Abstract

Three-dimensional chirped Airy Complex-variable-function Gaussian vortex (CACGV) wave packets in a strongly nonlocal nonlinear medium (SNNM) are studied. By varying the distribution parameter, CACGV wave packets can rotate stably in a SNNM in different forms, including dipoles, elliptic vortices, and doughnuts. Numerical simulation results for the CACGV wave packets agree well with theoretical analysis results under zero perturbation. The Poynting vector related to the physics of the rotation phenomenon and the angular momentum as a torque corresponding to the force are also presented. Finally, the radiation forces of CACGV wave packets acting on a nanoparticle in a SNNM are discussed.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Three-dimensional localized chirped Airy-circular wave packets in free space

Guanwen Zhao, Shijie Chen, Zhengzhong Huang, and Dongmei Deng
J. Opt. Soc. Am. A 35(9) 1645-1652 (2018)

Propagation properties of spatiotemporal chirped Airy Gaussian vortex wave packets in a quadratic index medium

Xi Peng, Yulian Peng, Dongdong Li, Liping Zhang, Jingli Zhuang, Fang Zhao, Xingyu Chen, Xiangbo Yang, and Dongmei Deng
Opt. Express 25(12) 13527-13538 (2017)

Three-dimensional localized Airy-Gaussian wave packets in a gradient-index medium

Zhanhong Li, Yangyang Gong, Zhengzhong Huang, Dongmei Deng, Rong Hu, and Shangyou Chen
J. Opt. Soc. Am. A 36(8) 1385-1394 (2019)

