Abstract

We address the stability of light bullets supported by Bessel optical lattices with out-of-phase modulation of the linear and nonlinear refractive indices. We show that spatial modulation of the nonlinearity significantly modifies the shapes and stability domains of the light bullets. The addressed bullets can be stable, provided that the peak intensity does not exceed a critical value. We show that the width of the stability domain in terms of the propagation constant may be controlled by varying the nonlinearity modulation depth. In particular, we show that the maximum energy of the stable bullets grows with increasing nonlinearity modulation depth.

© 2009 Optical Society of America

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2009

2008

2007

C. R. Rosberg, F. H. Bennet, D. N. Neshev, P. D. Rasmussen, O. Bang, W. Krolikowski, A. Bjarklev, and Y. S. Kivshar, "Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers," Opt. Express 15, 12145 (2007).
[CrossRef] [PubMed]

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, "Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities," Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, "Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices," Phys. Lett. A 367, 149 (2007).
[CrossRef]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, "Solitary waves under the competition of linear and nonlinear periodic potentials," J. Phys. A 40, 14151 (2007).
[CrossRef]

2006

D. Blömer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tünnermann, "Nonlinear refractive index of fs-laser-written waveguides in fused silica," Opt. Express 14, 2151 (2006).
[CrossRef] [PubMed]

R. Zhang, J. Telpel, and H. Glessen, "Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation," Opt. Express 14, 6800 (2006).
[CrossRef] [PubMed]

F. Ye, Y. V. Kartashov, and L. Torner, "Asymmetric matter-wave solitons at nonlinear interfaces," Phys. Rev. A 74, 063616 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, "Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity," Phys. Rev. E 73, 026601 (2006).
[CrossRef]

Y. V. Bludov and V. V. Konotop, "Localized modes in arrays of boson-fermion mixtures," Phys. Rev. A 74, 043616 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Three-dimensional spatiotemporal solitons in nonlocal nonlinear media," Phys. Rev. E 73, 025601 (2006).
[CrossRef]

2005

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, "Spatiotemporal optical solitons," J. Opt. B 7, R53 (2005).
[CrossRef]

A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830 (2005).
[CrossRef] [PubMed]

H. Sakaguchi and B. A. Malomed, "Matter-wave solitons in nonlinear optical lattices," Phys. Rev. E 72, 046610 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

M. T. Primatarowa, K. T. Stoychev, and R. S. Kamburova, "Interaction of solitons with extended nonlinear defects," Phys. Rev. E 72, 036608 (2005).
[CrossRef]

F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314 (2005).
[CrossRef] [PubMed]

A. Zoubir, M. Richardson, L. Canioni, A. Brocas, and L. Sarger, "Optical properties of infrared femtosecond laser modified fused silica and application to waveguide fabrication," J. Opt. Soc. Am. B 22, 2138 (2005).
[CrossRef]

2004

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in a low-dimensional periodic potential," Phys. Rev. A 70, 053613 (2004).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice," Phys. Rev. E 70, 055603 (2004).
[CrossRef]

2003

M. Öster, M. Johansson, and A. Eriksson, "Enhanced mobility of strongly localized modes in waveguide arrays by inversion of stability," Phys. Rev. E 67, 056606 (2003).
[CrossRef]

2002

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

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619 (2002).
[CrossRef]

2001

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

2000

A. Desyatnikov, A. Maimistov, and B. Malomed, "Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity," Phys. Rev. E 61, 3107 (2000).
[CrossRef]

F. K. Fatemi, K. M. Jones and P. D. Lett, "Observation of optically induced Feshbach resonances in collisions of cold atoms," Phys. Rev. Lett. 85, 4462 (2000).
[CrossRef] [PubMed]

1999

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4361 (1999).
[CrossRef]

1998

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, "Observation of temporal solitons in second-harmonic generation with titled pulses," Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

J. L. Roberts, N. R. Claussen, J. P. Burke, C. H. Greene, E. A. Cornell, and C. E. Wieman, "Resonant magnetic field control of elastic scattering in cold 85Rb," Phys. Rev. Lett. 81, 5109 (1998).
[CrossRef]

1995

A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Energy localization in nonlinear fiber arrays: Collapse-effect compressor," Phys. Rev. Lett. 75, 73 (1995).
[CrossRef] [PubMed]

1994

1993

1992

1990

Abdullaev, F.

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, "Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices," Phys. Lett. A 367, 149 (2007).
[CrossRef]

Abdullaev, F. K.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, "Generalized neighbor-interaction models induced by nonlinear lattices," Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Abdumalikov, A.

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, "Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices," Phys. Lett. A 367, 149 (2007).
[CrossRef]

Aceves, A. B.

Baizakov, B. B.

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in a low-dimensional periodic potential," Phys. Rev. A 70, 053613 (2004).
[CrossRef]

Bang, O.

