Abstract

By using the diffractive optical elements written onto a spatial light modulator, we experimentally obtain optical regular triple-cusp beams. Their propagation characteristics and topological structures are subsequently investigated. The experimental results demonstrate that each cusp of an optical regular triple-cusp beam, similar to the main lobe of an Airy beam, propagates along curved paths in free space, hence tends to adopt the “transverse acceleration” property. Moreover, we experimentally prove that optical regular triple-cusp beams can resist local distorted deformation. Such beams can thus be applied in adverse optical environments, such as a probe for the exploration of microscopic world and as an energy source for research on high-field laser–matter interactions.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett.35(12), 2082–2084 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  19. T. Poston and I. Stewart, Catastrophe Theory and Its Application (Pitman, 1978).
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    [CrossRef]
  21. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16(17), 12880–12891 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-17-12880 .
    [CrossRef] [PubMed]

2012 (2)

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85(1), 013815 (2012).
[CrossRef]

Y. Kaganovsky and E. Heyman, “Nonparaxial wave analysis of three-dimensional Airy beams,” J. Opt. Soc. Am. A29(5), 671–688 (2012).
[CrossRef] [PubMed]

2011 (4)

W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials,” Opt. Lett.36(7), 1164–1166 (2011).
[CrossRef] [PubMed]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam Generated by In-Plane Diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-Accelerating Self-Trapped Optical Beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

2010 (6)

2009 (2)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

V. Pasiskevicius, “Engineering Airy beams,” Nat. Photonics3(7), 374–375 (2009).
[CrossRef]

2008 (3)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

J. F. Nye, “Unfolding higher-order wave dislocation clusters and catastrophe theory,” J. Opt. A, Pure Appl. Opt.10(7), 075010 (2008).
[CrossRef]

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16(17), 12880–12891 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-17-12880 .
[CrossRef] [PubMed]

2007 (1)

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

Abdollahpour, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

Alonso, M. A.

Barwick, S.

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

Broky, J.

Chen, R. P.

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85(1), 013815 (2012).
[CrossRef]

Chen, Z.

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-Accelerating Self-Trapped Optical Beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett.35(12), 2082–2084 (2010).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(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. Express16(17), 12880–12891 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-17-12880 .
[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] [PubMed]

Chu, X. X.

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85(1), 013815 (2012).
[CrossRef]

Couairon, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

Dogariu, A.

Faccio, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

Fuerschbach, K.

Heyman, E.

Hu, Y.

Huang, S.

Kaganovsky, Y.

Kaminer, I.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-Accelerating Self-Trapped Optical Beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

Kivshar, Y. S.

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Li, J. X.

Li, L.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam Generated by In-Plane Diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

Li, T.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam Generated by In-Plane Diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

Liu, W.

Lotti, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

Lou, C.

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

Miroshnichenko, A. E.

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,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Neshev, D. N.

Nye, J. F.

J. F. Nye, “Unfolding higher-order wave dislocation clusters and catastrophe theory,” J. Opt. A, Pure Appl. Opt.10(7), 075010 (2008).
[CrossRef]

Panagiotopoulos, P.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

Papazoglou, D. G.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

Pasiskevicius, V.

V. Pasiskevicius, “Engineering Airy beams,” Nat. Photonics3(7), 374–375 (2009).
[CrossRef]

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Rolland, J. P.

Salandrino, A.

Segev, M.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-Accelerating Self-Trapped Optical Beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[CrossRef] [PubMed]

Shadrivov, I. V.

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,” Science324(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. Express16(17), 12880–12891 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-17-12880 .
[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] [PubMed]

Thompson, K. P.

Tian, J. G.

Tzortzakis, S.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

Vo, S.

Wang, S. M.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam Generated by In-Plane Diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

Xu, J.

Zang, W. P.

Zhang, C.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam Generated by In-Plane Diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

Zhang, P.

Zhou, G. Q.

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85(1), 013815 (2012).
[CrossRef]

Zhu, S. N.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam Generated by In-Plane Diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt. (1)

J. F. Nye, “Unfolding higher-order wave dislocation clusters and catastrophe theory,” J. Opt. A, Pure Appl. Opt.10(7), 075010 (2008).
[CrossRef]

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

Nat. Photonics (2)

V. Pasiskevicius, “Engineering Airy beams,” Nat. Photonics3(7), 374–375 (2009).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. A (2)

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A84(2), 021807 (2011).
[CrossRef]

X. X. Chu, G. Q. Zhou, and R. P. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85(1), 013815 (2012).
[CrossRef]

Phys. Rev. Lett. (3)

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam Generated by In-Plane Diffraction,” Phys. Rev. Lett.107(12), 126804 (2011).
[CrossRef] [PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-Accelerating Self-Trapped Optical Beams,” Phys. Rev. Lett.106(21), 213903 (2011).
[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] [PubMed]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense Airy beams,” Science324(5924), 229–232 (2009).
[CrossRef] [PubMed]

Other (3)

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial College Press, 2004).

T. Poston and I. Stewart, Catastrophe Theory and Its Application (Pitman, 1978).

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Filamentation of Femtosecond Self-Bending Airy Beams,” IEEE. OSA/CLEO/IQEC. 978–1-55752–869–8/09 (2009).

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Figures (6)

Fig. 1
Fig. 1

Experimental setup for generating optical RTBs. L, lens; SF, space filtering; HP, halfwave plate; BS, beam splitter.

Fig. 2
Fig. 2

Phase masks for generating optical RTBs. In the gray-scale pattern, the phase is wrapped between 0 and 2π, black corresponds to 0 and white to 2π radians and the gray level being 256.

Fig. 3
Fig. 3

Recorded 2D intensity distribution of an optical RTB at (a) z = 0 cm, (b) z = 1.5 cm, (c) z = 3 cm, (d) z = 4.5 cm, and (e) z = 6 cm. Corresponding theoretical simulation results at these same distances (f)–(j).

Fig. 4
Fig. 4

3D propagating sketch configuration of optical RTBs.

Fig. 5
Fig. 5

Ballistic trajectory as the propagation distance for the transverse acceleration of one cusp of an optical RTB based on experimentally measured results. The solid line shows fitted line, with the black dots representing the measured values.

Fig. 6
Fig. 6

Self-healing of an optical RTB when its one cusp point is blocked. Observed intensity profile at (a) the input z = 0, (b) z = 6mm, (c) z = 12mm and (d) z = 18mm from the obstacle.

Equations (2)

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I(x,y,z)=|E(x,y,z) | 2 ,
E(x,y,z)=A dξ dηexp{i[( ξ 3 + η 3 )/3( ξ 2 η+ξ η 2 ) z( ξ 2 + η 2 )+xξ+yη)]},

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