Abstract

Controlling the trajectory of circular Airy beams (CABs) by negative launch angles would greatly reduce their abruptly autofocusing property. By numerically simulating the propagation of a circular Airy vortex beam with different initial launch angles, we demonstrate in this paper that a larger topological charge of optical vortex (OV) is quite helpful to enhance the abruptly autofocusing property under different launch angles (especially for negative launch angles), without affecting the focal position and trajectory. Two opposite OVs would attract each other and partially overlap in the focal plane of CAB under different launch angles, causing even stronger autofocusing. As the distance between two OVs increases, the focal intensity contrast would decrease, especially for a beam with positive launch angles, whose autofocusing property decreases much more quickly with the distance.

© 2018 Optical Society of America

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References

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    [Crossref]
  2. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
    [Crossref]
  3. I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675–3677 (2011).
    [Crossref]
  4. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
    [Crossref]
  5. Y. Jiang, K. Huang, and X. Lu, “Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle,” Opt. Express 21, 24413–24421 (2013).
    [Crossref]
  6. Y. Jiang, Z. Cao, H. Shao, W. Zheng, B. Zeng, and X. Lu, “Trapping two types of particles by modified circular Airy beams,” Opt. Express 24, 18072–18081 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  15. S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416–2418 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  20. B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18, 055504 (2016).
    [Crossref]
  21. I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36, 1890–1892 (2011).
    [Crossref]
  22. I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85, 023828 (2012).
    [Crossref]
  23. P. Vaveliuk, A. Lencina, J. A. Rodrigo, and O. M. Matos, “Symmetric Airy beams,” Opt. Lett. 39, 2370–2373 (2014).
    [Crossref]
  24. R.-S. Penciu, K. G. Makris, and N. K. Efremidis, “Nonparaxial abruptly autofocusing beams,” Opt. Lett. 41, 1042–1045 (2016).
    [Crossref]
  25. Z. Zhao, C. Xie, D. Ni, Y. Zhang, Y. Li, F. Courvoisier, and M. Hu, “Scaling the abruptly autofocusing beams in the direct-space,” Opt. Express 25, 30598–30605 (2017).
    [Crossref]
  26. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008).
    [Crossref]
  27. L. Yu, M. Huang, M. Chen, W. Chen, W. Huang, and Z. Zhu, “Quasi-discrete Hankel transform,” Opt. Lett. 23, 409–411 (1998).
    [Crossref]
  28. M. Guizar-Sicairos and J. C. Gutiérrez-Vega, “Computation of quasi-discrete Hankel transforms of integer order for propagating optical wave fields,” J. Opt. Soc. Am. A 21, 53–58 (2004).
    [Crossref]
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    [Crossref]

2017 (6)

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase memory preserving harmonics from abruptly autofocusing beams,” Phys. Rev. Lett. 119, 223901 (2017).
[Crossref]

C. Liu, J. Liu, L. Niu, X. Wei, K. Wang, and Z. Yang, “Terahertz circular Airy vortex beams,” Sci. Rep. 7, 3891 (2017).
[Crossref]

J. Zhang, Y. Li, Z. Tian, and D. Lei, “Controllable autofocusing properties of conical circular Airy beams,” Opt. Commun. 391, 116–120 (2017).
[Crossref]

M. Chen, S. Huang, and W. Shao, “Tight focusing of radially polarized circular Airy vortex beams,” Opt. Commun. 402, 672–677 (2017).
[Crossref]

D. Ye, X. Peng, M. Zhou, Y. Xin, and M. Song, “Simulation of generation and dynamics of polarization singularities with circular Airy beams,” J. Opt. Soc. Am. A 34, 1957–1960 (2017).
[Crossref]

Z. Zhao, C. Xie, D. Ni, Y. Zhang, Y. Li, F. Courvoisier, and M. Hu, “Scaling the abruptly autofocusing beams in the direct-space,” Opt. Express 25, 30598–30605 (2017).
[Crossref]

2016 (3)

2015 (2)

2014 (2)

2013 (4)

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416–2418 (2013).
[Crossref]

Y. Jiang, K. Huang, and X. Lu, “Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle,” Opt. Express 21, 24413–24421 (2013).
[Crossref]

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref]

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013).
[Crossref]

2012 (3)

2011 (4)

2010 (1)

2008 (1)

2004 (1)

1998 (1)

1993 (1)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[Crossref]

Broky, J.

Cao, Z.

Chen, B.

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18, 055504 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, and D. Deng, “Propagation of sharply autofocused ring Airy Gaussian vortex beams,” Opt. Express 23, 19288–19298 (2015).
[Crossref]

Chen, C.

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18, 055504 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, and D. Deng, “Propagation of sharply autofocused ring Airy Gaussian vortex beams,” Opt. Express 23, 19288–19298 (2015).
[Crossref]

Chen, M.