References

  • View by:
  • |
  • |
  • |

  1. D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
    [Crossref]
  2. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
    [Crossref]
  3. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
    [Crossref]
  4. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
    [Crossref]
  5. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
    [Crossref]
  6. J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13(2), 79–80 (1988).
    [Crossref]
  7. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
    [Crossref]
  8. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
    [Crossref]
  9. D. Bongiovanni, B. Wetzel, Y. Hu, Z. Chen, and R. Morandotti, “Optimal compression and energy confinement of optical Airy bullets,” Opt. Express 24(23), 26454–26463 (2016).
    [Crossref]
  10. W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
    [Crossref]
  11. Y. Peng, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Self-accelerating Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian light bullets in free space,” Opt. Express 24(17), 18973–18985 (2016).
    [Crossref]
  12. W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Airy-Tricomi-Gaussian compressed light bullets,” Eur. Phys. J. Plus 131(2), 42 (2016).
    [Crossref]
  13. X. Peng, Y. Peng, D. Li, L. Zhang, J. Zhuang, F. Zhao, X. Chen, X. Yang, and D. Deng, “Propagation properties of spatiotemporal chirped Airy Gaussian vortex wave packets in a quadratic index medium,” Opt. Express 25(12), 13527–13538 (2017).
    [Crossref]
  14. J. Zhuang, D. Deng, X. Chen, F. Zhao, X. Peng, D. Li, and L. Zhang, “Spatiotemporal sharply autofocused dual-Airy-ring Airy Gaussian vortex wave packets,” Opt. Lett. 43(2), 222–225 (2018).
    [Crossref]
  15. N. K. Efremidis, Z. Chen, M. Segev, and D. N. Christodoulides, “Airy beams and accelerating waves: an overview of recent advances,” Optica 6(5), 686–701 (2019).
    [Crossref]
  16. H. Nagar and Y. Roichman, “Deep-penetration fluorescence imaging through dense yeast cells suspensions using Airy beams,” Opt. Lett. 44(8), 1896–1899 (2019).
    [Crossref]
  17. B. Wei, S. Qi, S. Liu, P. Li, Y. Zhang, L. Han, J. Zhong, W. Hu, Y. Lu, and J. Zhao, “Auto-transition of vortex- to vector-Airy beams via liquid crystal q-Airy-plates,” Opt. Express 27(13), 18848–18857 (2019).
    [Crossref]
  18. R. Wang, S. He, S. Chen, J. Zhang, W. Shu, H. Luo, and S. Wen, “Electrically driven generation of arbitrary vector vortex beams on the hybrid-order Poincaré sphere,” Opt. Lett. 43(15), 3570–3573 (2018).
    [Crossref]
  19. X. Sui, J. Zhao, B. Liu, Z. Yan, C. Cao, and S. Zhou, “Self-accelerating fan-shaped beams along arbitrary trajectories: a new tool for optical manipulation,” J. Opt. 19(1), 015611 (2017).
    [Crossref]
  20. J. Zhou, Y. Liu, Y. Ke, H. Luo, and S. Wen, “Generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases,” Opt. Lett. 40(13), 3193–3196 (2015).
    [Crossref]
  21. P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channels generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
    [Crossref]
  22. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
    [Crossref]
  23. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27(16), 1460–1462 (2002).
    [Crossref]
  24. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
    [Crossref]
  25. C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91(7), 073901 (2003).
    [Crossref]
  26. C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in highly nonlocal medium,” Phys. Rev. Lett. 92(11), 113902 (2004).
    [Crossref]
  27. A. W. Snyder and D. J. Mitchell, “Accessible Solitons,” Science 276(5318), 1538–1541 (1997).
    [Crossref]
  28. D. Deng, Q. Guo, and W. Hu, “Complex-variable-function Gaussian beam in strongly nonlocal nonlinear media,” Phys. Rev. A 79(2), 023803 (2009).
    [Crossref]
  29. D. Deng, Q. Guo, and W. Hu, “Complex-variable-function-Gaussian solitons,” Opt. Lett. 34(1), 43–45 (2009).
    [Crossref]
  30. S. Lopez-Aguayo and J. C. Gutiérrez-Vega, “Elliptically modulated self-trapped singular beams in nonlocal nonlinear media: ellipticons,” Opt. Express 15(26), 18326–18338 (2007).
    [Crossref]
  31. W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 061801 (2007).
    [Crossref]
  32. G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).
    [Crossref]
  33. G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express 23(19), 24612–24625 (2015).
    [Crossref]
  34. Z. Dai, Z. Yang, S. Zhang, and Z. Pang, “Propagation of anomalous vortex beams in strongly nonlocal nonlinear media,” Opt. Commun. 350, 19–27 (2015).
    [Crossref]
  35. L. Song, Z. Yang, X. Li, and S. Zhang, “Controllable Gaussian-shaped soliton clusters in strongly nonlocal media,” Opt. Express 26(15), 19182–19198 (2018).
    [Crossref]
  36. F. Zang, Y. Wang, and L. Li, “Self-induced periodic interfering behavior of dual Airy beam in strongly nonlocal medium,” Opt. Express 27(10), 15079–15090 (2019).
    [Crossref]
  37. Z. Wu, Z. Wang, H. Guo, W. Wang, and Y. Gu, “Self-accelerating Airy-laguerre-Gaussian light bullets in a two-dimensional strongly nonlocal nonlinear medium,” Opt. Express 25(24), 30468–30478 (2017).
    [Crossref]
  38. O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66(4), 046619 (2002).
    [Crossref]
  39. Y. Zhang, M. Belić, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
    [Crossref]
  40. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  41. H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008).
    [Crossref]
  42. D. Deng and Q. Guo, “Airy complex variable function Gaussian beams,” New J. Phys. 11(10), 103029 (2009).
    [Crossref]
  43. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
    [Crossref]

2019 (4)

2018 (3)

2017 (3)

2016 (3)

2015 (5)

2014 (1)

G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).
[Crossref]

2010 (2)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

2009 (4)

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channels generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref]

D. Deng, Q. Guo, and W. Hu, “Complex-variable-function Gaussian beam in strongly nonlocal nonlinear media,” Phys. Rev. A 79(2), 023803 (2009).
[Crossref]

