Abstract

We demonstrate both experimentally and theoretically controlled acceleration of one- and two-dimensional Airy beams in optically induced refractive-index potentials. Enhancement as well as reduction of beam acceleration are realized by changing the index gradient, while the beam shape is maintained during propagation through the linear optical potential. Our results of active acceleration manipulation in graded media are pertinent to Airy-type beam propagation in various environments.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2011 (5)

2010 (7)

2009 (2)

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

2008 (2)

2007 (2)

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 2139011 (2007).
[CrossRef]

1979 (1)

M. V. Berry and N. L. Balazs, J. Phys. A 12, L5 (1979).
[CrossRef]

Arie, A.

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581(2010).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Balazs, N. L.

M. V. Berry and N. L. Balazs, J. Phys. A 12, L5 (1979).
[CrossRef]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, J. Phys. A 12, L5 (1979).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 2139011 (2007).
[CrossRef]

Chen, Z.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

Chremmos, I.

Christodoulides, D. N.

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 2139011 (2007).
[CrossRef]

Dolev, I.

Efremidis, N.

Efremidis, N. K.

Ellenbogen, T.

I. Dolev, T. Ellenbogen, and A. Arie, Opt. Lett. 35, 1581(2010).
[CrossRef] [PubMed]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Fleischer, J. W.

S. Jia, J. Lee, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

Ganany-Padowicz, A.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Greenfield, E.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef] [PubMed]

Hu, Y.

Huang, S.

Jia, S.

S. Jia, J. Lee, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

Kivshar, Y. S.

Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Lee, J.

S. Jia, J. Lee, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

Liu, W.

Lou, C.

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

Mills, M.

Miroshnichenko, A. E.

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Neshev, D. N.

Papazoglou, D. G.

Polynkin, P.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

Prakash, J.

Raz, O.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef] [PubMed]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

Salandrino, A.

Segev, M.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef] [PubMed]

Shadrivov, I. V.

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Opt. Lett. 33, 207 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 2139011 (2007).
[CrossRef]

Tzortzakis, S.

Voloch-Bloch, N.

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

Walasik, W.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef] [PubMed]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

Xu, J.

Zhang, P.

Zhang, Z.

J. Phys. A (1)

M. V. Berry and N. L. Balazs, J. Phys. A 12, L5 (1979).
[CrossRef]

Nat. Photon. (3)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
[CrossRef]

T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nat. Photon. 3, 395 (2009).
[CrossRef]

J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
[CrossRef]

Opt. Lett. (11)

Phys. Rev. Lett. (3)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 2139011 (2007).
[CrossRef]

S. Jia, J. Lee, and J. W. Fleischer, Phys. Rev. Lett. 104, 253904 (2010).
[CrossRef] [PubMed]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
[CrossRef] [PubMed]

Science (1)

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Theoretical results of 1D Airy beams propagating in a medium with different index gradients δ n . (a) Normal propagation at δ n = 0 . (b) Enhanced and (c) reduced acceleration at δ n > 0 and δ n < 0 , respectively; (d) no acceleration at δ n = δ n c . (e) Plot of acceleration as a function of δ n under different x 0 . The white dashed lines mark the position of the central lobe at the output in (a), and the arrows illustrate the index gradient.

Fig. 2
Fig. 2

(a), (b) Schematic of the experimental setup. A biased SBN crystal is illuminated by nonuniform white light from x z plane, while the Airy beam is launched along the z direction. (c) Plot of induced refractive-index change along the x direction where two vertical dashed lines define the graded index area for beam control.

Fig. 3
Fig. 3

Experimental (a1)–(f1) and numerical (a2)–(f2) results showing acceleration suppression (a)–(c) and enhancement (d)–(f) of the 1D Airy beam. Shown from left to right are input, output after 10 mm of propagation through a uniform (middle) and graded (right) index medium. White dashed lines mark the output beam position from the uniform medium for reference. Arrows in (c1), (f1) indicate the refractive-index gradient.

Fig. 4
Fig. 4

Experimental (a1)–(f1) and numerical (a2)–(f2) results showing acceleration suppression (a)–(c) and enhancement (d)–(f) of the 2D Airy beam. Other descriptions are the same as those for Fig. 3.

Equations (2)

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i φ z + 1 2 k 2 φ = k n Δ n φ ,
ϕ ( x , z ) = Ai [ ( x z 2 4 k 2 x 0 3 δ n z 2 2 n ) / x 0 + i a z k x 0 ] · exp [ a x a 2 ( 1 k 2 x 0 3 + δ n n ) z 2 i 12 ( 1 k 3 x 0 6 + 2 k δ n 2 n 2 + 3 δ n n k x 0 3 ) z 3 + i a 2 2 k z + i ( 1 2 k x 0 3 + k δ n n ) z x ] .

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