Abstract

This paper investigates theoretically and numerically on the electro-optical coupling (EOC) for a circular Airy beam (CAB) propagating along the optical axis of a uniaxial crystal after deducing the wave coupling equations of EOC. For a circularly polarized incident CAB, EOC can be used to generate vortex beam by coupling the incident left-handed component into the right-handed vortex component with a vortex topological charge of 2. What’s more, EOC plays important role in enhancing or suppressing the abrupt autofocusing, the most important property of CABs, for both left-handed and right-handed components. Near the focal plane, EOC can result in electrically controllable optical “needle” and “cage”, which shall be interesting in micromanipulation. In addition, EOC can influence or even forbid the exchange between spin angular momentum (SAM) and orbit angular momentum (OAM). For a linearly polarized incident CAB, its two Cartesian field components of the beam cannot only couple their powers to each other, but also lead to the changes of the intensity pattern and polarization distributions. The polarization state becomes spatially inhomogeneous, and possesses vortex phase with a topological charge of 2 during propagation. EOC presents a new way to control an Airy beam fast and efficiently.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref] [PubMed]

2017 (2)

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “The propagation characteristics of circular Airy beam with low-pass filtering modification,” Proc. SPIE 10256, 102561L (2017).
[Crossref]

G. Zheng, X. Deng, S. Xu, and Q. Wu, “Propagation dynamics of a circular Airy beam in a uniaxial crystal,” Appl. Opt. 56(9), 2444–2448 (2017).
[Crossref] [PubMed]

2016 (2)

H. Zhong, Y. Zhang, M. R. Belić, C. Li, F. Wen, Z. Zhang, and Y. Zhang, “Controllable circular Airy beams via dynamic linear potential,” Opt. Express 24(7), 7495–7506 (2016).
[Crossref] [PubMed]

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

2015 (2)

W. G. Zhu and W. L. She, “Tightly focusing vector circular airy beam through a hard aperture,” Opt. Commun. 334, 303–307 (2015).
[Crossref]

Y. Jiang, X. Zhu, W. Yu, H. Shao, W. Zheng, and X. Lu, “Propagation characteristics of the modified circular Airy beam,” Opt. Express 23(23), 29834–29841 (2015).
[Crossref] [PubMed]

2014 (3)

P. Li, S. Liu, T. Peng, G. Xie, X. Gan, and J. Zhao, “Spiral autofocusing Airy beams carrying power-exponent-phase vortices,” Opt. Express 22(7), 7598–7606 (2014).
[Crossref] [PubMed]

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

M.-L. Zhou, C.-D. Chen, B. Chen, X. Peng, Y.-L. Peng, and D.-M. Deng, “Propagation of an Airy-Gaussian beam in uniaxial crystals,” Chin. Phys. B 24(12), 124102 (2014).
[Crossref]

2013 (3)

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. M. Deng, C. D. Chen, X. Zhao, and H. G. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110(3), 433–436 (2013).
[Crossref]

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013).
[Crossref] [PubMed]

2012 (6)

2011 (7)

I. Skab, Y. Vasylkiv, I. Smaga, and R. Vlokh, “Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals,” Phys. Rev. A 84(4), 043815 (2011).
[Crossref]

R. Dasgupta, S. Ahlawat, R. S. Verma, and P. K. Gupta, “Optical orientation and rotation of trapped red blood cells with Laguerre-Gaussian mode,” Opt. Express 19(8), 7680–7688 (2011).
[Crossref] [PubMed]

P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, “Trapping and transporting aerosols with a single optical bottle beam generated by moiré techniques,” Opt. Lett. 36(8), 1491–1493 (2011).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

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(15), 2883–2885 (2011).
[Crossref] [PubMed]

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(18), 3675–3677 (2011).
[Crossref] [PubMed]

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(18), 3675–3677 (2011).
[Crossref] [PubMed]

2010 (2)

2008 (2)

L. Chen and W. She, “Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam,” Opt. Lett. 33(7), 696–698 (2008).
[Crossref] [PubMed]

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

2007 (1)

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

2006 (1)

2003 (1)

2002 (1)

2001 (2)

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Ahlawat, S.

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Belic, M. R.

Broky, J.

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

Chen, B.

M.-L. Zhou, C.-D. Chen, B. Chen, X. Peng, Y.-L. Peng, and D.-M. Deng, “Propagation of an Airy-Gaussian beam in uniaxial crystals,” Chin. Phys. B 24(12), 124102 (2014).
[Crossref]

Chen, C.

