Abstract

We introduce the propagation of the first-order chirped Airy vortex beams (FCAiV) in a chiral medium analytically. Results show that the FCAiV beams split into the left circularly polarized vortex (LCPV) beams and the right circularly polarized vortex (RCPV) beams, which have totally different propagation trajectories in the chiral medium. In this paper, we investigate the effects of the first-order chirped parameter β, the chiral parameter γ and the optical vortex on the propagation process of the FCAiV beams. It is shown that the propagation trajectory of the FCAiV beams declines with the chirped parameter increasing. Besides, the increase of the chiral parameter acting on the LCPV beams makes the relative position between the main lobe and the optical vortex further while the effect on the RCPV beams is the opposite. Furthermore, the relative position between the main lobe and the optical vortex contributes to the position of the intensity focusing. Meanwhile, with the chiral parameter increasing, the maximum gradient and scattering forces of the LCPV beams decrease but those of the RCPV beams will increase during the propagation. It is significant that we can control the propagation trajectory, the intensity focusing position and the radiation forces of the FCAiV beams by varying the chirped parameter and the chiral parameter.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  8. P. Polynkin, M. Kolesik, and J. V. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
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    [Crossref]
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2017 (3)

J. Zhang, Z. Pang, L. Feng, T. Zhong, L. Wang, and D. Deng, “Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs,” Chin. Opt. Lett. 15(6), 060501 (2017).
[Crossref]

L. Feng, J. Zhang, Z. Pang, L. Wang, T. Zhong, X. Yang, and D. Deng, “Propagation properties of the chirped Airy beams through the gradient-index medium,” Opt. Commun. 402, 60–65 (2017).
[Crossref]

S. Hua, Y. Liu, H. Zhang, L. Tang, and Y. Feng, “Propagation of an Airy-Gaussian-Vortex beam in a chiral medium,” Opt. Commun. 388, 29–37 (2017).
[Crossref]

2016 (1)

F. Deng, W. Yu, J. Huang, R. Zhao, J. Lin, and D. Deng, “Propagation of Airy-Gaussian beams in a chiral medium,” Eur. Phys. J. D. 70(4), 87 (2016).
[Crossref]

2015 (2)

2014 (1)

X. Liu and D. Zhao, “Propagation of a vortex Airy beam in chiral medium,” Opt. Commun. 321, 6–10 (2014).
[Crossref]

2013 (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] [PubMed]

2012 (1)

2011 (2)

2010 (2)

H. Dai, Y. Liu, D. Luo, and X. Sun, “Propagation dynamics of an optical vortex imposed on an Airy beam,” Opt. Lett. 35(23), 4075–4077 (2010).
[Crossref] [PubMed]

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 (2)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, and J. V. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (2)

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

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[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]

1992 (1)

J. Melinger, S. Gandhi, A. Hariharan, J. Tull, and W. Warren, “Generation of Narrowband Inversion with Broadband Laser Pulses,” Phys. Rev. Lett. 68(13), 2000–2003 (1992).
[Crossref] [PubMed]

1979 (1)

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

1970 (1)

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]

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]

Balazs, N. L.

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

Baumgartl, J.

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

Belic, M.

Berry, M. V.

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

Broky, J.

Chremmos, I.

Christodoulides, D. N.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

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

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

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

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

Collins, S. A.

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] [PubMed]

Dai, H.

Deng, D.

L. Feng, J. Zhang, Z. Pang, L. Wang, T. Zhong, X. Yang, and D. Deng, “Propagation properties of the chirped Airy beams through the gradient-index medium,” Opt. Commun. 402, 60–65 (2017).
[Crossref]

J. Zhang, Z. Pang, L. Feng, T. Zhong, L. Wang, and D. Deng, “Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs,” Chin. Opt. Lett. 15(6), 060501 (2017).
[Crossref]

F. Deng, W. Yu, J. Huang, R. Zhao, J. Lin, and D. Deng, “Propagation of Airy-Gaussian beams in a chiral medium,” Eur. Phys. J. D. 70(4), 87 (2016).
[Crossref]

Deng, F.

F. Deng, W. Yu, J. Huang, R. Zhao, J. Lin, and D. Deng, “Propagation of Airy-Gaussian beams in a chiral medium,” Eur. Phys. J. D. 70(4), 87 (2016).
[Crossref]

Dholakia, K.

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

Dogariu, A.

Du, X.

Feng, L.

J. Zhang, Z. Pang, L. Feng, T. Zhong, L. Wang, and D. Deng, “Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs,” Chin. Opt. Lett. 15(6), 060501 (2017).
[Crossref]

L. Feng, J. Zhang, Z. Pang, L. Wang, T. Zhong, X. Yang, and D. Deng, “Propagation properties of the chirped Airy beams through the gradient-index medium,” Opt. Commun. 402, 60–65 (2017).
[Crossref]

Feng, Y.

