Abstract

We show numerically that by using radial symmetric lattices, the focal spot characteristics and filament peak intensity of high-power autofocusing waves can be controlled. The lattice induced diffraction is able to isolate the main on-axis peak and control the focus position. In addition, at higher power the lattice can control and stabilize the peak intensity of the filament over an extended distance.

© 2014 Optical Society of America

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    [CrossRef]
  2. J. M. Manceau, A. Averchi, F. Bonaretti, D. Faccio, P. Di Trapani, A. Couairon, and S. Tzortzakis, Opt. Lett. 34, 2165 (2009).
    [CrossRef]
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    [CrossRef]
  4. S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, Phys. Rev. E 64, 057401 (2001).
    [CrossRef]
  5. H. S. Chakraborty, M. B. Gaarde, and A. Couairon, Opt. Lett. 31, 3662 (2006).
    [CrossRef]
  6. P. Panagiotopoulos, N. K. Efremidis, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, Phys. Rev. A 82, 061803(R) (2010).
    [CrossRef]
  7. M. Bellec, P. Panagiotopoulos, D. G. Papazoglou, N. K. Efremidis, A. Couairon, and S. Tzortzakis, Phys. Rev. Lett. 109, 113905 (2012).
    [CrossRef]
  8. D. Abdollahpour, P. Panagiotopoulos, M. Turconi, O. Jedrkiewicz, D. Faccio, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, Opt. Express 17, 5052 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Science 324, 229 (2009).
    [CrossRef]
  16. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
    [CrossRef]
  17. J. Baumgartl, M. Mazilu, and K. Dholakia, Nat. Photonics 2, 675 (2008).
    [CrossRef]
  18. N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
    [CrossRef]
  19. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, Opt. Lett. 36, 1842 (2011).
    [CrossRef]
  20. P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, Nat. Commun. 4, 2622 (2013).
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  21. P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 2883 (2011).
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    [CrossRef]
  23. P. Panagiotopoulos, A. Couairon, N. K. Efremidis, D. G. Papazoglou, and S. Tzortzakis, Opt. Express 19, 10057 (2011).
    [CrossRef]
  24. S. Suntsov, D. Abdollahpour, D. G. Papazoglou, P. Panagiotopoulos, A. Couairon, and S. Tzortzakis, Appl. Phys. Lett. 103, 021106 (2013).
    [CrossRef]
  25. S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, Appl. Phys. Lett. 94, 251104 (2009).
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2013 (2)

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, Nat. Commun. 4, 2622 (2013).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, P. Panagiotopoulos, A. Couairon, and S. Tzortzakis, Appl. Phys. Lett. 103, 021106 (2013).
[CrossRef]

2012 (2)

M. Bellec, P. Panagiotopoulos, D. G. Papazoglou, N. K. Efremidis, A. Couairon, and S. Tzortzakis, Phys. Rev. Lett. 109, 113905 (2012).
[CrossRef]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

2011 (3)

2010 (3)

N. K. Efremidis and D. N. Christodoulides, Opt. Lett. 35, 4045 (2010).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

P. Panagiotopoulos, N. K. Efremidis, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, Phys. Rev. A 82, 061803(R) (2010).
[CrossRef]

2009 (5)

2008 (4)

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

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, Phys. Rev. A 77, 043814 (2008).
[CrossRef]

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

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Opt. Express 16, 12880 (2008).
[CrossRef]

2007 (2)

2006 (1)

2003 (1)

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

2001 (1)

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, Phys. Rev. E 64, 057401 (2001).
[CrossRef]

1979 (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

1975 (1)

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Abdollahpour, D.

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, P. Panagiotopoulos, A. Couairon, and S. Tzortzakis, Appl. Phys. Lett. 103, 021106 (2013).
[CrossRef]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

D. Abdollahpour, P. Panagiotopoulos, M. Turconi, O. Jedrkiewicz, D. Faccio, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, Opt. Express 17, 5052 (2009).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, Appl. Phys. Lett. 94, 251104 (2009).
[CrossRef]

André, Y. B.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Averchi, A.

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Baumgartl, J.

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

Bellec, M.

M. Bellec, P. Panagiotopoulos, D. G. Papazoglou, N. K. Efremidis, A. Couairon, and S. Tzortzakis, Phys. Rev. Lett. 109, 113905 (2012).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Bonaretti, F.