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

Chen, C. D.

D. M. Deng, C. D. Chen, X. Zhao, and H. G. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110(3), 433–436 (2013).
[Crossref]

Chen, C.-D.

M.-L. Zhou, C.-D. Chen, B. Chen, X. Peng, Y.-L. Peng, and D.-M. Deng, “Propagation of an Airy-Gaussian beam in uniaxial crystals,” Chin. Phys. B 24(12), 124102 (2014).
[Crossref]

Chen, L.

Chen, R.

Chen, Z.

Chong, C. T.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

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(2), 023828 (2012).
[Crossref]

Christodoulides, D. N.

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(2), 023828 (2012).
[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(18), 3675–3677 (2011).
[Crossref] [PubMed]

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(15), 2883–2885 (2011).
[Crossref] [PubMed]

P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, “Trapping and transporting aerosols with a single optical bottle beam generated by moiré techniques,” Opt. Lett. 36(8), 1491–1493 (2011).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

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(18), 3675–3677 (2011).
[Crossref] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[Crossref] [PubMed]

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

Chu, X.

Ciattoni, A.

Cincotti, G.

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]

Crosignani, B.

Dasgupta, R.

Deng, D.

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

Deng, D. M.

D. M. Deng, C. D. Chen, X. Zhao, and H. G. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110(3), 433–436 (2013).
[Crossref]

Deng, D.-M.

M.-L. Zhou, C.-D. Chen, B. Chen, X. Peng, Y.-L. Peng, and D.-M. Deng, “Propagation of an Airy-Gaussian beam in uniaxial crystals,” Chin. Phys. B 24(12), 124102 (2014).
[Crossref]

Deng, F.

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

Deng, X.

Deng, X. Q.

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “The propagation characteristics of circular Airy beam with low-pass filtering modification,” Proc. SPIE 10256, 102561L (2017).
[Crossref]

Di Porto, P.

Dogariu, A.

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

Efremidis, N. K.

Gan, X.

Gupta, P. K.

Hernandez, D.

Huang, J.

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

Huang, K.

Huang, S.

Hwang, C. Y.

C. Y. Hwang, K. Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photonics J. 4(1), 174–180 (2012).
[Crossref]

Jiang, Y.

Kim, K. Y.

C. Y. Hwang, K. Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photonics J. 4(1), 174–180 (2012).
[Crossref]

Lee, B.

C. Y. Hwang, K. Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photonics J. 4(1), 174–180 (2012).
[Crossref]

Lee, W. K.

W. L. She and W. K. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[Crossref]

Li, C.

Li, H. G.

D. M. Deng, C. D. Chen, X. Zhao, and H. G. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110(3), 433–436 (2013).
[Crossref]

Li, P.

Liu, S.

Lu, X.

Lukyanchuk, B.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Mills, M. S.

Palma, C.

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]

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. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

Peng, T.

Peng, X.

M.-L. Zhou, C.-D. Chen, B. Chen, X. Peng, Y.-L. Peng, and D.-M. Deng, “Propagation of an Airy-Gaussian beam in uniaxial crystals,” Chin. Phys. B 24(12), 124102 (2014).
[Crossref]

Peng, Y.-L.

M.-L. Zhou, C.-D. Chen, B. Chen, X. Peng, Y.-L. Peng, and D.-M. Deng, “Propagation of an Airy-Gaussian beam in uniaxial crystals,” Chin. Phys. B 24(12), 124102 (2014).
[Crossref]

Prakash, J.

Salazar, M.

Shao, H.

She, W.

She, W. L.

W. G. Zhu and W. L. She, “Tightly focusing vector circular airy beam through a hard aperture,” Opt. Commun. 334, 303–307 (2015).
[Crossref]

W. L. She and W. K. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[Crossref]

Sheppard, C.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Shi, L. P.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Siviloglou, G. A.

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

Skab, I.

I. Skab, Y. Vasylkiv, I. Smaga, and R. Vlokh, “Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals,” Phys. Rev. A 84(4), 043815 (2011).
[Crossref]

Smaga, I.

I. Skab, Y. Vasylkiv, I. Smaga, and R. Vlokh, “Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals,” Phys. Rev. A 84(4), 043815 (2011).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Tang, H.

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. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

Vasylkiv, Y.

I. Skab, Y. Vasylkiv, I. Smaga, and R. Vlokh, “Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals,” Phys. Rev. A 84(4), 043815 (2011).
[Crossref]

Verma, R. S.