D. Deng, Q. Guo, and W. Hu, “Complex-variable-function-Gaussian solitons,” Opt. Lett. 34(1), 43–45 (2009).
[Crossref]

D. Deng and Q. Guo, “Airy complex variable function Gaussian beams,” New J. Phys. 11(10), 103029 (2009).
[Crossref]

2008 (3)

2007 (3)

2005 (2)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

2004 (1)

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in highly nonlocal medium,” Phys. Rev. Lett. 92(11), 113902 (2004).
[Crossref]

2003 (1)

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91(7), 073901 (2003).
[Crossref]

2002 (3)

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27(16), 1460–1462 (2002).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66(4), 046619 (2002).
[Crossref]

1997 (1)

A. W. Snyder and D. J. Mitchell, “Accessible Solitons,” Science 276(5318), 1538–1541 (1997).
[Crossref]

1996 (1)

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

1988 (1)

1979 (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

Alfano, R. R.

Asakura, T.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in highly nonlocal medium,” Phys. Rev. Lett. 92(11), 113902 (2004).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91(7), 073901 (2003).
[Crossref]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27(16), 1460–1462 (2002).
[Crossref]

Balazs, N. L.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Bang, O.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66(4), 046619 (2002).
[Crossref]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Belic, M.

Belic, M. R.

W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Airy-Tricomi-Gaussian compressed light bullets,” Eur. Phys. J. Plus 131(2), 42 (2016).
[Crossref]

W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
[Crossref]

Berry, M. V.

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Bongiovanni, D.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Broky, J.

Brzdakiewicz, K. A.

Buryak, A. V.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Cao, C.

X. Sui, J. Zhao, B. Liu, Z. Yan, C. Cao, and S. Zhou, “Self-accelerating fan-shaped beams along arbitrary trajectories: a new tool for optical manipulation,” J. Opt. 19(1), 015611 (2017).
[Crossref]

Cao, H.

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref]

Chen, B.

Chen, R.

G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).
[Crossref]

Chen, S.

Chen, X.

Chen, Z.

Cheng, W.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Christodoulides, D. N.

N. K. Efremidis, Z. Chen, M. Segev, and D. N. Christodoulides, “Airy beams and accelerating waves: an overview of recent advances,” Optica 6(5), 686–701 (2019).
[Crossref]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channels generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref]

Cohen, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in highly nonlocal medium,” Phys. Rev. Lett. 92(11), 113902 (2004).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91(7), 073901 (2003).
[Crossref]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Dai, Z.

Z. Dai, Z. Yang, S. Zhang, and Z. Pang, “Propagation of anomalous vortex beams in strongly nonlocal nonlinear media,” Opt. Commun. 350, 19–27 (2015).
[Crossref]

Deng, D.

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Dogariu, A.

Durnin, J.

Eberly, J. H.

Efremidis, N. K.

Gu, Y.

Guo, H.

Guo, Q.

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express 23(19), 24612–24625 (2015).
[Crossref]

D. Deng, Q. Guo, and W. Hu, “Complex-variable-function-Gaussian solitons,” Opt. Lett. 34(1), 43–45 (2009).
[Crossref]

D. Deng and Q. Guo, “Airy complex variable function Gaussian beams,” New J. Phys. 11(10), 103029 (2009).
[Crossref]

D. Deng, Q. Guo, and W. Hu, “Complex-variable-function Gaussian beam in strongly nonlocal nonlinear media,” Phys. Rev. A 79(2), 023803 (2009).
[Crossref]

Gutiérrez-Vega, J. C.

Han, L.

Harada, Y.

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

He, S.

Hu, W.

Hu, Y.

Ke, Y.

Koleskik, M.

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channels generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref]

Krolikowski, W.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66(4), 046619 (2002).
[Crossref]

Lederer, F.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Li, D.

Li, L.

Li, P.

Li, X.

Liang, G.

Liu, B.

