Abstract

We introduce a general approach for generation of sets of three-dimensional quasi-nonspreading wave packets propagating in linear media, also referred to as linear light bullets. The spectrum of rigorously nonspreading wave packets in media with anomalous group velocity dispersion is localized on the surface of a sphere, thus drastically restricting the possible wave packet shapes. However, broadening slightly the spectrum affords the generation of a large variety of quasi-nonspreading distributions featuring complex topologies and shapes in space and time that are of interest in different areas, such as biophysics or nanosurgery. Here we discuss the method and show several illustrative examples of its potential.

© 2011 Optical Society of America

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  1. M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
    [CrossRef]
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    [CrossRef]
  3. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  4. J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
    [CrossRef]
  5. C. Lopez-Mariscal, M. A. Bandres, J. C. Gutierrez-Vega, and S. Chavez-Cerda, Opt. Express 13, 2364 (2005).
    [CrossRef] [PubMed]
  6. S. Lopez-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  8. M. A. Porras, Opt. Lett. 26, 1364 (2001).
    [CrossRef]
  9. S. Longhi, Phys. Rev. E 68, 066612 (2003).
    [CrossRef]
  10. M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
    [CrossRef]
  11. S. Longhi, Opt. Lett. 29, 147 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

S. Lopez-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef] [PubMed]

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

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

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

2009

2005

2004

S. Longhi, Opt. Lett. 29, 147 (2004).
[CrossRef] [PubMed]

M. A. Porras and P. Di Trapani, Phys. Rev. E 69, 066606 (2004).
[CrossRef]

2003

S. Longhi, Phys. Rev. E 68, 066612 (2003).
[CrossRef]

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

2001

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

R. Piestun, Opt. Photon. News 12, 28 (2001).
[CrossRef]

M. A. Porras, Opt. Lett. 26, 1364 (2001).
[CrossRef]

1997

H. Sonajalg, M. Rätsep, and P. Saari, Opt. Lett. 22, 310 (1997).
[CrossRef] [PubMed]

P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, Opt. Commun. 136, 207 (1997).
[CrossRef]

1990

1987

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

Abdollahpour, D.

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

Bandres, M. A.

Bartelt, H.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Chavez-Cerda, S.

C. Lopez-Mariscal, M. A. Bandres, J. C. Gutierrez-Vega, and S. Chavez-Cerda, Opt. Express 13, 2364 (2005).
[CrossRef] [PubMed]

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Chong, A.

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

Christodoulides, D. N.

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

Dallaire, M.

Dholakia, K.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

Di Trapani, P.

M. A. Porras and P. Di Trapani, Phys. Rev. E 69, 066606 (2004).
[CrossRef]

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Eilenberger, F.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Fagerholm, J.

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, Opt. Commun. 136, 207 (1997).
[CrossRef]

Friberg, A. T.

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, Opt. Commun. 136, 207 (1997).
[CrossRef]

Gunn-Moore, F.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

Gutierrez-Vega, J. C.

C. Lopez-Mariscal, M. A. Bandres, J. C. Gutierrez-Vega, and S. Chavez-Cerda, Opt. Express 13, 2364 (2005).
[CrossRef] [PubMed]

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Iturbe-Castillo, M. D.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Kartashov, Y. V.

S. Lopez-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef] [PubMed]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Kobelke, J.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Lederer, F.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Longhi, S.

Lopez-Aguayo, S.

S. Lopez-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef] [PubMed]

Lopez-Mariscal, C.

Mazilu, M.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

McCarthy, N.

Miceli, J. J.

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

Minardi, S.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

New, G. H. C.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Nolte, S.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Papazoglou, D. G.

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

Pertsch, T.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Piche, M.

Piestun, R.

R. Piestun, Opt. Photon. News 12, 28 (2001).
[CrossRef]

Porras, M. A.

M. A. Porras and P. Di Trapani, Phys. Rev. E 69, 066606 (2004).
[CrossRef]

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

M. A. Porras, Opt. Lett. 26, 1364 (2001).
[CrossRef]

Ramirez, G. A.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Rätsep, M.