Vlokh, R.

I. Skab, Y. Vasylkiv, I. Smaga, and R. Vlokh, “Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals,” Phys. Rev. A 84(4), 043815 (2011).
[Crossref]

Wang, H.

Wang, H. F.

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Wang, M.

Wen, F.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Wu, Q.

Wu, Q. Y.

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “The propagation characteristics of circular Airy beam with low-pass filtering modification,” Proc. SPIE 10256, 102561L (2017).
[Crossref]

Wu, Z.

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

Xie, G.

Xu, S.

Xu, S. X.

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “The propagation characteristics of circular Airy beam with low-pass filtering modification,” Proc. SPIE 10256, 102561L (2017).
[Crossref]

Yang, X.

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

Yu, W.

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

Y. Jiang, X. Zhu, W. Yu, H. Shao, W. Zheng, and X. Lu, “Propagation characteristics of the modified circular Airy beam,” Opt. Express 23(23), 29834–29841 (2015).
[Crossref] [PubMed]

Zhang, P.

Zhang, W.

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

Zhang, Y.

Zhang, Z.

Zhao, J.

Zhao, R.

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

Zhao, X.

D. M. Deng, C. D. Chen, X. Zhao, and H. G. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110(3), 433–436 (2013).
[Crossref]

Zhao, Y.

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

Zheng, G.

Zheng, G. L.

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “The propagation characteristics of circular Airy beam with low-pass filtering modification,” Proc. SPIE 10256, 102561L (2017).
[Crossref]

Zheng, W.

Zhong, H.

Zhou, G.

Zhou, M.-L.

M.-L. Zhou, C.-D. Chen, B. Chen, X. Peng, Y.-L. Peng, and D.-M. Deng, “Propagation of an Airy-Gaussian beam in uniaxial crystals,” Chin. Phys. B 24(12), 124102 (2014).
[Crossref]

Zhu, W.

Zhu, W. G.

W. G. Zhu and W. L. She, “Tightly focusing vector circular airy beam through a hard aperture,” Opt. Commun. 334, 303–307 (2015).
[Crossref]

Zhu, X.

Appl. Opt. (1)

Appl. Phys. B (1)

D. M. Deng, C. D. Chen, X. Zhao, and H. G. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B 110(3), 433–436 (2013).
[Crossref]

Chin. Phys. B (2)

M.-L. Zhou, C.-D. Chen, B. Chen, X. Peng, Y.-L. Peng, and D.-M. Deng, “Propagation of an Airy-Gaussian beam in uniaxial crystals,” Chin. Phys. B 24(12), 124102 (2014).
[Crossref]

W. Yu, R. Zhao, F. Deng, J. Huang, C. Chen, X. Yang, Y. Zhao, and D. Deng, “Propagation of Airy Gaussian vortex beams in uniaxial crystals,” Chin. Phys. B 25(4), 044201 (2016).
[Crossref]

IEEE Photonics J. (1)

C. Y. Hwang, K. Y. Kim, and B. Lee, “Dynamic control of circular Airy beams with linear optical potentials,” IEEE Photonics J. 4(1), 174–180 (2012).
[Crossref]

J. Opt. Soc. Am. A (3)

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. Photonics (1)

H. F. Wang, L. P. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2(8), 501–505 (2008).
[Crossref]

Opt. Commun. (2)

W. G. Zhu and W. L. She, “Tightly focusing vector circular airy beam through a hard aperture,” Opt. Commun. 334, 303–307 (2015).
[Crossref]

W. L. She and W. K. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. 195(1-4), 303–311 (2001).
[Crossref]

Opt. Express (9)

G. Zheng, H. Wang, and W. She, “Wave coupling theory of Quasi-Phase-Matched linear electro-optic effect,” Opt. Express 14(12), 5535–5540 (2006).
[Crossref] [PubMed]

R. Dasgupta, S. Ahlawat, R. S. Verma, and P. K. Gupta, “Optical orientation and rotation of trapped red blood cells with Laguerre-Gaussian mode,” Opt. Express 19(8), 7680–7688 (2011).
[Crossref] [PubMed]

H. Tang, L. Chen, and W. She, “The spatially varying polarization of a focused Gaussian beam in quasi-phase-matched superlattice under electro-optic effect,” Opt. Express 18(24), 25000–25007 (2010).
[Crossref] [PubMed]

