A quasi-discrete Hankel transform for nonlinear beam propagation |
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Authors: | You Kai-Ming Wen Shuang-Chun Chen Lie-Zun Wang You-Wen and Hu Yong-Hua |
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Institution: | School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China; Key Laboratory of Micro/Nano Optoelectronic Devices of Ministry of Education, School of Computer and Communication, Hunan University, Changsha 410082, China; Department of Physics and Electronic Information Science, Hengyang Normal University, Hengyang 421008, China |
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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. |
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Keywords: | Hankel transform Kerr medium nonlinear propagation |
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