The fast Fourier transform for optical beam propagation
| Autor: | Cheng Chia, 陳政嘉 |
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| Rok vydání: | 2005 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 93 In order to analyze the Z-scan experimental results, we need to deal with the propagation of distorted mode laser beams in the free space. As Huygens-Fresnel principle has long been used to handle wave propagation, we substitute into the Huygens-Fresnel integral the spatial distributions of intensity and phase (or correspondingly the electric field) of a laser beam at the exit surface of the sample to calculate the intensity distribution at the aperture. In this thesis, we write two different programs to perform this integral. The first one directly executes this integral in cylindrical coordinates and the second one regards the Huygens-Fresnel integral as a two dimensional convolutions and then use the fast Fourier transform (FFT) technique to execute one forward and one reverse transform to complete the integral. To test these two programs, we substitute the distributions of intensities and phases, or correspondingly the electric fields, of a mode laser beam at several different z positions relative to the beam waist into the integral to calculate the intensity distributions at other z positions. We then compare the numerical results with the analytical results derived according to the Gauss beam formula. In the following chapters, we show the comparisons of program generated results and the analytical results. Also, we discuss how to adjust the parameters to maximize the accuracy of the programs. Since our programs generate results highly close to the analytical results, we are going to use it to deal with the propagation of distorted mode laser beam in the near future. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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