Abstract

We use caustic beam shaping on 100 fs pulses to experimentally generate nonparaxial accelerating beams along a 60° circular arc, moving laterally by 14 µm over a 28 µm propagation length. This is the highest degree of transverse acceleration reported to our knowledge. Using diffraction integral theory and numerical beam propagation simulations, we show that circular acceleration trajectories represent a unique class of nonparaxial diffraction-free beam profile which also preserves the femtosecond temporal structure in the vicinity of the caustic.

© 2012 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. J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photon. 2, 675 (2008).
    [CrossRef]
  3. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
    [CrossRef]
  4. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photon. 4, 103 (2010).
    [CrossRef]
  5. I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
    [CrossRef]
  6. A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
    [CrossRef]
  7. E. Greenfield, M. Segev, W. Walasik, and O. Raz, Phys. Rev. Lett. 106, 213902 (2011).
    [CrossRef]
  8. 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]
  9. J. F. Nye, Natural Focusing and Fine Structure of Light(Institute of Physics Publishing, 1999).
  10. I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett.108, 163901 (2012).
  11. Y. Kaganovsky and E. Heyman, J. Opt. Soc. Am. B 28, 1243 (2011).
    [CrossRef]

2011

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

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

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]

Y. Kaganovsky and E. Heyman, J. Opt. Soc. Am. B 28, 1243 (2011).
[CrossRef]

2010

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

2009

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

2008

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

2007

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

Abdollahpour, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Baumgartl, J.

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

Bekenstein, R.

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

Broky, J.

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

Chong, A.

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

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

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

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

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

Couairon, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Courvoisier, F.

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, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dudley, J. M.

Faccio, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[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]

Heyman, E.

Y. Kaganovsky and E. Heyman, J. Opt. Soc. Am. B 28, 1243 (2011).
[CrossRef]

Jacquot, M.

Kaganovsky, Y.

Y. Kaganovsky and E. Heyman, J. Opt. Soc. Am. B 28, 1243 (2011).
[CrossRef]

Kaminer, I.

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

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

Kolesik, M.

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

Lacourt, P. A.

Lotti, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Mathis, A.

Mazilu, M.

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

Moloney, J. V.

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

Nemirovsky, J.

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

Nye, J. F.

J. F. Nye, Natural Focusing and Fine Structure of Light(Institute of Physics Publishing, 1999).

Panagiotopoulos, P.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Papazoglou, D. G.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Polynkin, P.

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

Raz, O.

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

Renninger, W. H.

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

Segev, M.

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

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

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

Siviloglou, G. A.

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

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

Tzortzakis, S.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Walasik, W.

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

Wise, F. W.

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

J. Opt. Soc. Am. B

Y. Kaganovsky and E. Heyman, J. Opt. Soc. Am. B 28, 1243 (2011).
[CrossRef]

Nat. Photon.

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

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

Opt. Express

Phys. Rev. A

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807 (2011).
[CrossRef]

Phys. Rev. Lett.

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

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

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

Science

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

Other

J. F. Nye, Natural Focusing and Fine Structure of Light(Institute of Physics Publishing, 1999).

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

Supplementary Material (1)

» Media 1: MOV (321 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

(a) Numerical (top) and experimental (bottom) intensity distributions of a circular accelerating beam. The corresponding target caustic is shown as the white dashed line. (b) Propagation geometry of the caustic beam. (c) Comparison of the numerical (line), and experimental (circles) intensity profile normal to the caustic at points P and Q as indicated. In (c) we also show the analytic result from Eq. (1) with the dashed curve.

Fig. 2.
Fig. 2.

(a) Evolution of the primary lobe size with propagation. The dashed line corresponds to the analytical model of Eq. (1), the solid curve to the numerical propagation, and the circles to experimental results. (b) Evolution of the intensity along the caustic with the propagation distance. (c) Snapshots of a 15 fs pulse at various points along its propagation. The corresponding propagation times are 40, 80, 140, and 230 fs (Media 1).

Fig. 3.
Fig. 3.

Intensity distribution of a 15 fs pulse at propagation distances as shown as a function of co-moving time and distance from the caustic.

Equations (1)

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IM(u)=(2ck)2/3kz2π1+c2I0(yM)Ai2[(2k2R(z))1/3u].

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