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, "Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities," Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Bennet, F. H.

Bjarklev, A.

Blömer, D.

Bludov, Y. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, "Generalized neighbor-interaction models induced by nonlinear lattices," Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Y. V. Bludov and V. V. Konotop, "Localized modes in arrays of boson-fermion mixtures," Phys. Rev. A 74, 043616 (2006).
[CrossRef]

Bolger, J. A.

Brocas, A.

Burke, J. P.

J. L. Roberts, N. R. Claussen, J. P. Burke, C. H. Greene, E. A. Cornell, and C. E. Wieman, "Resonant magnetic field control of elastic scattering in cold 85Rb," Phys. Rev. Lett. 81, 5109 (1998).
[CrossRef]

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, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Caironi, D.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, "Observation of temporal solitons in second-harmonic generation with titled pulses," Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Canioni, L.

Carrasco, S.

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

Chen, F.

Claussen, N. R.

J. L. Roberts, N. R. Claussen, J. P. Burke, C. H. Greene, E. A. Cornell, and C. E. Wieman, "Resonant magnetic field control of elastic scattering in cold 85Rb," Phys. Rev. Lett. 81, 5109 (1998).
[CrossRef]

Cornell, E. A.

J. L. Roberts, N. R. Claussen, J. P. Burke, C. H. Greene, E. A. Cornell, and C. E. Wieman, "Resonant magnetic field control of elastic scattering in cold 85Rb," Phys. Rev. Lett. 81, 5109 (1998).
[CrossRef]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Three-dimensional spatiotemporal solitons in nonlocal nonlinear media," Phys. Rev. E 73, 025601 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice," Phys. Rev. E 70, 055603 (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, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

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

Danielius, R.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, "Observation of temporal solitons in second-harmonic generation with titled pulses," Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

De Angelis, C.

Desyatnikov, A.

A. Desyatnikov, A. Maimistov, and B. Malomed, "Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity," Phys. Rev. E 61, 3107 (2000).
[CrossRef]

Di Trapani, P.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, "Observation of temporal solitons in second-harmonic generation with titled pulses," Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Dmitriev, S. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, "Generalized neighbor-interaction models induced by nonlinear lattices," Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Dreisow, F.

Dubietis, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, "Observation of temporal solitons in second-harmonic generation with titled pulses," Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Edmundson, D. E.

Efremidis, N. K.

Eggleton, B. J.

Enns, R. H.

Eriksson, A.

M. Öster, M. Johansson, and A. Eriksson, "Enhanced mobility of strongly localized modes in waveguide arrays by inversion of stability," Phys. Rev. E 67, 056606 (2003).
[CrossRef]

Fatemi, F. K.

F. K. Fatemi, K. M. Jones and P. D. Lett, "Observation of optically induced Feshbach resonances in collisions of cold atoms," Phys. Rev. Lett. 85, 4462 (2000).
[CrossRef] [PubMed]

Fuerbach, A.

Galimzyanov, R.

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, "Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices," Phys. Lett. A 367, 149 (2007).
[CrossRef]

Glessen, H.

Greene, C. H.

J. L. Roberts, N. R. Claussen, J. P. Burke, C. H. Greene, E. A. Cornell, and C. E. Wieman, "Resonant magnetic field control of elastic scattering in cold 85Rb," Phys. Rev. Lett. 81, 5109 (1998).
[CrossRef]

Hizanidis, K.

Johansson, M.

M. Öster, M. Johansson, and A. Eriksson, "Enhanced mobility of strongly localized modes in waveguide arrays by inversion of stability," Phys. Rev. E 67, 056606 (2003).
[CrossRef]

Jones, C. K. R. T.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, "Solitary waves under the competition of linear and nonlinear periodic potentials," J. Phys. A 40, 14151 (2007).
[CrossRef]

Jones, K. M.

F. K. Fatemi, K. M. Jones and P. D. Lett, "Observation of optically induced Feshbach resonances in collisions of cold atoms," Phys. Rev. Lett. 85, 4462 (2000).
[CrossRef] [PubMed]

Kamburova, R. S.

M. T. Primatarowa, K. T. Stoychev, and R. S. Kamburova, "Interaction of solitons with extended nonlinear defects," Phys. Rev. E 72, 036608 (2005).
[CrossRef]

Kartashov, Y. V.

L. Torner and Y. V. Kartashov, "Light bullets in optical tandems," Opt. Lett. 34, 1129 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity," Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index," Opt. Lett. 33, 2173 (2008).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Three-dimensional spatiotemporal solitons in nonlocal nonlinear media," Phys. Rev. E 73, 025601 (2006).
[CrossRef]

F. Ye, Y. V. Kartashov, and L. Torner, "Asymmetric matter-wave solitons at nonlinear interfaces," Phys. Rev. A 74, 063616 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice," Phys. Rev. E 70, 055603 (2004).
[CrossRef]

Kevrekidis, P. G.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, "Generalized neighbor-interaction models induced by nonlinear lattices," Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, "Solitary waves under the competition of linear and nonlinear periodic potentials," J. Phys. A 40, 14151 (2007).
[CrossRef]

Kip, D.

