Abstract

We address the concept of three-dimensional light bullet formation in structures where nonlinearity and dispersion are contributed by different materials, including metamaterials, which are used at their best to create suitable conditions where bullets can form. The particular geometry considered here consists of alternating rings made of highly dispersive but weakly nonlinear media and strongly nonlinear but weakly dispersive media. We show that light bullets form for a wide range of parameters.

© 2009 Optical Society of America

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  1. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B 7, R53 (2005).
  2. Y. Silberberg, Opt. Lett. 15, 1282 (1990).
    [CrossRef] [PubMed]
  3. A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981).
    [CrossRef]
  4. P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielis, and A. Piskarskas, Phys. Rev. Lett. 81, 570 (1998).
    [CrossRef]
  5. X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
    [CrossRef]
  6. D. E. Edmundson and R. H. Enns, Opt. Lett. 17, 586 (1992).
    [CrossRef] [PubMed]
  7. O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
    [CrossRef]
  8. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
    [CrossRef]
  9. A. Desyatnikov, A. Maimistov, and B. Malomed, Phys. Rev. E 61, 3107 (2000).
    [CrossRef]
  10. D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
    [CrossRef] [PubMed]
  11. G. Fibich and B. Ilan, Opt. Lett. 29, 887 (2004).
    [CrossRef] [PubMed]
  12. B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. A 70, 053613 (2004).
    [CrossRef]
  13. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 70, 055603(R) (2004).
    [CrossRef]
  14. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
    [CrossRef] [PubMed]
  15. A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
    [CrossRef]
  16. L. Berge and S. Skupin, Phys. Rev. Lett. 100, 113902 (2008).
    [CrossRef] [PubMed]
  17. L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, Opt. Commun. 199, 277 (2001).
    [CrossRef]
  18. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
    [CrossRef]
  19. H. Sakaguchi and B. A. Malomed, Phys. Rev. A 75, 063825 (2007).
    [CrossRef]

2008 (1)

L. Berge and S. Skupin, Phys. Rev. Lett. 100, 113902 (2008).
[CrossRef] [PubMed]

2007 (2)

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

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 75, 063825 (2007).
[CrossRef]

2006 (2)

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
[CrossRef]

2005 (2)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B 7, R53 (2005).

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

2004 (3)

G. Fibich and B. Ilan, Opt. Lett. 29, 887 (2004).
[CrossRef] [PubMed]

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. A 70, 053613 (2004).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 70, 055603(R) (2004).
[CrossRef]

2002 (2)

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

2001 (1)

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, Opt. Commun. 199, 277 (2001).
[CrossRef]

2000 (1)

A. Desyatnikov, A. Maimistov, and B. Malomed, Phys. Rev. E 61, 3107 (2000).
[CrossRef]

1999 (1)

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

1998 (1)

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielis, and A. Piskarskas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

1992 (1)

1990 (1)

1981 (1)

A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981).
[CrossRef]

Baizakov, B. B.

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. A 70, 053613 (2004).
[CrossRef]

Bang, O.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Berge, L.

L. Berge and S. Skupin, Phys. Rev. Lett. 100, 113902 (2008).
[CrossRef] [PubMed]

Buryak, A. V.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Caironi, D.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielis, and A. Piskarskas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Carrasco, S.

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, Opt. Commun. 199, 277 (2001).
[CrossRef]

Couairon, A.

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

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 70, 055603(R) (2004).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, Opt. Commun. 199, 277 (2001).
[CrossRef]

Danielis, R.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielis, and A. Piskarskas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Desyatnikov, A.

A. Desyatnikov, A. Maimistov, and B. Malomed, Phys. Rev. E 61, 3107 (2000).
[CrossRef]

Dubietis, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielis, and A. Piskarskas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Edmundson, D. E.

Enns, R. H.

Fibich, G.

Ilan, B.

Kanashov, A. A.

A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981).
[CrossRef]

Kartashov, Y. V.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 70, 055603(R) (2004).
[CrossRef]

Krolikowski, W.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 70, 055603(R) (2004).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Liu, X.

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Maimistov, A.