X. Sui, J. Zhao, B. Liu, Z. Yan, C. Cao, and S. Zhou, “Self-accelerating fan-shaped beams along arbitrary trajectories: a new tool for optical manipulation,” J. Opt. 19(1), 015611 (2017).
[Crossref]

Liu, S.

Liu, Y.

Lopez-Aguayo, S.

Lu, Y.

Luo, H.

Malomed, B. A.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref]

Mazilu, D.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Miceli, J. J.

Mihalache, D.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, “Accessible Solitons,” Science 276(5318), 1538–1541 (1997).
[Crossref]

Moloney, J. V.

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channels generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref]

Morandotti, R.

Nagar, H.

Pang, Z.

Z. Dai, Z. Yang, S. Zhang, and Z. Pang, “Propagation of anomalous vortex beams in strongly nonlocal nonlinear media,” Opt. Commun. 350, 19–27 (2015).
[Crossref]

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in highly nonlocal medium,” Phys. Rev. Lett. 92(11), 113902 (2004).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91(7), 073901 (2003).
[Crossref]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27(16), 1460–1462 (2002).
[Crossref]

Peng, X.

Peng, Y.

Polynkin, P.

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channels generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref]

Qi, S.

Rasmussen, J. J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66(4), 046619 (2002).
[Crossref]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Roichman, Y.

Rotschild, C.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref]

Ru, G.

G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).
[Crossref]

Segev, M.

N. K. Efremidis, Z. Chen, M. Segev, and D. N. Christodoulides, “Airy beams and accelerating waves: an overview of recent advances,” Optica 6(5), 686–701 (2019).
[Crossref]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref]

Shu, W.

Siviloglou, G. A.

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, “Accessible Solitons,” Science 276(5318), 1538–1541 (1997).
[Crossref]

Song, L.

Sui, X.

X. Sui, J. Zhao, B. Liu, Z. Yan, C. Cao, and S. Zhou, “Self-accelerating fan-shaped beams along arbitrary trajectories: a new tool for optical manipulation,” J. Opt. 19(1), 015611 (2017).
[Crossref]

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

Sztul, H. I.

Torner, L.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Torres, J. P.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Towers, I.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

Wang, R.

Wang, W.

Wang, Y.

Wang, Z.

Wei, B.

Wen, S.

Wetzel, B.

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Wu, P.

Wu, Z.

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66(4), 046619 (2002).
[Crossref]

Yan, Z.

X. Sui, J. Zhao, B. Liu, Z. Yan, C. Cao, and S. Zhou, “Self-accelerating fan-shaped beams along arbitrary trajectories: a new tool for optical manipulation,” J. Opt. 19(1), 015611 (2017).
[Crossref]

Yang, X.

Yang, Z.

L. Song, Z. Yang, X. Li, and S. Zhang, “Controllable Gaussian-shaped soliton clusters in strongly nonlocal media,” Opt. Express 26(15), 19182–19198 (2018).
[Crossref]

Z. Dai, Z. Yang, S. Zhang, and Z. Pang, “Propagation of anomalous vortex beams in strongly nonlocal nonlinear media,” Opt. Commun. 350, 19–27 (2015).
[Crossref]

Yi, L.

W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 061801 (2007).
[Crossref]

Yin, N.

Zang, F.

Zhang, J.

Zhang, L.

Zhang, S.

L. Song, Z. Yang, X. Li, and S. Zhang, “Controllable Gaussian-shaped soliton clusters in strongly nonlocal media,” Opt. Express 26(15), 19182–19198 (2018).
[Crossref]

Z. Dai, Z. Yang, S. Zhang, and Z. Pang, “Propagation of anomalous vortex beams in strongly nonlocal nonlinear media,” Opt. Commun. 350, 19–27 (2015).
[Crossref]

Zhang, Y.

Zhang, Y. Q.

W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Airy-Tricomi-Gaussian compressed light bullets,” Eur. Phys. J. Plus 131(2), 42 (2016).
[Crossref]

W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
[Crossref]

Zhao, F.

Zhao, J.

