Abstract

We experimentally demonstrate self-accelerating Bessel-like optical beams propagating along arbitrary trajectories in free space. With computer-generated holography, such beams are designed to follow different controllable trajectories while their main lobe transverse profiles remain nearly invariant and symmetric. Examples include parabolic, snake-like, hyperbolic, hyperbolic secant, and even three-dimensional spiraling trajectories. The self-healing property of such beams is also demonstrated. This new class of optical beams can be considered as a hybrid between accelerating and nonaccelerating nondiffracting beams that may find a variety of applications.

© 2013 Optical Society of America

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    [CrossRef]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  3. E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
    [CrossRef]
  4. Y. Hu, G. A. Siviloglou, P. Zhang, D. N. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
    [CrossRef]
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    [CrossRef]
  20. P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
    [CrossRef]

2012

I. Dolev, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, Opt. Lett. 37, 1736 (2012).
[CrossRef]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, Opt. Lett. 37, 5003 (2012).
[CrossRef]

2011

2010

2009

2008

2007

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

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Aleahmad, P.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

Baumgartl, J.

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

Bekenstein, R.

I. Dolev, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Biegert, J.

Bowlan, P.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Cannan, D.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef]

Chen, Z.

Chremmos, I. D.

Christodoulides, D. N.

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, Opt. Lett. 37, 5003 (2012).
[CrossRef]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 1491 (2011).
[CrossRef]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 2883(2011).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

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

Y. Hu, G. A. Siviloglou, P. Zhang, D. N. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012).

Cizmar, T.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).
[CrossRef]

Clerici, M.

Courvoisier, F.

Dalgarno, H.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).
[CrossRef]

Dholakia, K.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).
[CrossRef]

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

Di Trapani, P.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dolev, I.

I. Dolev, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Dudley, J. M.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Efremidis, N. K.

Faccio, D.

Froehly, L.

Furfaro, L.

Giust, R.

Greenfield, E.

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

Gunn-Moore, F.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).
[CrossRef]

Hernandez, D.

Hu, Y.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef]

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, Opt. Lett. 35, 2260 (2010).
[CrossRef]

Y. Hu, G. A. Siviloglou, P. Zhang, D. N. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012).

Huang, S.

Jacquot, M.

Jarutis, V.

Jedrkiewicz, O.

Kaminer, I.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

Lacourt, P. A.

Li, T.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

Lõhmus, M.

Lotti, A.

Lou, C.

Marchington, R.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).
[CrossRef]

Mathis, A.

Matijošius, A.

Mazilu, M.

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

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Mills, M. S.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 2883(2011).
[CrossRef]

Miri, M.-A.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

Morandotti, R.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef]

Morris, J.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).
[CrossRef]

Nemirovsky, J.

I. Dolev, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Piksarv, P.

Piskarskas, A.

Prakash, J.

Raz, O.

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

Rubino, E.

Saari, P.

Salandrino, A.

Salazar, M.

Segev, M.

I. Dolev, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

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

Siviloglou, G. A.

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

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Y. Hu, G. A. Siviloglou, P. Zhang, D. N. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012).

Trapani, P. D.

Trebino, R.

Valtna-Lukner, H.

Walasik, W.

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

Xu, J.

Yin, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef]

Zhang, P.

Zhang, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

Zhang, Z.

J. Opt.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).
[CrossRef]

Nat. Photonics

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

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

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

I. Dolev, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef]

Other

Y. Hu, G. A. Siviloglou, P. Zhang, D. N. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup for generating self-accelerating Bessel-like beams via computer-generated holography. SLM, spatial light modulator; H, hologram; L, lens; CCD, charge-coupled device.

Fig. 2.
Fig. 2.

Numerical and experimental demonstrations of a self-accelerating Bessel-like beam along a parabolic trajectory. (a) Computer-generated hologram; (b) numerically simulated side-view propagation of the generated beam; (c)–(f) snapshots of the transverse intensity patterns taken at the planes marked by the dashed lines in (b); and (g) experimentally recorded transverse beam patterns at different positions marked in the predesigned parabolic trajectory (dashed curve) corresponding to (b).

Fig. 3.
Fig. 3.

Experimental demonstration of self-accelerating Bessel-like beams along a snake-like [(a), (d)], a hyperbolic [(b), (e)], and a hyperbolic secant [(c), (f)] trajectory. In (a)–(c), the solid curves plot the predesigned trajectories and the circles represent experimental data. (d)–(f) Recorded transverse beam patterns at different positions marked in the predesigned trajectories (dashed curve) corresponding to (a)–(c), respectively.

Fig. 4.
Fig. 4.

Experimental demonstration of self-accelerating Bessel-like beams along a 3D curved trajectory. (a) Measured (circles) versus the predesigned (solid curve) beam trajectory; (b)–(e) transverse beam patterns at different marked positions in (a), where the cross marks the center of the reference Gaussian beam.

Fig. 5.
Fig. 5.

Numerical and experimental results of the self-healing property of a Bessel-like beam along a hyperbolic trajectory. (a) Hologram and (b) numerical simulation of the side-view propagation of the generated beam, when its main lobe is partially blocked by an opaque wire. (c)–(f) Display the transverse intensity snapshots from the simulation (top) and experiment (bottom) at different planes marked in (b).

Equations (2)

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u(x,y)=exp((x2+y2)/w2)exp[iQ(x,y)],
Q(x,y)=k020z{[f(ζ)]2+[g(ζ)]2(β/k0)2}dζk0(fx)2+(gy)22z,β2z2/k02=[xf(z)+zf(z)]2+[yg(z)+zg(z)]2,

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