Abstract

We report the observation of arbitrary accelerating beams (ABs) designed using a nonparaxial description of optical caustics. We use a spatial light modulator-based setup and techniques of Fourier optics to generate circular and Weber beams subtending over 95 deg of arc. Applying a complementary binary mask also allows the generation of periodic ABs taking the forms of snake-like trajectories, and the application of a rotation to the caustic allows the first experimental synthesis of optical ABs upon the surface of a sphere in three dimensions.

© 2013 Optical Society of America

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  1. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  2. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
    [CrossRef]
  3. P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, Phys. Rev. Lett. 109, 193901 (2012).
    [CrossRef]
  4. M. A. Bandres and B. M. Rodriguez-Lara, New J. Phys. 15, 013054 (2013).
    [CrossRef]
  5. P. Aleahmad, M. A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 109, 203902 (2012).
    [CrossRef]
  6. L. Froehly, F. Courvoisier, A. Mathis, M. Jacquot, L. Furfaro, R. Giust, P. A. Lacourt, and J. M. Dudley, Opt. Express 19, 16455 (2011).
    [CrossRef]
  7. E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
    [CrossRef]
  8. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, Phys. Rev. A 85, 023828 (2012).
    [CrossRef]
  9. F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, Opt. Lett. 37, 1736 (2012).
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  10. P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 002820 (2012).
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    [CrossRef]
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2013 (1)

M. A. Bandres and B. M. Rodriguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

2012 (7)

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

I. Kaminer, 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]

D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, Phys. Rev. A 85, 023828 (2012).
[CrossRef]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 002820 (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]

M. A. Alonso and M. A. Bandres, Opt. Lett. 37, 5175 (2012).
[CrossRef]

2011 (2)

2007 (1)

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

2006 (1)

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, Opt. Express 14, 011277 (2006).
[CrossRef]

1999 (1)

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]

Alonso, M. A.

Bandres, M. A.

M. A. Bandres and B. M. Rodriguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

M. A. Alonso and M. A. Bandres, Opt. Lett. 37, 5175 (2012).
[CrossRef]

Bekenstein, R.

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

Broky, J.

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

Campos, J.

Cannan, D.

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, 002820 (2012).
[CrossRef]

Chen, Z.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 002820 (2012).
[CrossRef]

D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, Phys. Rev. A 85, 023828 (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]

Chremmos, D.

D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, Phys. Rev. A 85, 023828 (2012).
[CrossRef]

Christodoulides, D. N.

D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, Phys. Rev. A 85, 023828 (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]

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

Cottrell, D. M.

Courvoisier, F.

Davis, J. A.

Dogariu, A.

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

Dudley, J. M.

Efremidis, N. K.

D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, Phys. Rev. A 85, 023828 (2012).
[CrossRef]

Froehly, L.

Furfaro, L.

Giust, R.

Greenfield, E.

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

E. Greenfield, I. Kaminer, and M. Segev, in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FW1A.2.

Hu, Y.

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, 002820 (2012).
[CrossRef]

Jacquot, M.

Kaminer, I.

I. Kaminer, 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, I. Kaminer, and M. Segev, in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FW1A.2.

Lacourt, P. A.

Lasser, T.

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, Opt. Express 14, 011277 (2006).
[CrossRef]

Leitgeb, R. A.

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, Opt. Express 14, 011277 (2006).
[CrossRef]

Leutenegger, M.

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, Opt. Express 14, 011277 (2006).
[CrossRef]

Li, T.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 002820 (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]

Mathis, A.

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]

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, 002820 (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]

Moreno, I.

Nemirovsky, J.

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

Rao, R.

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, Opt. Express 14, 011277 (2006).
[CrossRef]

Raz, O.

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

Rodriguez-Lara, B. M.

M. A. Bandres and B. M. Rodriguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

Salandrino, A.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 002820 (2012).
[CrossRef]

Segev, M.

I. Kaminer, 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]

E. Greenfield, I. Kaminer, and M. Segev, in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FW1A.2.

Siviloglou, G. A.

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

Walasik, W.

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

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]

Yzuel, M. J.

Zhang, P.

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, 002820 (2012).
[CrossRef]

Zhang, X.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 002820 (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]

Appl. Opt. (1)

New J. Phys. (1)

M. A. Bandres and B. M. Rodriguez-Lara, New J. Phys. 15, 013054 (2013).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (1)

D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, Phys. Rev. A 85, 023828 (2012).
[CrossRef]

Phys. Rev. Lett. (5)

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

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

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

I. Kaminer, 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]

Other (1)

E. Greenfield, I. Kaminer, and M. Segev, in Frontiers in Optics 2012/Laser Science XXVIII, OSA Technical Digest (online) (Optical Society of America, 2012), paper FW1A.2.

Supplementary Material (1)

» Media 1: AVI (1257 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup. Target AB is generated from the Fourier plane of a MO by applying a phase-mask to a SLM. A prefiltering stage (Fourier plane of L1) removes the unmodulated zero-order of diffraction. L1, L2, and L3 are lenses of focal lengths 500, 250, and 200 mm, respectively.

Fig. 2.
Fig. 2.

Experimental intensity distributions: (a) parabolic Weber beam, (b) circular Mathieu beam, and (c) quartic beam. Adjacent subfigures in each case show expanded views at points A and B. The white dashed lines show the target trajectories. Vertical and horizontal scales are identical.

Fig. 3.
Fig. 3.

Periodic circular and parabolic beams. Dashed lines show target trajectories. Vertical and horizontal scales are identical. (a), (e) numerical results. (b), (f) Experimental results. (c), (g) Detailed view near trajectory extremum. (d), (h) Experimental line profiles along the caustics showing periodicities of 11.1±2μm (d) and 18.8±1μm (h).

Fig. 4.
Fig. 4.

Experimental spherically shaped field. (a), (b) 3D isointensity surfaces of the experimental beam at 30% of maximal intensity. Media 1 shows rotation. Inset: rotation phase mask (unwrapped). (c), (d) Cross sections in xy and xz planes. White dashed lines show the cross sections of a 50 μm radius half-sphere. Scaling is identical in all directions.

Equations (1)

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Φc(yF)yF=kc(z)zzc(z)f;yF=fzc(z)1+[zc(z)]2,

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