A. Desyatnikov, A. Maimistov, and B. Malomed, Phys. Rev. E 61, 3107 (2000).
[CrossRef]

Malomed, B.

A. Desyatnikov, A. Maimistov, and B. Malomed, Phys. Rev. E 61, 3107 (2000).
[CrossRef]

Malomed, B. A.

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 75, 063825 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B 7, R53 (2005).

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. A 70, 053613 (2004).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 70, 055603(R) (2004).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B 7, R53 (2005).

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 70, 055603(R) (2004).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, Opt. Commun. 199, 277 (2001).
[CrossRef]

Mysyrowicz, A.

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

Piskarskas, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielis, and A. Piskarskas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Rasmussen, J. J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Rubenchik, A. M.

A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981).
[CrossRef]

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 75, 063825 (2007).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

Salerno, M.

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. A 70, 053613 (2004).
[CrossRef]

Silberberg, Y.

Skupin, S.

L. Berge and S. Skupin, Phys. Rev. Lett. 100, 113902 (2008).
[CrossRef] [PubMed]

Torner, L.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B 7, R53 (2005).

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 70, 055603(R) (2004).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, Opt. Commun. 199, 277 (2001).
[CrossRef]

Torres, J. P.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, Opt. Commun. 199, 277 (2001).
[CrossRef]

Towers, I.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Trapani, P. Di

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielis, and A. Piskarskas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Valiulis, G.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielis, and A. Piskarskas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B 7, R53 (2005).

Wise, F. W.

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

J. Opt. B (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B 7, R53 (2005).

Opt. Commun. (1)

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, Opt. Commun. 199, 277 (2001).
[CrossRef]

Opt. Lett. (3)

Phys. Rep. (1)

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

Phys. Rev. A (2)

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. A 70, 053613 (2004).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 75, 063825 (2007).
[CrossRef]

Phys. Rev. E (5)

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 70, 055603(R) (2004).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. E 73, 025601(R) (2006).
[CrossRef]

A. Desyatnikov, A. Maimistov, and B. Malomed, Phys. Rev. E 61, 3107 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielis, and A. Piskarskas, Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, Phys. Rev. Lett. 82, 4631 (1999).
[CrossRef]

L. Berge and S. Skupin, Phys. Rev. Lett. 100, 113902 (2008).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Physica D (1)

A. A. Kanashov and A. M. Rubenchik, Physica D 4, 122 (1981).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Isosurface plots showing output patterns after propagation at ξ = 2 of input Gaussian signals in linear tandem structures with (a), (b) d = 20 ; (c) d = 0.8 ; and (d) d = 0.4 . In (a) the dispersion in the central domain is set to β = 2 . In (b)–(d), β = 0.1 .

Fig. 2
Fig. 2

Soliton profiles in tandem structures with d = 0.4 and S = 0.5 . (a), (c) b = 0.3 ; (b), (d) b = 0.85 . In (a), (b) the central domain is linear, while in (c), (d) the central domain is nonlinear.

Fig. 3
Fig. 3

Energy versus propagation constant for (a) different S values at d = 0.4 and (b) different d values at S = 0.5 . The circles in (a) correspond to the solitons shown in Figs. 2a, 2b. In (b) the domain width takes values d = 0.8 , 0.6, 0.4, 0.2, and 0.1 from the lower to the upper curve. (c) Perturbation growth rate versus b at k = 0 , S = 0.5 . In (a)–(c) the central domain is linear. (d) Growth rate versus b at k = 1 , d = 1.2 , S = 0.5 in the structure with linear (1) and nonlinear (2) central domains.

Fig. 4
Fig. 4

(a) Isosurface plots at ξ = 0 (left) and ξ = 128 (right) showing stable propagation of a light bullet in a tandem structure with a linear central domain with β = 2 , and (b) isosurface plots at ξ = 0 (left) and ξ = 72 (right) showing unstable propagation of a light bullet in tandem with a nonlinear central domain with β = 0.1 . In all cases b = 0.3 , d = 0.4 , S = 0.5 .

Equations (1)

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i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) + β ( η , ζ ) 2 2 q τ 2 + σ ( η , ζ ) q q 2 1 + S q 2 .

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