S. Hua, Y. Liu, H. Zhang, L. Tang, and Y. Feng, “Propagation of an Airy-Gaussian-Vortex beam in a chiral medium,” Opt. Commun. 388, 29–37 (2017).
[Crossref]

Gandhi, S.

J. Melinger, S. Gandhi, A. Hariharan, J. Tull, and W. Warren, “Generation of Narrowband Inversion with Broadband Laser Pulses,” Phys. Rev. Lett. 68(13), 2000–2003 (1992).
[Crossref] [PubMed]

Giamalaki, M.

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]

Hariharan, A.

J. Melinger, S. Gandhi, A. Hariharan, J. Tull, and W. Warren, “Generation of Narrowband Inversion with Broadband Laser Pulses,” Phys. Rev. Lett. 68(13), 2000–2003 (1992).
[Crossref] [PubMed]

Hua, S.

S. Hua, Y. Liu, H. Zhang, L. Tang, and Y. Feng, “Propagation of an Airy-Gaussian-Vortex beam in a chiral medium,” Opt. Commun. 388, 29–37 (2017).
[Crossref]

Huang, J.

F. Deng, W. Yu, J. Huang, R. Zhao, J. Lin, and D. Deng, “Propagation of Airy-Gaussian beams in a chiral medium,” Eur. Phys. J. D. 70(4), 87 (2016).
[Crossref]

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, and J. V. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

Lin, J.

F. Deng, W. Yu, J. Huang, R. Zhao, J. Lin, and D. Deng, “Propagation of Airy-Gaussian beams in a chiral medium,” Eur. Phys. J. D. 70(4), 87 (2016).
[Crossref]

Liu, X.

X. Liu and D. Zhao, “Propagation of a vortex Airy beam in chiral medium,” Opt. Commun. 321, 6–10 (2014).
[Crossref]

Liu, Y.

Luo, D.

Mazilu, M.

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

Melinger, J.

J. Melinger, S. Gandhi, A. Hariharan, J. Tull, and W. Warren, “Generation of Narrowband Inversion with Broadband Laser Pulses,” Phys. Rev. Lett. 68(13), 2000–2003 (1992).
[Crossref] [PubMed]

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, and J. V. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

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] [PubMed]

Pang, Z.

L. Feng, J. Zhang, Z. Pang, L. Wang, T. Zhong, X. Yang, and D. Deng, “Propagation properties of the chirped Airy beams through the gradient-index medium,” Opt. Commun. 402, 60–65 (2017).
[Crossref]

J. Zhang, Z. Pang, L. Feng, T. Zhong, L. Wang, and D. Deng, “Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs,” Chin. Opt. Lett. 15(6), 060501 (2017).
[Crossref]

Papazoglou, D. G.

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] [PubMed]

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]

Polynkin, P.

P. Polynkin, M. Kolesik, and J. V. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12891 (2008).
[Crossref] [PubMed]

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

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

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

Sun, X.

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]

Tang, L.

S. Hua, Y. Liu, H. Zhang, L. Tang, and Y. Feng, “Propagation of an Airy-Gaussian-Vortex beam in a chiral medium,” Opt. Commun. 388, 29–37 (2017).
[Crossref]

Tull, J.

J. Melinger, S. Gandhi, A. Hariharan, J. Tull, and W. Warren, “Generation of Narrowband Inversion with Broadband Laser Pulses,” Phys. Rev. Lett. 68(13), 2000–2003 (1992).
[Crossref] [PubMed]

Tzortzakis, S.

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] [PubMed]

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, L.

L. Feng, J. Zhang, Z. Pang, L. Wang, T. Zhong, X. Yang, and D. Deng, “Propagation properties of the chirped Airy beams through the gradient-index medium,” Opt. Commun. 402, 60–65 (2017).
[Crossref]

J. Zhang, Z. Pang, L. Feng, T. Zhong, L. Wang, and D. Deng, “Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs,” Chin. Opt. Lett. 15(6), 060501 (2017).
[Crossref]

Wang, R.

Warren, W.

J. Melinger, S. Gandhi, A. Hariharan, J. Tull, and W. Warren, “Generation of Narrowband Inversion with Broadband Laser Pulses,” Phys. Rev. Lett. 68(13), 2000–2003 (1992).
[Crossref] [PubMed]

Yang, X.

L. Feng, J. Zhang, Z. Pang, L. Wang, T. Zhong, X. Yang, and D. Deng, “Propagation properties of the chirped Airy beams through the gradient-index medium,” Opt. Commun. 402, 60–65 (2017).
[Crossref]

Ye, Y.

