research, the anisotropic twisted Gaussion Schell-model beam is a better math-physics model to describe real lasers. So the research of its transformation properties and spectrum changes have much significance. In the usual lives, sometimes people prefer to obtain the beam of single form of symmetric properties. So either how to diagonalize the general beam into undistorted and simple astigmatic beam without twist or how to symmetrize into stigmatic beam with twist is worth being further studied both theoretically and practically.A very interesting subject in Laser Optics, i.e. the laser beam characterization and classification, is discussed. The current classification of laser beams is reviewed.Based on the second-order moments method and Wigner distribution function, and in accordance with their spatial symmetry, laser beams can be classified as three types, i.e. stigmatic (ST) beams, simple astigmatic (SA) beams and general astigmatic (GA) beams. On the other hand, according to their spatial coherence, there are two types of laser beams, namely, partially coherent beams and fully coherent beams. The independent characteristic parameters of different types of laser beams and their relation are analyzed.Based on the laser beam classification in accordance with the special symmetry and spatial coherence, the parametric characterization of laser beams is studied. The anisotropic twisted Gaussion Schell-model beam, isotropic twisted Gaussian Schell-model beam, anisotropic Gaussian Schell-model beam, rotated astigmatic Gaussian Schell- model beam, aligned astigmatic Gaussian Schell- model beam, stigmatic Gaussian Schell- model beam, general astigmatic Gaussian beam, rotated astigmatic Gaussian beam, aligned astigmatic Gaussian beam, and stigmatic Gaussian beam are taken as typical illustrative examples, their classification and the number of independent beam parameters are analyzed. Some related problems are also discussed.Based on the 4x4 second-order moments matrix, the A42 factor and intrinsic astigmatism a of general optical beams are studied. The analytical expressions for the M2 factor and intrinsic astigmatism a of some typical types of beam, such as the general astigmatic beam, rotationally simple astigmatic beam, aligned simple astigmatic beam and stigmatic beam, are given and analyzed. It is shown that the twist results is an increase of the intrinsic astigmatism, but doesn't affect the M2 factor in general.Based on the propagation law of the second-order moments matrix, the twisted anisotropic Gaussian-schell model (AGSM) beams propagating in free space and focused by a lens are studied. The explicit propagation equations of beam parameters and detailed numerical calculation results are given to illustrate the propagation properties of AGSM beams and focused AGSM beams. In particular,the influence of twist term and spatial correlation length on their properties is analyzed.On the basis of the Wigner distribution function and second-order moments matrix methods, the diagonalization and symmetrization of anisotropic twisted Gaussian Schell-model beams are studied. The synthesis procedure' for AGSM beams is described and illustrated with numerical examples. It is shdwn that an AGSM beam can be transformed into an aligned simple astigmatic (ASA) beam by four steps and then transformed into a stigmatic beam with twist by subsequent two steps.By using the Wigner distribution function, a general closed-form expression for the spectrum of AGSM...