G. Zhou, R. Chen, and X. Chu, “Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis,” Opt. Express 20(3), 2196–2205 (2012).
[Crossref] [PubMed]

Y. Jiang, K. Huang, and X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012).
[Crossref] [PubMed]

W. Zhu and W. She, “Electrically controlling spin and orbital angular momentum of a focused light beam in a uniaxial crystal,” Opt. Express 20(23), 25876–25883 (2012).
[Crossref] [PubMed]

P. Li, S. Liu, T. Peng, G. Xie, X. Gan, and J. Zhao, “Spiral autofocusing Airy beams carrying power-exponent-phase vortices,” Opt. Express 22(7), 7598–7606 (2014).
[Crossref] [PubMed]

Y. Jiang, X. Zhu, W. Yu, H. Shao, W. Zheng, and X. Lu, “Propagation characteristics of the modified circular Airy beam,” Opt. Express 23(23), 29834–29841 (2015).
[Crossref] [PubMed]

H. Zhong, Y. Zhang, M. R. Belić, C. Li, F. Wen, Z. Zhang, and Y. Zhang, “Controllable circular Airy beams via dynamic linear potential,” Opt. Express 24(7), 7495–7506 (2016).
[Crossref] [PubMed]

Opt. Lett. (9)

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013).
[Crossref] [PubMed]

W. Zhu and W. She, “Electro-optically generating and controlling right- and left-handed circularly polarized multiring modes of light beams,” Opt. Lett. 37(14), 2823–2825 (2012).
[Crossref] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[Crossref] [PubMed]

P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, “Trapping and transporting aerosols with a single optical bottle beam generated by moiré techniques,” Opt. Lett. 36(8), 1491–1493 (2011).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

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(15), 2883–2885 (2011).
[Crossref] [PubMed]

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(18), 3675–3677 (2011).
[Crossref] [PubMed]

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(18), 3675–3677 (2011).
[Crossref] [PubMed]

L. Chen and W. She, “Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam,” Opt. Lett. 33(7), 696–698 (2008).
[Crossref] [PubMed]

Phys. Rev. A (3)

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(2), 023828 (2012).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

I. Skab, Y. Vasylkiv, I. Smaga, and R. Vlokh, “Spin-to-orbital momentum conversion via electro-optic Pockels effect in crystals,” Phys. Rev. A 84(4), 043815 (2011).
[Crossref]

Phys. Rev. Lett. (1)

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

Proc. SPIE (1)

G. L. Zheng, X. Q. Deng, S. X. Xu, and Q. Y. Wu, “The propagation characteristics of circular Airy beam with low-pass filtering modification,” Proc. SPIE 10256, 102561L (2017).
[Crossref]

Sci. Rep. (1)

X. Lu, Z. Wu, W. Zhang, and L. Chen, “Polarization singularities and orbital angular momentum sidebands from rotational symmetry broken by the Pockels effect,” Sci. Rep. 4(1), 4865 (2014).
[Crossref] [PubMed]

Other (2)

Y. Hu, G. A. Siviloglou, P. Zhang, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Self-accelerating Airy Beams: Generation, Control, and Applications,” in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen, and R. Morandotti, eds. (Springer, 2012), pp. 1–46.

A. Yariv, Optical Waves in Crystals (Wiley, 1983).

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Figures (8)

Fig. 1
Fig. 1 Intensity distributions (I/Im) of E+ (dark solid line) and E- (red dash line) with different external electric fields: (a) E0 = 0 kV/mm; (b) E0 = 5 kV/mm; (c) E0 = 10 kV/mm; (d) E0 = 15 kV/mm.
Fig. 2
Fig. 2 Propagation dynamics of E+ (a) and E- (b) with 0 kV/mm external electric field.
Fig. 3
Fig. 3 Propagation dynamics of E+ (a) and E- (b) with 5 kV/mm external electric field..
Fig. 4
Fig. 4 Intensity patterns (I/Im) of the beam when the external electric field E0 = 5kV/mm at z = 10 mm: (a) initial distribution of the beam; (b) interference pattern of | E (r,φ,z) / max(| E (r,φ,z) | )+exp[i( k 0 n 0 1 n e 2 γ 13 E 0 z)] | 2 ; (c) intensity distributions of E+; (d) intensity distributions of E-.
Fig. 5
Fig. 5 Plots of Φs(z)/Φs(0) (solid line) and Φo(z)/Φs(0) (dash line) of a CAB vs propagation distance with different external electric field.
Fig. 6
Fig. 6 Intensity patterns of Ix/Im with different external electric fields at z = 10 mm: (a) E0 = 0 kV/mm; (b) E0 = 5 kV/mm; (c) E0 = 10 kV/mm; (d) E0 = 15 kV/mm.
Fig. 7
Fig. 7 Intensity patterns of Iy/Im with different external electric fields at z = 10 mm: (a) E0 = 0 kV/mm; (b) E0 = 5 kV/mm; (c) E0 = 10 kV/mm; (d) E0 = 15 kV/mm.
Fig. 8
Fig. 8 Polarization distribution with different external electric fields at z = 10 mm: (a) E0 = 0 kV/mm; (b) E0 = 5 kV/mm. The size of the ellipse denotes the beam intensity.