Yu, W.

F. Deng, W. Yu, J. Huang, R. Zhao, J. Lin, and D. Deng, “Propagation of Airy-Gaussian beams in a chiral medium,” Eur. Phys. J. D. 70(4), 87 (2016).
[Crossref]

Zhang, H.

S. Hua, Y. Liu, H. Zhang, L. Tang, and Y. Feng, “Propagation of an Airy-Gaussian-Vortex beam in a chiral medium,” Opt. Commun. 388, 29–37 (2017).
[Crossref]

Zhang, J.

L. Feng, J. Zhang, Z. Pang, L. Wang, T. Zhong, X. Yang, and D. Deng, “Propagation properties of the chirped Airy beams through the gradient-index medium,” Opt. Commun. 402, 60–65 (2017).
[Crossref]

J. Zhang, Z. Pang, L. Feng, T. Zhong, L. Wang, and D. Deng, “Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs,” Chin. Opt. Lett. 15(6), 060501 (2017).
[Crossref]

Zhang, L.

Zhang, Y.

Zhao, D.

Zhao, R.

F. Deng, W. Yu, J. Huang, R. Zhao, J. Lin, and D. Deng, “Propagation of Airy-Gaussian beams in a chiral medium,” Eur. Phys. J. D. 70(4), 87 (2016).
[Crossref]

Zhong, T.

L. Feng, J. Zhang, Z. Pang, L. Wang, T. Zhong, X. Yang, and D. Deng, “Propagation properties of the chirped Airy beams through the gradient-index medium,” Opt. Commun. 402, 60–65 (2017).
[Crossref]

J. Zhang, Z. Pang, L. Feng, T. Zhong, L. Wang, and D. Deng, “Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs,” Chin. Opt. Lett. 15(6), 060501 (2017).
[Crossref]

Zhong, W.

Zhu, D.

Zhuang, F.

Am. J. Phys. (1)

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

Chin. Opt. Lett. (1)

Eur. Phys. J. D. (1)

F. Deng, W. Yu, J. Huang, R. Zhao, J. Lin, and D. Deng, “Propagation of Airy-Gaussian beams in a chiral medium,” Eur. Phys. J. D. 70(4), 87 (2016).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

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] [PubMed]

Nat. Photon. (1)

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

Opt. Commun. (4)

S. Hua, Y. Liu, H. Zhang, L. Tang, and Y. Feng, “Propagation of an Airy-Gaussian-Vortex beam in a chiral medium,” Opt. Commun. 388, 29–37 (2017).
[Crossref]

X. Liu and D. Zhao, “Propagation of a vortex Airy beam in chiral medium,” Opt. Commun. 321, 6–10 (2014).
[Crossref]

L. Feng, J. Zhang, Z. Pang, L. Wang, T. Zhong, X. Yang, and D. Deng, “Propagation properties of the chirped Airy beams through the gradient-index medium,” Opt. Commun. 402, 60–65 (2017).
[Crossref]

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]

Opt. Express (2)

Opt. Lett. (6)

Phys. Rev. Lett. (4)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

J. Melinger, S. Gandhi, A. Hariharan, J. Tull, and W. Warren, “Generation of Narrowband Inversion with Broadband Laser Pulses,” Phys. Rev. Lett. 68(13), 2000–2003 (1992).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, and J. V. Moloney, “Filamentation of Femtosecond Laser Airy Beams in Water,” Phys. Rev. Lett. 103(12), 123902 (2009).
[Crossref] [PubMed]

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]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved Plasma Channel Generation Using Ultraintense Airy beams,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

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Figures (10)