B. Wei, S. Qi, S. Liu, P. Li, Y. Zhang, L. Han, J. Zhong, W. Hu, Y. Lu, and J. Zhao, “Auto-transition of vortex- to vector-Airy beams via liquid crystal q-Airy-plates,” Opt. Express 27(13), 18848–18857 (2019).
[Crossref]

X. Sui, J. Zhao, B. Liu, Z. Yan, C. Cao, and S. Zhou, “Self-accelerating fan-shaped beams along arbitrary trajectories: a new tool for optical manipulation,” J. Opt. 19(1), 015611 (2017).
[Crossref]

Zhong, J.

Zhong, W.

Zhong, W. P.

W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Airy-Tricomi-Gaussian compressed light bullets,” Eur. Phys. J. Plus 131(2), 42 (2016).
[Crossref]

W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
[Crossref]

Zhou, G.

G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).
[Crossref]

Zhou, J.

Zhou, M.

Zhou, S.

X. Sui, J. Zhao, B. Liu, Z. Yan, C. Cao, and S. Zhou, “Self-accelerating fan-shaped beams along arbitrary trajectories: a new tool for optical manipulation,” J. Opt. 19(1), 015611 (2017).
[Crossref]

Zhu, D.

Zhuang, J.

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47(3), 264–267 (1979).
[Crossref]

Eur. Phys. J. Plus (1)

W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Airy-Tricomi-Gaussian compressed light bullets,” Eur. Phys. J. Plus 131(2), 42 (2016).
[Crossref]

J. Opt. (1)

X. Sui, J. Zhao, B. Liu, Z. Yan, C. Cao, and S. Zhou, “Self-accelerating fan-shaped beams along arbitrary trajectories: a new tool for optical manipulation,” J. Opt. 19(1), 015611 (2017).
[Crossref]

J. Opt. B: Quantum Semiclassical Opt. (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Laser Phys. Lett. (1)

G. Zhou, R. Chen, and G. Ru, “Propagation of an Airy beam in a strongly nonlocal nonlinear media,” Laser Phys. Lett. 11(10), 105001 (2014).
[Crossref]

Nat. Photonics (2)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

New J. Phys. (1)

D. Deng and Q. Guo, “Airy complex variable function Gaussian beams,” New J. Phys. 11(10), 103029 (2009).
[Crossref]

Opt. Commun. (2)

Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124(5-6), 529–541 (1996).
[Crossref]

Z. Dai, Z. Yang, S. Zhang, and Z. Pang, “Propagation of anomalous vortex beams in strongly nonlocal nonlinear media,” Opt. Commun. 350, 19–27 (2015).
[Crossref]

Opt. Express (12)

L. Song, Z. Yang, X. Li, and S. Zhang, “Controllable Gaussian-shaped soliton clusters in strongly nonlocal media,” Opt. Express 26(15), 19182–19198 (2018).
[Crossref]

F. Zang, Y. Wang, and L. Li, “Self-induced periodic interfering behavior of dual Airy beam in strongly nonlocal medium,” Opt. Express 27(10), 15079–15090 (2019).
[Crossref]

Z. Wu, Z. Wang, H. Guo, W. Wang, and Y. Gu, “Self-accelerating Airy-laguerre-Gaussian light bullets in a two-dimensional strongly nonlocal nonlinear medium,” Opt. Express 25(24), 30468–30478 (2017).
[Crossref]

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express 23(19), 24612–24625 (2015).
[Crossref]

S. Lopez-Aguayo and J. C. Gutiérrez-Vega, “Elliptically modulated self-trapped singular beams in nonlocal nonlinear media: ellipticons,” Opt. Express 15(26), 18326–18338 (2007).
[Crossref]

X. Peng, Y. Peng, D. Li, L. Zhang, J. Zhuang, F. Zhao, X. Chen, X. Yang, and D. Deng, “Propagation properties of spatiotemporal chirped Airy Gaussian vortex wave packets in a quadratic index medium,” Opt. Express 25(12), 13527–13538 (2017).
[Crossref]