M. Chen, S. Huang, and W. Shao, “Tight focusing of radially polarized circular Airy vortex beams,” Opt. Commun. 402, 672–677 (2017).
[Crossref]

L. Yu, M. Huang, M. Chen, W. Chen, W. Huang, and Z. Zhu, “Quasi-discrete Hankel transform,” Opt. Lett. 23, 409–411 (1998).
[Crossref]

Chen, W.

Chen, Z.

Chremmos, I.

Chremmos, I. D.

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85, 023828 (2012).
[Crossref]

Christodoulides, D. N.

Cottrell, D. M.

Couairon, A.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref]

Courvoisier, F.

Davis, J. A.

Deng, D.

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18, 055504 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, and D. Deng, “Propagation of sharply autofocused ring Airy Gaussian vortex beams,” Opt. Express 23, 19288–19298 (2015).
[Crossref]

Dogariu, A.

Efremidis, N. K.

Fedorov, V. Y.

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase memory preserving harmonics from abruptly autofocusing beams,” Phys. Rev. Lett. 119, 223901 (2017).
[Crossref]

Gan, X.

Guizar-Sicairos, M.

Guo, H.

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18, 055504 (2016).
[Crossref]

Gutiérrez-Vega, J. C.

Hu, M.

Huang, K.

Huang, M.

Huang, S.

M. Chen, S. Huang, and W. Shao, “Tight focusing of radially polarized circular Airy vortex beams,” Opt. Commun. 402, 672–677 (2017).
[Crossref]

Huang, W.

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[Crossref]

Jiang, Y.

Koulouklidis, A. D.

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase memory preserving harmonics from abruptly autofocusing beams,” Phys. Rev. Lett. 119, 223901 (2017).
[Crossref]

Lei, D.

J. Zhang, Y. Li, Z. Tian, and D. Lei, “Controllable autofocusing properties of conical circular Airy beams,” Opt. Commun. 391, 116–120 (2017).
[Crossref]

Lencina, A.

Li, P.

Li, Y.

Z. Zhao, C. Xie, D. Ni, Y. Zhang, Y. Li, F. Courvoisier, and M. Hu, “Scaling the abruptly autofocusing beams in the direct-space,” Opt. Express 25, 30598–30605 (2017).
[Crossref]

J. Zhang, Y. Li, Z. Tian, and D. Lei, “Controllable autofocusing properties of conical circular Airy beams,” Opt. Commun. 391, 116–120 (2017).
[Crossref]

Liu, C.

C. Liu, J. Liu, L. Niu, X. Wei, K. Wang, and Z. Yang, “Terahertz circular Airy vortex beams,” Sci. Rep. 7, 3891 (2017).
[Crossref]

Liu, J.

C. Liu, J. Liu, L. Niu, X. Wei, K. Wang, and Z. Yang, “Terahertz circular Airy vortex beams,” Sci. Rep. 7, 3891 (2017).
[Crossref]

Liu, S.

Lu, X.

Makris, K. G.

Matos, O. M.

Mills, M. S.

Ni, D.

Niu, L.

C. Liu, J. Liu, L. Niu, X. Wei, K. Wang, and Z. Yang, “Terahertz circular Airy vortex beams,” Sci. Rep. 7, 3891 (2017).
[Crossref]

Paltoglou, V.

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013).
[Crossref]

Panagiotopoulos, P.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref]

Papazoglou, D. G.

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase memory preserving harmonics from abruptly autofocusing beams,” Phys. Rev. Lett. 119, 223901 (2017).
[Crossref]

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref]

Penciu, R.-S.

Peng, T.

Peng, X.

Peng, Y.

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18, 055504 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, and D. Deng, “Propagation of sharply autofocused ring Airy Gaussian vortex beams,” Opt. Express 23, 19288–19298 (2015).
[Crossref]

Prakash, J.

Rodrigo, J. A.

Sand, D.

Shao, H.

Shao, W.

M. Chen, S. Huang, and W. Shao, “Tight focusing of radially polarized circular Airy vortex beams,” Opt. Commun. 402, 672–677 (2017).
[Crossref]

Siviloglou, G. A.

Song, M.

Tian, Z.

J. Zhang, Y. Li, Z. Tian, and D. Lei, “Controllable autofocusing properties of conical circular Airy beams,” Opt. Commun. 391, 116–120 (2017).
[Crossref]

Tzortzakis, S.

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase memory preserving harmonics from abruptly autofocusing beams,” Phys. Rev. Lett. 119, 223901 (2017).
[Crossref]

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref]

Vaveliuk, P.

von Klitzing, W.

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013).
[Crossref]

Wang, K.

C. Liu, J. Liu, L. Niu, X. Wei, K. Wang, and Z. Yang, “Terahertz circular Airy vortex beams,” Sci. Rep. 7, 3891 (2017).
[Crossref]

Wang, M.

Wei, X.

C. Liu, J. Liu, L. Niu, X. Wei, K. Wang, and Z. Yang, “Terahertz circular Airy vortex beams,” Sci. Rep. 7, 3891 (2017).
[Crossref]

Xie, C.

