A quasi-discrete Hankel transform for nonlinear beam propagation  

作　　者：游开明 文双春 陈列尊 王友文 胡勇华 

机构地区：[1]School of Information Engineering,Wuhan University of Technology [2]Department of Physics and Electronic Information Science,Hengyang Normal University [3]Key Laboratory of Micro/Nano Optoelectronic Devices of Ministry of Education,School of Computer and Communication,Hunan University

出　　处：《Chinese Physics B》2009年第9期3893-3899,共7页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos 10674045 and 60538010);the National Natural Science Foundation of Hunan Province,China (Grant No 08jj3001)

摘　　要：We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.

关 键 词：Hankel transform Kerr medium nonlinear propagation 

分 类 号：O437[机械工程—光学工程]