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The Application of Expanded form of Complex Gaussian Function to Study Propagation and Transformation of Laser Beams

Author: TuHaiHua
Tutor: TaoXiangYang
School: Jiangxi Normal University
Course: Theoretical Physics
Keywords: Laser beam A paraxial ABCD Optical System : Collins formula Complex Gaussian function expansion method Recursive method
CLC: O437
Type: Master's thesis
Year: 2004
Downloads: 186
Quote: 0
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Abstract


The laser beam transmission and transformation of the topics at the forefront in the field of laser technology research, such as the laser beam through a paraxial ABCD optical system, transmission and transformation characteristics is an important topic. 1970 Collins complex optical system diffraction integral with ABCD matrix elements linked deduced Collins formula provides an effective tool to study the beam through a paraxial ABCD optical system, transmission and transformation. So far, many literature from the Collins integral formula, the various types of beam diaphragm or aperture diffraction effects can be ignored in case of transmission and transformation of extensive research has been carried out. However, the transmission of the laser beam is often limited by the diaphragm aperture diffraction effects on the beam characteristics can not be ignored, so limited by apertures of the laser beam transmission and transformation of research is necessary. In recent years, limited by apertures of the laser beam transmission and transformation of research mainly looking for resolution or approximate analytical formula, analytical formulas physical meaning not only directly, but also to facilitate the transmission of the beam in the applied single-aperture system or multi-stop system provide scientific and transform to solve, especially in the study of beam transmission and switching problems in a multi-aperture optical system can save a large number of the computer, so as to actual optical system design and implementation. Papers on laser beam by the transmission characteristics of the apertured conducted in-depth research. Its main tasks are: complex Gaussian function expansion method model of the Gaussian beam, Hermite - Gaussian (HG) beams, Laguerre - Gaussian (LG) beams through a paraxial ABCD optical system limited by apertures transmission characteristics, derived the beam transmission and transformation of the analytical formula, thus greatly reduce the computing time on a small computer. Complex Gaussian function expansion method models the physical explanation of the complex constants of the complex Gaussian function with a clear physical meaning. Complex Gaussian function expansion complex constant, to find a new set of complex constants, new parameters than literature in describing door function parameters is more accurate, more flat, compared the results with the direct integration of the Collins formula analytic formulas using the obtained results in the new parameter calculating the error is smaller. Hermite - Gaussian (HG) beams through a paraxial ABCD optical system limited by apertures characteristics of the transmission and transformation of by Hermite polynomials recursive form, with the iterative algorithm, obtained Hermite with recursive method - Gaussian (HG) beams through a paraxial ABCD optical system limited by apertures resolution formula.

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CLC: > Mathematical sciences and chemical > Physics > Optics > Nonlinear optical ( light and matter)
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