D. Bongiovanni, B. Wetzel, Y. Hu, Z. Chen, and R. Morandotti, “Optimal compression and energy confinement of optical Airy bullets,” Opt. Express 24(23), 26454–26463 (2016).
[Crossref]

W. P. Zhong, M. R. Belić, and Y. Q. Zhang, “Three-dimensional localized Airy-Laguerre-Gaussian wave packets in free space,” Opt. Express 23(18), 23867–23876 (2015).
[Crossref]

Y. Peng, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Self-accelerating Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian light bullets in free space,” Opt. Express 24(17), 18973–18985 (2016).
[Crossref]

B. Wei, S. Qi, S. Liu, P. Li, Y. Zhang, L. Han, J. Zhong, W. Hu, Y. Lu, and J. Zhao, “Auto-transition of vortex- to vector-Airy beams via liquid crystal q-Airy-plates,” Opt. Express 27(13), 18848–18857 (2019).
[Crossref]

Y. Zhang, M. Belić, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
[Crossref]

H. I. Sztul and R. R. Alfano, “The Poynting vector and angular momentum of Airy beams,” Opt. Express 16(13), 9411–9416 (2008).
[Crossref]

Opt. Lett. (9)

D. Deng, Q. Guo, and W. Hu, “Complex-variable-function-Gaussian solitons,” Opt. Lett. 34(1), 43–45 (2009).
[Crossref]

R. Wang, S. He, S. Chen, J. Zhang, W. Shu, H. Luo, and S. Wen, “Electrically driven generation of arbitrary vector vortex beams on the hybrid-order Poincaré sphere,” Opt. Lett. 43(15), 3570–3573 (2018).
[Crossref]

J. Zhuang, D. Deng, X. Chen, F. Zhao, X. Peng, D. Li, and L. Zhang, “Spatiotemporal sharply autofocused dual-Airy-ring Airy Gaussian vortex wave packets,” Opt. Lett. 43(2), 222–225 (2018).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32(8), 979–981 (2007).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. 33(3), 207–209 (2008).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13(2), 79–80 (1988).
[Crossref]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, “Nonlocal spatial soliton interactions in nematic liquid crystals,” Opt. Lett. 27(16), 1460–1462 (2002).
[Crossref]

J. Zhou, Y. Liu, Y. Ke, H. Luo, and S. Wen, “Generation of Airy vortex and Airy vector beams based on the modulation of dynamic and geometric phases,” Opt. Lett. 40(13), 3193–3196 (2015).
[Crossref]

H. Nagar and Y. Roichman, “Deep-penetration fluorescence imaging through dense yeast cells suspensions using Airy beams,” Opt. Lett. 44(8), 1896–1899 (2019).
[Crossref]

Optica (1)

Phys. Rev. A (2)

D. Deng, Q. Guo, and W. Hu, “Complex-variable-function Gaussian beam in strongly nonlocal nonlinear media,” Phys. Rev. A 79(2), 023803 (2009).
[Crossref]

W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75(6), 061801 (2007).
[Crossref]

Phys. Rev. E (1)

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66(4), 046619 (2002).
[Crossref]

Phys. Rev. Lett. (5)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95(21), 213904 (2005).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91(7), 073901 (2003).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in highly nonlocal medium,” Phys. Rev. Lett. 92(11), 113902 (2004).
[Crossref]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, “Stable spinning optical solitons in three dimensions,” Phys. Rev. Lett. 88(7), 073902 (2002).
[Crossref]

Science (2)

A. W. Snyder and D. J. Mitchell, “Accessible Solitons,” Science 276(5318), 1538–1541 (1997).
[Crossref]

P. Polynkin, M. Koleskik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channels generation using ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref]

