Abstract

We present a theoretical and experimental exhibit that accelerates quasi-Airy beams propagating along arbitrarily appointed parabolic trajectories and directions in free space. We also demonstrate that such quasi-Airy beams can be generated by a tunable phase pattern, where two disturbance factors are introduced. The topological structures of quasi-Airy beams are readily manipulated with tunable phase patterns. Quasi-Airy beams still possess the characteristics of non-diffraction, self-healing to some extent, although they are not the solutions for paraxial wave equation. The experiments show the results are consistent with theoretical predictions. It is believed that the property of propagation along arbitrarily desired parabolic trajectories will provide a broad application in trapping atom and living cell manipulation.

© 2016 Optical Society of America

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References

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    [Crossref]
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2015 (2)

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, and D. Deng, “Propagation of sharply autofocused ring Airy Gaussian vortex beams,” Opt. Express 23(15), 19288–19298 (2015).
[Crossref] [PubMed]

2013 (2)

2012 (1)

2011 (4)

2010 (2)

2009 (3)

2008 (4)

2007 (2)

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]

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

2003 (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

1979 (1)

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

Abramochkin, E.

Balazs, N. L.

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

Bandres, M. A.

Baumgartl, J.

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

Berry, M. V.

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

Bleckmann, F.

Broky, J.

Chen, B.

Chen, C.

Chen, R.

R. Chen and C. Ying, “Beam propagation factor of an Airy beam,” J. Opt. 13(13), 459–462 (2011).

Chen, Z.

Christodoulides, D. N.

Courvoisier, F.

Dally, A.

Dan, D.

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Deng, D.

Desyatnikov, A. S.

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.

Dudley, J. M.

Froehly, L.

Frohnhaus, J.

Furfaro, L.

Giust, R.

Greenfield, E.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[Crossref] [PubMed]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Heyman, E.

Hu, Y.

Huang, S.

Isenhower, L.

Jacquot, M.

Kaganovsky, Y.

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,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

Krolikowski, W.

Lacourt, P. A.

Lei, M.

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Li, M.

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Liang, Y.

Linden, S.

Lou, C.

Mathis, A.

Mazilu, M.

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

Min, J.

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Minovich, A.

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]

Neshev, D. N.

Peng, T.

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Peng, X.

Peng, Y.

Polynkin, P.

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]

Raz, O.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[Crossref] [PubMed]

Razueva, E.

Rode, A. V.

Saffman, M.

Segev, M.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[Crossref] [PubMed]

Shvedov, V. G.

Siviloglou, G. A.

Song, D.

Walasik, W.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[Crossref] [PubMed]

Williams, W.

Xu, J.

Yan, S.

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Yang, Y.

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Yao, B.

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Ye, Z.

Ying, C.

R. Chen and C. Ying, “Beam propagation factor of an Airy beam,” J. Opt. 13(13), 459–462 (2011).

Yu, X.

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Zhang, P.

Zhang, X.

Zhou, M.

Am. J. Phys. (1)

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

J. Opt. (1)

R. Chen and C. Ying, “Beam propagation factor of an Airy beam,” J. Opt. 13(13), 459–462 (2011).

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

Nat. Photonics (1)

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

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (7)

Phys. Lett. A (1)

S. Yan, M. Li, B. Yao, X. Yu, M. Lei, D. Dan, Y. Yang, J. Min, and T. Peng, “Accelerating nondiffracting beams,” Phys. Lett. A 379(12), 983–987 (2015).
[Crossref]

Phys. Rev. Lett. (2)

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]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106(21), 213902 (2011).
[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,” Science 324(5924), 229–232 (2009).
[Crossref] [PubMed]

Other (3)

M. Berry and C. Upstill, “Catastrophe optics: morphologies of caustics and their diffraction patterns,” in Progress in Optics, E. Wolf ed. (Elsevier, 1980), pp. 257–346.