Bourayou, R.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Broky, J.

Chakraborty, H. S.

Chen, Z.

Christodoulides, D. N.

Couairon, A.

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, Nat. Commun. 4, 2622 (2013).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, P. Panagiotopoulos, A. Couairon, and S. Tzortzakis, Appl. Phys. Lett. 103, 021106 (2013).
[CrossRef]

M. Bellec, P. Panagiotopoulos, D. G. Papazoglou, N. K. Efremidis, A. Couairon, and S. Tzortzakis, Phys. Rev. Lett. 109, 113905 (2012).
[CrossRef]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

P. Panagiotopoulos, A. Couairon, N. K. Efremidis, D. G. Papazoglou, and S. Tzortzakis, Opt. Express 19, 10057 (2011).
[CrossRef]

P. Panagiotopoulos, N. K. Efremidis, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, Phys. Rev. A 82, 061803(R) (2010).
[CrossRef]

D. Abdollahpour, P. Panagiotopoulos, M. Turconi, O. Jedrkiewicz, D. Faccio, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, Opt. Express 17, 5052 (2009).
[CrossRef]

J. M. Manceau, A. Averchi, F. Bonaretti, D. Faccio, P. Di Trapani, A. Couairon, and S. Tzortzakis, Opt. Lett. 34, 2165 (2009).
[CrossRef]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, Phys. Rev. A 77, 043814 (2008).
[CrossRef]

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

H. S. Chakraborty, M. B. Gaarde, and A. Couairon, Opt. Lett. 31, 3662 (2006).
[CrossRef]

Dholakia, K.

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

Di Trapani, P.

Ding, L. e.

Dogariu, A.

Efremidis, N. K.

Faccio, D.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

D. Abdollahpour, P. Panagiotopoulos, M. Turconi, O. Jedrkiewicz, D. Faccio, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, Opt. Express 17, 5052 (2009).
[CrossRef]

J. M. Manceau, A. Averchi, F. Bonaretti, D. Faccio, P. Di Trapani, A. Couairon, and S. Tzortzakis, Opt. Lett. 34, 2165 (2009).
[CrossRef]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, Phys. Rev. A 77, 043814 (2008).
[CrossRef]

Franco, M.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, Phys. Rev. A 77, 043814 (2008).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, Phys. Rev. E 64, 057401 (2001).
[CrossRef]

Frey, S.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Gaarde, M. B.

Hüller, S.

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, Phys. Rev. E 64, 057401 (2001).
[CrossRef]

Jedrkiewicz, O.

Kasparian, J.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Kolesik, M.

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

Lotti, A.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

Lu, P.

Manceau, J. M.

Marburger, J. H.

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Mazilu, M.

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

Mejean, G.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Mills, M. S.

Moloney, J. V.

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

Mora, P.

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, Phys. Rev. E 64, 057401 (2001).
[CrossRef]

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, Phys. Rev. E 64, 057401 (2001).
[CrossRef]

Panagiotopoulos, P.

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, Nat. Commun. 4, 2622 (2013).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, P. Panagiotopoulos, A. Couairon, and S. Tzortzakis, Appl. Phys. Lett. 103, 021106 (2013).
[CrossRef]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

M. Bellec, P. Panagiotopoulos, D. G. Papazoglou, N. K. Efremidis, A. Couairon, and S. Tzortzakis, Phys. Rev. Lett. 109, 113905 (2012).
[CrossRef]

P. Panagiotopoulos, A. Couairon, N. K. Efremidis, D. G. Papazoglou, and S. Tzortzakis, Opt. Express 19, 10057 (2011).
[CrossRef]

P. Panagiotopoulos, N. K. Efremidis, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, Phys. Rev. A 82, 061803(R) (2010).
[CrossRef]

D. Abdollahpour, P. Panagiotopoulos, M. Turconi, O. Jedrkiewicz, D. Faccio, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, Opt. Express 17, 5052 (2009).
[CrossRef]

Papazoglou, D.

Papazoglou, D. G.