Other (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1. (a1)-(c1) Snapshots describing the initial CACGV wave packets $\Psi _{CAcosCGV}(X,Y,T,0)$ with different $b$. (a2)-(c2) The normalized intensity and (a3)-(c3) phase distributions of $\Psi _{CAcosCGV}(X,Y,0,0)$. $a=0.1$.
Fig. 2.
Fig. 2. Propagation dynamic of the 3D CAcosCGV wave packets with different chirp parameter. $c_{1}=-1$ and $c_{2}=0$ in the first row, $c_{1}=1$ and $c_{2}=0$ in the second row, $c_{1}=0$ and $c_{2}=-1$ in the third row. $b=1.5$.
Fig. 3.
Fig. 3. Snapshots describing the CAsinCGV wave packets $\Psi _{sin}(X,Y,T,Z)$. $b=1.5$ in the first row, $b=10$ in the second row. (b) and (e) $c_{1}=1$, $c_{2}=0$, (c) and (f) $c_{1}=0$, $c_{2}=-1$.
Fig. 4.
Fig. 4. Numerical simulation of snapshots describing the CAcosCGV (the first row) and CAsinCGV (the second row) wave packets in a SNNM. (a) and (d) $\delta =0$, (b) and (e) $\delta =0.003$, (c) and (f) $\delta =0.05$. $Z=2\pi /3$, $c_{1}=1$, $b=1.5$.
Fig. 5.
Fig. 5. Poynting vector of the CAcosCGV (the first row) and CAsinCGV (the second row) wave packets at different positions in a SNNM. $b=1.5$.
Fig. 6.
Fig. 6. Transverse angular momentum density of the CAcosCGV (the first row) and CAsinCGV (the second row) wave packets at different positions in a SNNM. $b=1.5$.
Fig. 7.
Fig. 7. The transverse patterns (background) and plots (white line) of the scattering force (the first row) and the gradient force (the second row) of the CAcosCGV wave packets on a Rayleight particle. $b=1.5$.
Fig. 8.
Fig. 8. The transverse patterns (background) and plots (white line) of the scattering force (the first row) and the gradient force (the second row) of the CAsinCGV wave packets on a Rayleight particle. $b=1.5$.

Equations (13)

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

2iΨz+1k2Ψk22Ψt2+2kΔnn0Ψ=0,
2iΨZ+2Ψη(X2+Y2)Ψ=0,
Ψ(X,Y,T,0)=ϕCGV(X,Y,0)A(T,0).
2iAZ+2AT2=0,
2iϕCGVZ+2ϕCGVX2+2ϕCGVY2η2(X2+Y2)ϕCGV=0.
A(T,Z)=dAi[d(Tc1Zd4Z2+iaZ)]exp[ad(Tc1Zd2Z2)]×exp[id(c1T+c2T2+d2TZ+a22Zc122Zc1d2Z2d212Z3)],
ϕCGV(X,Y,0)=f(X+iYb)exp[X2+Y22](X+iY),
ϕcosCGV(X,Y,Z)=cos(X+iYbexp(iZ))exp[X2+Y22+2iZ](X+iY),
ϕsinCGV(X,Y,Z)=sin(X+iYbexp(iZ))exp[X2+Y22+2iZ](X+iY).
ΨCAcosCGV(X,Y,T,Z)=cos(X+iYbexp(iZ))exp[X2+Y22+2iZ](X+iY)×dAi[d(Tc1Zd4Z2+iaZ)]exp[ad(Tc1Zd2Z2)]×exp[id(c1T+c2T2+d2TZ+a22Zc122Zc1d2Z2d212Z3)],
ΨCAsinCGV(X,Y,T,Z)=sin(X+iYbexp(iZ))exp[X2+Y22+2iZ](X+iY)×dAi[d(Tc1Zd4Z2+iaZ)]exp[ad(Tc1Zd2Z2)]×exp[id(c1T+c2T2+d2TZ+a22Zc122Zc1d2Z2d212Z3)].
Fscat=128n1π5r063λ4c0(n21n2+2)2Iez,
Fgrad=2πn1r03c0n21n2+2I,