Please wait a minute...
Chin. Phys. B, 2009, Vol. 18(9): 3893-3899    DOI: 10.1088/1674-1056/18/9/046
CLASSICAL AREAS OF PHENOMENOLOGY Prev   Next  

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.
Keywords:  Hankel transform      Kerr medium      nonlinear propagation  
Received:  16 December 2008      Revised:  08 January 2009      Accepted manuscript online: 
PACS:  42.65.Hw (Phase conjugation; photorefractive and Kerr effects)  
  02.30.Gp (Special functions)  
  02.30.Uu (Integral transforms)  
  42.25.Bs (Wave propagation, transmission and absorption)  
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

[1] Nonlinear propagation of an intense Laguerre-Gaussian laser pulse in a plasma channel
Mingping Liu(刘明萍), Zhen Zhang(张震), and Suhui Deng(邓素辉). Chin. Phys. B, 2021, 30(5): 055204.
[2] Fractional squeezing-Hankel transform based on the induced entangled state representations
Cui-Hong Lv(吕翠红), Su-Qing Zhang(张苏青), Wen Xu(许雯). Chin. Phys. B, 2018, 27(9): 094206.
[3] Entanglement of two two-level atoms trapped in coupled cavities with a Kerr medium
Wu Qin (吴琴), Zhang Zhi-Ming (张智明). Chin. Phys. B, 2014, 23(3): 034203.
[4] Enhancing stationary optomechanical entanglement with Kerr medium
Zhang Dan (张丹), Zhang Xiao-Ping (张小平), Zheng Qiang (郑强). Chin. Phys. B, 2013, 22(6): 064206.
[5] Partial entropy change and entanglement in the mixed state for a Jaynes-Cummings model with Kerr medium
Zhang Yu-Qing(张玉青), Tan Lei(谭磊), Zhu Zhong-Hua(朱中华), Xiong Zu-Zhou(熊祖周), and Liu Li-Wei(刘利伟). Chin. Phys. B, 2010, 19(2): 024210.
[6] Nonlinear images of scatterers in chirped pulsed laser beams
Hu Yong-Hua(胡勇华), Wang You-Wen(王友文), Wen Shuang-Chun(文双春), and Fan Dian-Yuan(范滇元). Chin. Phys. B, 2010, 19(11): 114207.
[7] Self-compression of femtosecond pulses in argon with a power close to the self-focusing threshold
Chen Xiao-Wei(陈晓伟), Zeng Zhi-Nan(曾志男), Dai Jun(戴君), Li Xiao-Fang(李小芳), Li Ru-Xin(李儒新), and Xu Zhi-Zhan(徐至展) . Chin. Phys. B, 2008, 17(5): 1826-1832.
[8] Fidelity of quantum information for V-type three-level atom interacting with a number state light field in Kerr medium
Liu Su-Mei(刘素梅), He An-Zhi(贺安之), and Ji Yun-Jing(纪运景). Chin. Phys. B, 2008, 17(4): 1248-1253.
[9] (3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material
Hu Yong-Hua(胡勇华), Fu Xi-Quan(傅喜泉), Wen Shuang-Chun(文双春), Su Wen-Hua(苏文华), and Fan Dian-Yuan(范滇元). Chin. Phys. B, 2006, 15(12): 2970-2976.
[10] Entropy evolution properties in a system of two entangled atoms interacting with light field
Liu Tang-Kun (刘堂昆), Wang Ji-Suo (王继锁), Feng Jian (冯健), Zhan Ming-Sheng (詹明生). Chin. Phys. B, 2005, 14(3): 536-540.
[11] Photon statistics of the micromaser with a Kerr medium
Wu Shu-Dong (吴曙东), Zhan Zhi-Ming (詹志明), Jin Li-Xia (金丽霞). Chin. Phys. B, 2002, 11(12): 1272-1275.
[12] FILAMENTATION INSTABILITY OF LASER BEAMS IN NONLOCAL NONLINEAR MEDIA
Wen Shuang-chun (文双春), Fan Dian-yuan (范滇元). Chin. Phys. B, 2001, 10(11): 1032-1036.
No Suggested Reading articles found!