Xie, G.

Xin, Y.

Yang, Z.

C. Liu, J. Liu, L. Niu, X. Wei, K. Wang, and Z. Yang, “Terahertz circular Airy vortex beams,” Sci. Rep. 7, 3891 (2017).
[Crossref]

Ye, D.

Yu, L.

Yu, W.

Zeng, B.

Zhang, J.

J. Zhang, Y. Li, Z. Tian, and D. Lei, “Controllable autofocusing properties of conical circular Airy beams,” Opt. Commun. 391, 116–120 (2017).
[Crossref]

Zhang, P.

Zhang, Y.

Zhang, Z.

Zhao, J.

Zhao, Z.

Zheng, W.

Zhou, M.

Zhu, X.

Zhu, Z.

J. Mod. Opt. (1)

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[Crossref]

J. Opt. (1)

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18, 055504 (2016).
[Crossref]

J. Opt. Soc. Am. A (2)

Nat. Commun. (1)

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref]

Opt. Commun. (2)

M. Chen, S. Huang, and W. Shao, “Tight focusing of radially polarized circular Airy vortex beams,” Opt. Commun. 402, 672–677 (2017).
[Crossref]

J. Zhang, Y. Li, Z. Tian, and D. Lei, “Controllable autofocusing properties of conical circular Airy beams,” Opt. Commun. 391, 116–120 (2017).
[Crossref]

Opt. Express (8)

Opt. Lett. (10)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33, 207–209 (2008).
[Crossref]

L. Yu, M. Huang, M. Chen, W. Chen, W. Huang, and Z. Zhu, “Quasi-discrete Hankel transform,” Opt. Lett. 23, 409–411 (1998).
[Crossref]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36, 1890–1892 (2011).
[Crossref]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and O. M. Matos, “Symmetric Airy beams,” Opt. Lett. 39, 2370–2373 (2014).
[Crossref]

R.-S. Penciu, K. G. Makris, and N. K. Efremidis, “Nonparaxial abruptly autofocusing beams,” Opt. Lett. 41, 1042–1045 (2016).
[Crossref]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref]

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36, 3675–3677 (2011).
[Crossref]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref]

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416–2418 (2013).
[Crossref]

Phys. Rev. A (2)

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87, 043637 (2013).
[Crossref]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85, 023828 (2012).
[Crossref]

Phys. Rev. Lett. (1)

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase memory preserving harmonics from abruptly autofocusing beams,” Phys. Rev. Lett. 119, 223901 (2017).
[Crossref]

Sci. Rep. (1)

C. Liu, J. Liu, L. Niu, X. Wei, K. Wang, and Z. Yang, “Terahertz circular Airy vortex beams,” Sci. Rep. 7, 3891 (2017).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Intensity distributions of CAVBs with different launch angles in the input plane: (a) n=0; (b) n=1; (c) n=2. (d) Amplitude distribution. Corresponding parameters are r0=1  mm, w=80  μm, a=0.1.
Fig. 2.
Fig. 2. Abruptly autofocusing property of CAVBs with different initial launch angles under different decaying factors: left column [(a), (c), (e), (g)] a=0.1; right column [(b), (d), (f), (h)] a=0.05, and different topological charges: (a), (b) n=0; (c), (d) n=1; (e), (f) n=2; (g), (h) n=3.
Fig. 3.
Fig. 3. Intensity profiles of a CAVB in the focal plane: (a) n=1; (b) n=3. Other parameters are the same as in Fig. 1.
Fig. 4.
Fig. 4. Parabolic trajectories of CAVBs with different launch angles: (a) v=2; (b) v=1. Other parameters are the same as in Fig. 1.
Fig. 5.
Fig. 5. (a) Intensity profile and (b)–(d) phase patterns of a CAVB imposed by two opposite OVs: (b) v=2; (c) v=0; (d) v=1. Corresponding parameters are n=1, rk=0.5  mm, r0=1  mm, w=80  μm, a=0.1.
Fig. 6.
Fig. 6. (a)–(c) Intensity profiles and (d)–(f) phase patterns of a CVAB with two opposite OVs in the focal plane. (a),(d) v=2; (b),(e) v=0; (c),(f) v=1. The inset arrows denote the positions of the two OVs.
Fig. 7.
Fig. 7. Abruptly autofocusing property of a CVAB with two opposite OVs located at different positions: (a) rk=0.2  mm; (b) rk=0.5  mm; (c) rk=0.8  mm. Other parameters are the same as in Fig. 5.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

u(r,ϕ)=CAi(r0rw)exp(ar0rw)exp(ivr0rw)×(reiϕrkeiϕk)n,
u(r,ϕ,z)=2πeinϕ0g˜(k)Jn(2πkr)e2iπzλ2k2dk,
g˜(k)=2π0g(r)Jn(2πkr)rdr,
u(r,ϕ)=CAi(r0rw)exp(ar0rw)exp(ivr0rw)×(reiϕrk)n(reiϕ+rk)n.

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