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, P. Panagiotopoulos, A. Couairon, and S. Tzortzakis, Appl. Phys. Lett. 103, 021106 (2013).
[CrossRef]

M. Bellec, P. Panagiotopoulos, D. G. Papazoglou, N. K. Efremidis, A. Couairon, and S. Tzortzakis, Phys. Rev. Lett. 109, 113905 (2012).
[CrossRef]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

P. Panagiotopoulos, A. Couairon, N. K. Efremidis, D. G. Papazoglou, and S. Tzortzakis, Opt. Express 19, 10057 (2011).
[CrossRef]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, Opt. Lett. 36, 1842 (2011).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

P. Panagiotopoulos, N. K. Efremidis, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, Phys. Rev. A 82, 061803(R) (2010).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, Appl. Phys. Lett. 94, 251104 (2009).
[CrossRef]

Peng, Y.

Polesana, P.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, Phys. Rev. A 77, 043814 (2008).
[CrossRef]

Polynkin, P.

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

Prade, B.

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, Phys. Rev. E 64, 057401 (2001).
[CrossRef]

Prakash, J.

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Salmon, E.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Sauerbrey, R.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Siviloglou, G. A.

Suntsov, S.

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, P. Panagiotopoulos, A. Couairon, and S. Tzortzakis, Appl. Phys. Lett. 103, 021106 (2013).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, Appl. Phys. Lett. 94, 251104 (2009).
[CrossRef]

Tong, Y.

Turconi, M.

Tzortzakis, S.

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, Nat. Commun. 4, 2622 (2013).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, P. Panagiotopoulos, A. Couairon, and S. Tzortzakis, Appl. Phys. Lett. 103, 021106 (2013).
[CrossRef]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. A 86, 013842 (2012).
[CrossRef]

M. Bellec, P. Panagiotopoulos, D. G. Papazoglou, N. K. Efremidis, A. Couairon, and S. Tzortzakis, Phys. Rev. Lett. 109, 113905 (2012).
[CrossRef]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, Opt. Lett. 36, 1842 (2011).
[CrossRef]

P. Panagiotopoulos, A. Couairon, N. K. Efremidis, D. G. Papazoglou, and S. Tzortzakis, Opt. Express 19, 10057 (2011).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

P. Panagiotopoulos, N. K. Efremidis, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, Phys. Rev. A 82, 061803(R) (2010).
[CrossRef]

D. Abdollahpour, P. Panagiotopoulos, M. Turconi, O. Jedrkiewicz, D. Faccio, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, Opt. Express 17, 5052 (2009).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, Appl. Phys. Lett. 94, 251104 (2009).
[CrossRef]

J. M. Manceau, A. Averchi, F. Bonaretti, D. Faccio, P. Di Trapani, A. Couairon, and S. Tzortzakis, Opt. Lett. 34, 2165 (2009).
[CrossRef]

S. Tzortzakis, B. Prade, M. Franco, A. Mysyrowicz, S. Hüller, and P. Mora, Phys. Rev. E 64, 057401 (2001).
[CrossRef]

Wille, H.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Wolf, J. P.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Woste, L.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Wu, J.

Xu, Z.

Yang, X.

Yu, J.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Woste, Science 301, 61 (2003).
[CrossRef]

Zeng, H.

Zhang, P.

Zhang, Z.

Am. J. Phys. (1)

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
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Figures (3)

Fig. 1.
Fig. 1.

Input radial intensity distribution of the one Pcr ring-Airy (red) superimposed on the lattice refractive index modulation (gray).

Fig. 2.
Fig. 2.

Radial peak intensity along propagation for the one Pcr ring-Airy beam (a) without and (b) with lattice. (c) Peak intensity close to the focus position along propagation; without (dashed black line), with lattice (l = 6 rings) (red continuous line), and l = 1 ring (blue-dotted line). (d) Focus position as a function of the number of rings contained in the lattice.

Fig. 3.
Fig. 3.

Radial peak intensity of the 2.5 Pcr ring-Airy beam as a function of propagation distance z. (a) Ring-Airy without lattice, and single ring lattice with (b) Λ=350μm starting at z=24cm and (c) Λ=250μm starting at z=24cm.

Equations (2)

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Ez=i[K1(it)22+D(it)+k0Δn]E+i(ω0+it)2n0cPnlε0,
E0(r,t,z=0)=Ai(r0rw)exp[a(r0rw)]exp[t2tp2],

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