A quasi-discrete Hankel transform for nonlinear beam propagation
You Kai-Ming(游开明)a)c), Wen Shuang-Chun(文双春)a)b)†, Chen Lie-Zun(陈列尊)b)c), Wang You-Wen(王友文)b)c), and Hu Yong-Hua(胡勇华)b)
a School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China; b Key Laboratory of Micro/Nano Optoelectronic Devices of Ministry of Education, School of Computer and Communication, Hunan University, Changsha 410082, China; c Department of Physics and Electronic Information Science, Hengyang Normal University, Hengyang 421008, China
Abstract 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 $J'_0(0)=0$, 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 Parseval 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.
Received: 16 December 2008
Revised: 08 January 2009
Accepted manuscript online:
PACS:
42.65.Hw
(Phase conjugation; photorefractive and Kerr effects)
Fund: Project partially supported by the
National Natural Science Foundation of China (Grant Nos 10674045 and
60538010), and the National Natural Science Foundation of Hunan
Province, China (Grant
No 08jj3001).
Cite this article:
You Kai-Ming(游开明), Wen Shuang-Chun(文双春), Chen Lie-Zun(陈列尊), Wang You-Wen(王友文), and Hu Yong-Hua(胡勇华) A quasi-discrete Hankel transform for nonlinear beam propagation 2009 Chin. Phys. B 18 3893
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