Equations (19)

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

2 E(r)[E(r)]+ k 0 2 ε E(r)+ μ 0 ω 2 P EO (r)=0,
E(r)=E( r ,z)= d 2 k 2 exp(i k r ) E ˜ ( k ,z),
P(r)=P( r ,z)= d 2 k 2 exp(i k r ) P ˜ ( k ,z).
( 2 z 2 + k 0 2 n o 2 k y 2 ) E ˜ x + k x k y E ˜ y i k x z E ˜ z + μ 0 ω 2 P ˜ x EO =0,
( 2 z 2 + k 0 2 n o 2 k x 2 ) E ˜ y + k x k y E ˜ x i k y z E ˜ z + μ 0 ω 2 P ˜ y EO =0,
( k 0 2 n e 2 k 2 ) E ˜ z i k x z E ˜ x i k y z E ˜ y + μ 0 ω 2 P ˜ z EO =0.
2 z 2 E ˜ x i k x z E ˜ z + k x k y E ˜ y +[ k 0 2 n 0 2 (1 n e 2 γ 13 E 0 ) k y 2 ] E ˜ x =0,
2 z 2 E ˜ y i k y z E ˜ z + k x k y E ˜ x +[ k 0 2 n 0 2 (1 n e 2 γ 13 E 0 ) k x 2 ] E ˜ y =0,
[ k 0 2 n e 2 (1 n e 2 γ 33 E 0 ) k 2 ] E ˜ z i k x z E ˜ x i k y z E ˜ y =0.
E ˜ (k)= 1 2π 0 dr r J 0 (kr)E(r,0),
E( r,0 )=CAi( r 0 r w )exp( a r 0 r w ),
E ˜ ( k )=C w 2 ( r 0 w + k 2 w 2 )exp( a k 2 w 2 ) 3k r 0 + k 3 w 3 3k r 0 +3 k 3 w 3 J 0 ( k r 0 + k 3 w 3 3 )
E(r,ϕ,z)=exp(i k 0 n 0 1 n e 2 γ 13 E 0 z)[ Α (0) (r,z)+R(ϕ) Α (2) (r,z)],
A (n) (r,z)=π 0 dk[ exp( iz k 2 2 k 0 n 0 1 n e 2 γ 13 E 0 )+exp( iz n 0 k 2 1 n e 2 γ 13 E 0 2 k 0 n e 2 (1 n e 2 γ 33 E 0 ) ) ]k J n (kr) E ˜ (k) ,
R(ϕ)=[ cos2ϕ sin2ϕ sin2ϕ cos2ϕ ]
E x (r,ϕ,z)=exp(i k 0 n 0 1 n e 2 γ 13 E 0 z)[ A (0) (r,z)cosα+ A (2) (r,z)cos(2ϕα)], E y (r,ϕ,z)=exp(i k 0 n 0 1 n e 2 γ 13 E 0 z)[ A (0) (r,z)sinα+ A (2) (r,z)sin(2ϕα)].
E + (r,ϕ,z)=exp(i k 0 n 0 1 n e 2 γ 13 E 0 z) A (0) (r,z), E (r,ϕ,z)=exp[i( k 0 n 0 1 n e 2 γ 13 E 0 z+2φ)] A (2) (r,z).
W ± (z)= 1 2 W + (0)±4π 0 dkkcos( zΔ 2 k 0 n 0 1 n e 2 γ 13 E 0 k 2 ) | E ˜ + (k) | 2 ,
Φ s (z)= n o ε 0 c 2ω [ W + (z) W (z)], Φ o (z)=2 n o ε 0 c 2ω W (z).

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