Reivelt, K.

P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

Renninger, W. H.

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

Rodriguez-Dagnino, R. M.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Röpke, U.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Saari, P.

Salomaa, M. M.

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, Opt. Commun. 136, 207 (1997).
[CrossRef]

Schuster, K.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Silberberg, Y.

Sonajalg, H.

Stevenson, D. J.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

Suntsov, S.

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

Szameit, A.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Tepichin, E.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

Torner, L.

S. Lopez-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef] [PubMed]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Tünnermann, A.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

Tzortzakis, S.

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

Valiulis, G.

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

Vysloukh, V. A.

S. Lopez-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef] [PubMed]

Wise, F. W.

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

Laser Photon. Rev.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, Laser Photon. Rev. 4, 529 (2010).
[CrossRef]

Nat. Photon.

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

Opt. Commun.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. H. C. New, Opt. Commun. 195, 35 (2001).
[CrossRef]

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, Opt. Commun. 136, 207 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Photon. News

R. Piestun, Opt. Photon. News 12, 28 (2001).
[CrossRef]

Phys. Rev. E

S. Longhi, Phys. Rev. E 68, 066612 (2003).
[CrossRef]

M. A. Porras, G. Valiulis, and P. Di Trapani, Phys. Rev. E 68, 016613 (2003).
[CrossRef]

M. A. Porras and P. Di Trapani, Phys. Rev. E 69, 066606 (2004).
[CrossRef]

Phys. Rev. Lett.

P. Saari and K. Reivelt, Phys. Rev. Lett. 79, 4135 (1997).
[CrossRef]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, Phys. Rev. Lett. 105, 263901 (2010).
[CrossRef]

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

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

S. Lopez-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 105, 013902 (2010).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Isosurface plots at the level 0.08 max | q s | showing 3D field modulus distributions (top row), field modulus distributions in the plane τ = 0 (middle row), and corresponding spectra at the level 0.4 max | q k | (bottom row) of 3D wave packets generated at δ = 0.1 (left column), 0.4 (middle column), and 0.5 (right column). All isosurface plots are made partially transparent to show internal structure of the wave packet and its spectrum.

Fig. 2
Fig. 2

(a) Propagation distance at which peak amplitude of the wave packet from Fig. 1 decreases by 10% versus angular spectrum width. (b) Fraction of energy concentrated in the central bright spot versus angular spectrum width.

Fig. 3
Fig. 3

Left, field modulus distribution at the level 0.19 max | q s | (top row), field modulus distribution at η = 0 (middle row), and beam spectrum at the level 0.02 max | q k | (bottom row) for a wave packet composed of two Bessel-like pulsed beams. Center, field modulus distribution at the level 0.19 max | q s | (top row), field modulus distribution at τ = 0 (middle row), and spectrum at the level 0.14 max | q k | for a necklacelike wave packet. Right, field modulus distribution at the level 0.17 max | q s | (top row), field modulus distribution at τ = 0 (middle row), and spectrum at 0.36 max | q k | for a necklace wave packet with complex spatial distribution.

Fig. 4
Fig. 4

Left, field modulus distribution at the level 0.13 max | q s | (top row), field modulus distribution at τ = 0 (middle row), and beam spectrum at the level 0.02 max | q k | (bottom row) for a “hollow” wave packet. Center, field modulus distribution at the level 0.20 max | q s | (top row), field modulus distribution at η = 0 (middle row), and spectrum at the level 0.05 max | q k | for a spiraling wave packet. Right, field modulus distribution at the level 0.20 max | q s | (top row), field modulus distribution at τ = 0 (middle row), and spectrum at the level 0.16 max | q k | for spherically periodic wave packet (only several central rings are shown).

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 + 2 q τ 2 ) ,
q s = exp ( i k t 2 ξ / 2 ) 0 π d θ 0 2 π G ( θ , φ ) × exp [ i k t ( η cos φ sin θ + ζ sin φ sin θ + τ cos θ ) ] d φ ,

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