The Application Of Expanded Form Of Complex Gaussian Function To Study Propagation And Transformation Of Laser Beams

The propagation and transformation of laser beams is an advanced subject in the field of high-power lasers technology. To study the properties of propagation and transformation passing through a paraxial ABCD optical system is one of the most important problems. The Collins formula (1970) contacts the diffract integral of optical system complex with ABCD matrix and provides a mathematics tool for studying laser beams passing through paraxial ABCD optical system. Up to now, by using the Collins formula, the problem of propagation and transformation of all kinds of laser beams in the case of un-apertured or ignoring the effect of diffraction of aperture has been discussed in many literatures. However, the effect of aperture diffraction on beams is not able to neglected because the aperture confines the propagation of laser beams. Recently, the study of propagation and transformation of apertured laser beams is focused on looking for analytical expression or approximate analytical expression. Analytical expression has immediate physical meaning, and it not only facilitates the study to the problem of propagation and transformation of the system of single-aperture or the system of multi-aperture, but also saves computational time in studying the problem of propagation and transformation of the system of multi-aperture. Moreover, it offers scientific references to designation and realization of the practical optical system.This thesis researches the propagation that apertured laser beams by using complex Gaussian function. The thesis studies the character of propagation of Gaussian beam, Hermite-Gaussian beams, Laguerre-Gaussian beams passing through the paraxial ABCD optical system with hard-edged apertures, derives the analytical expression of laser beams, which saves much, time of operation in the microcomputer. At the same time, this thesis gives a physical explain for theexpanded form of complex Gaussian function and makes out the signification of the complex constant of complex Gaussian function in physics. The studies to the complex constant of complex Gaussian function helps to find a set of new complex constant which pictures the rectangle function more precisely than the one offered by literature, and which can find a good consistent with those by straightforward integral of the Collins formula. At last, with the recurrence algorithm, the character of propagation of Hermite-Gaussian beams passing through the paraxial ABCD optical system with a hard-edged aperture is also analyzed and the analytical expression is derived...