Fig. 1
Fig. 1 Intensity distributions of the FCAiV beams propagating through the chiral medium with γ=0.16/k, β=0.05. (a1)–(a3) represent the LCPV, RCPV and total intensity, respectively (x = y). (b1–b6) are the transverse intensity patterns taken by the dotted lines in (a1)–(a3).
Fig. 2
Fig. 2 All are the same as those in Fig. 1 except the intensity positions of choice and the chiral parameter γ= 0.28/k.
Fig. 3
Fig. 3 Intensity distributions of (a1)–(a4) the LCPV beams, (b1)–(b4) the RCPV beams and (c1)–(c4) the total beams in the chiral medium with γ=0.16/k, β=0.05, 0.5, 1, 2.
Fig. 4
Fig. 4 Intensity distribution of the LCPV beams with β=0.05, (a1)–(a4) γ=0.16/k, (b1)–(b4) γ=0.28/k (x = y).
Fig. 5
Fig. 5 All are the same as those in Fig. 4 except the RCPV beams and the intensity positions of choice (x = y).
Fig. 6
Fig. 6 All are the same as those in Fig. 4 except the total beams and the intensity positions of choice (x = y).
Fig. 7
Fig. 7 The interference terms with different chirped parameters and chiral parameters, (a1)–(a3) γ=0.16/k, (b1)–(b3) γ=0.28/k, (a1) and (b1) β=0.05, (a2) and (b2) β= 0.5, (a3) and (b3) β=1 (x = y).
Fig. 8
Fig. 8 The propagation trajectory (a, b) and the velocity (c, d) of the FCAiV beams in a chiral medium with β=0.05, (a) and (c) γ=0.16/k, (b) and (d) γ=0.28/k.
Fig. 9
Fig. 9 Maximum gradient force distribution of the LCPV beams (a1)–(a3) and the RCPV beams (b1)–(b3) during the propagation. (a1) and (b1) with β = 2 and γ = 0.16/k, (a2) and (b2) with β = 1 and γ = 0.16k, (a3) and (b3) with β = 1 and γ = 0.28/k.
Fig. 10
Fig. 10 All are the same as those in Fig. 9 except the maximum scattering force distribution.

Equations (15)

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E ( x 0 , y 0 , 0 ) = A 0 A i ( x 0 w 1 ) A i ( y 0 w 2 ) exp [ a x 0 w 1 + b y 0 w 2 + i β ( x 0 w 1 + y 0 w 2 ) ] ( x 0 w 1 + i y 0 w 2 ) ,
E ( x , y , z ) = i k 2 π B + E 0 ( x 0 , y 0 , 0 ) × exp { i k 2 B [ A ( x 0 2 + y 0 2 ) 2 ( x 0 x + y 0 y ) + D ( x 2 + y 2 ) ] } d x 0 d y 0 ,
E ( x , y , z ) = A 0 A exp [ Q ( x , y , z ) ] ( K 1 + K 2 + K 3 ) ,
Q ( x , y , z ) = i k D 2 B ( x 2 + y 2 ) 1 4 M ( N 1 2 + N 2 2 ) + 1 8 M 2 ( N 1 w 1 3 + N 2 w 2 3 ) 1 96 M 3 ( 1 w 1 6 + 1 w 2 6 ) , K 1 = A i [ f ( x ) ] A i [ g ( y ) ] [ ( N 1 2 w 1 M + 1 8 w 1 4 M 2 ) + i ( N 2 2 w 2 M + 1 8 w 2 4 M 2 ) ] , K 2 = i 2 M w 2 2 A i [ f ( x ) ] A i [ g ( y ) ] , K 3 = 1 2 M w 1 2 A i [ g ( y ) ] A i [ f ( x ) ] , M = i k A 2 B , N 1 = a + i β w 1 + i k x B , N 2 = b + i β w 2 + i k y B , f ( x ) = 1 16 w 1 4 M 2 N 1 2 w 1 M , g ( y ) = 1 16 w 2 4 M 2 N 2 2 w 2 M .
( A ( L ) B ( L ) C ( L ) D ( L ) ) = ( 1 z / n ( L ) 0 1 ) a n d ( A ( R ) B ( R ) C ( R ) D ( R ) ) = ( 1 z / n ( R ) 0 1 ) ,
E = E ( L ) ( x , y , z ) + E ( R ) ( x , y , z ) .
I = | E ( L ) ( x , y , z ) | 2 + | E ( R ) ( x , y , z ) | 2 + I i n t ,
I i n t = E ( L ) ( x , y , z ) E ( R ) * ( x , y , z ) + E ( R ) ( x , y , z ) E ( L ) * ( x , y , z ) ,
X 1 , ( L , R ) = z 2 4 k 2 A w 1 3 n ( L , R ) 2 z β k w 1 n ( L , R ) ,
V 1 , ( L , R ) = z 2 k 2 A w 1 3 n ( L , R ) 2 β k w 1 n ( L , R ) ,
X 2 , ( L , R ) = z 2 2 k 2 A w 1 3 n ( L , R ) 2 z β k w 1 n ( L , R ) ,
V 2 , ( L , R ) = z k 2 A w 1 3 n ( L , R ) 2 β k w 1 n ( L , R ) ,
F g r a d ( x , y , z ) = 2 π n 2 r 0 3 c ( m 2 1 m 2 + 2 ) I ( x , y , z ) ,
F s c a t ( x , y , z ) = 8 π n 2 k 4 r 0 6 3 c ( m 2 1 m 2 + 2 ) 2 I ( x , y , z ) e z ,
I ( x , y , z ) = c n 2 ε 0 | E ( x , y , z ) | 2 2 ,

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