T. Poston and I. Stewart, Catastrophe Theory and Its Applications, Vol. 2 (Dover, 1996).

Y. A. Kravtsov and Y. I. Orlov, Caustics, Catastrophes and Wave Fields (Springer-Verlag, 1993).

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Figures (9)

Fig. 1
Fig. 1 Intensity profiles of quasi-Airy beams at different conditions.
Fig. 2
Fig. 2 Experimental setup.
Fig. 3
Fig. 3 Tunable phase patterns and quasi-Airy beams.
Fig. 4
Fig. 4 Side view of quasi-Airy beam along y-z plane propagation.
Fig. 5
Fig. 5 Caustic surfaces.
Fig. 6
Fig. 6 The tunable trajectory of the main lobe and peak intensity, The solid line and dashed line denotes Y 1 and Y 2 , respectively.
Fig. 7
Fig. 7 Tunable propagation direction.
Fig. 8
Fig. 8 Experimental intensity profiles of quasi-Airy beams θ 1 =π/3 and θ 2 =7π/6 at propagation planes z = (a1) 0, (b1) 3cm, (c1) 6cm, (d1) 10cm, respectively. (a2-d2) The corresponding numerical results. (a3-d3) The corresponding numerical results of Airy beam. (a4-d4) The corresponding numerical results of quasi-Airy beam when α=95° .
Fig. 9
Fig. 9 Numerical intensity profiles of blocked quasi-Airy beams when θ 1 =3π/2 and θ 2 =π/4 at propagation plane z = (a1) 0, (b1) 3cm, (c1) 6cm, (d1) 10cm, respectively. (a2)-(d2) The corresponding experimental results. (a3-d3) The corresponding numerical results of Airy beam. (a4-d4) The corresponding numerical results of quasi-Airy beam when α=95° .

Equations (16)

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i ϕ z + 1 2k ( 2 ϕ x 2 + 2 ϕ y 2 )=0.
ϕ(x,y,z)=Ai[x (z/2 ) 2 +iaz]exp[ax( a z 2 /2 )i( z 3 / 12 )+i( a 2 z /2 )+i( xz /2 )) ×Ai[y (z/2 ) 2 +iaz]exp[ay( a z 2 /2 )i( z 3 / 12 )+i( a 2 z /2 )+i( yz /2 )).
Φ 1 ( k x , k y )=exp(a k x 2 )exp(i( k x 3 3 a 2 k x i a 3 )/3) ×exp(a k y 2 )exp(i( k y 3 3 a 2 k y i a 3 )/3).
Φ 2 ( k x , k y )=exp(a k x 2 )exp(i k x 3 /3)×exp(a k y 2 )exp(i k y 3 /3). =exp[a( k x 2 + k y 2 )]exp[i( k x 3 + k y 3 )/3]
k x = k x cos θ 1 k y sin θ 1 , k y = k x sin θ 2 + k y cos θ 2 .
Φ 2 ( k x , k y )=exp[a ( k x cos θ 1 k y sin θ 1 ) 2 a ( k x sin θ 2 + k y cos θ 2 ) 2 ] ×exp[i ( k x cos θ 1 k y sin θ 1 ) 3 /3+i ( k x sin θ 2 + k y cos θ 2 ) 3 /3].
f ( k x , k y )= ( k x cos θ 1 k y sin θ 1 ) 3 /3+ ( k x sin θ 2 + k y cos θ 2 ) 3 /3.
ϕ(x,y,z=0)= n=1,2 Ai( s n )exp(a s n ) , s n = (1) n1 xcos(α/2)/ r 0 ysin(α/2)/ r 0 .
Ai(x) ( π 2 x) 1/4 sin[ 2 3 (x) 3/2 + π 4 ].
ϕ(x,y,z=0)= A 0 + exp(i ψ 0 + )+ A 0 exp(i ψ 0 ) = ϕ 0 + (x,y)+ ϕ 0 (x,y),
ψ 0 ± =arcsin(sin[(2/3) ( s 1 ) 3/2 +π/4])×sin[(2/3) ( s 2 ) 3/2 +π/4],
A 0 ± =±(i/2) ( π 4 s 1 s 2 ) 1/4 .
X=x+ztan[ sin 1 ( x ψ 0 ± )], Y=y+ztan[ sin 1 ( y ψ 0 ± )].
Y 1 = λ 2 sin 3 (α/2) 4 π 2 r 0 3 z 2 ,
Y 2 = (13 sin 2 (α/2)) cos 2 (α/2) sin(α/2) λ 2 4 π 2 r 0 3 z 2 .
y= cos θ 1 sin θ 2 sin θ 1 +cos θ 2 x.

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