Kivshar, Y.

Kivshar, Y. S.

Kominis, Y.

Konotop, V. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, "Generalized neighbor-interaction models induced by nonlinear lattices," Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, "Solitary waves under the competition of linear and nonlinear periodic potentials," J. Phys. A 40, 14151 (2007).
[CrossRef]

Y. V. Bludov and V. V. Konotop, "Localized modes in arrays of boson-fermion mixtures," Phys. Rev. A 74, 043616 (2006).
[CrossRef]

Krolikowski, W.

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Three-dimensional spatiotemporal solitons in nonlocal nonlinear media," Phys. Rev. E 73, 025601 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice," Phys. Rev. E 70, 055603 (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, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Lett, P. D.

F. K. Fatemi, K. M. Jones and P. D. Lett, "Observation of optically induced Feshbach resonances in collisions of cold atoms," Phys. Rev. Lett. 85, 4462 (2000).
[CrossRef] [PubMed]

Liu, X.

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4361 (1999).
[CrossRef]

Luther, G. G.

A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Energy localization in nonlinear fiber arrays: Collapse-effect compressor," Phys. Rev. Lett. 75, 73 (1995).
[CrossRef] [PubMed]

Maimistov, A.

A. Desyatnikov, A. Maimistov, and B. Malomed, "Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity," Phys. Rev. E 61, 3107 (2000).
[CrossRef]

Malomed, B.

A. Desyatnikov, A. Maimistov, and B. Malomed, "Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity," Phys. Rev. E 61, 3107 (2000).
[CrossRef]

Malomed, B. A.

T. Mayteevarunyoo and B. A. Malomed, "Solitons in one-dimensional photonic crystals," J. Opt. Soc. Am. B 25, 1854 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Three-dimensional spatiotemporal solitons in nonlocal nonlinear media," Phys. Rev. E 73, 025601 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, "Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity," Phys. Rev. E 73, 026601 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, "Matter-wave solitons in nonlinear optical lattices," Phys. Rev. E 72, 046610 (2005).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, "Spatiotemporal optical solitons," J. Opt. B 7, R53 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in a low-dimensional periodic potential," 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, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Manela, O.

Mayteevarunyoo, T.

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Three-dimensional spatiotemporal solitons in nonlocal nonlinear media," Phys. Rev. E 73, 025601 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice," Phys. Rev. E 70, 055603 (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, "Stable spinning optical solitons in three dimensions," 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, "Three-dimensional spatiotemporal solitons in nonlocal nonlinear media," Phys. Rev. E 73, 025601 (2006).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, "Spatiotemporal optical solitons," J. Opt. B 7, R53 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice," Phys. Rev. E 70, 055603 (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, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

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

Neshev, D. N.

Nolte, S.

Nulsen, A.

Öster, M.

M. Öster, M. Johansson, and A. Eriksson, "Enhanced mobility of strongly localized modes in waveguide arrays by inversion of stability," Phys. Rev. E 67, 056606 (2003).
[CrossRef]

Perez-Garcia, V. M.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, "Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities," Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Piskarskas, A.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, "Observation of temporal solitons in second-harmonic generation with titled pulses," Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Primatarowa, M. T.

M. T. Primatarowa, K. T. Stoychev, and R. S. Kamburova, "Interaction of solitons with extended nonlinear defects," Phys. Rev. E 72, 036608 (2005).
[CrossRef]

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4361 (1999).
[CrossRef]

Rapti, Z.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, "Solitary waves under the competition of linear and nonlinear periodic potentials," J. Phys. A 40, 14151 (2007).
[CrossRef]

Rasmussen, J. J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Rasmussen, P. D.

Richardson, M.

Roberts, J. L.

J. L. Roberts, N. R. Claussen, J. P. Burke, C. H. Greene, E. A. Cornell, and C. E. Wieman, "Resonant magnetic field control of elastic scattering in cold 85Rb," Phys. Rev. Lett. 81, 5109 (1998).
[CrossRef]

Rosberg, C. R.

Rubenchik, A. M.

A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Energy localization in nonlinear fiber arrays: Collapse-effect compressor," Phys. Rev. Lett. 75, 73 (1995).
[CrossRef] [PubMed]

A. B. Aceves, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Multidimensional solitons in fiber arrays," Opt. Lett. 19,329 (1994).
[CrossRef] [PubMed]

Runde, D.

Rüter, C. E.

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, "Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity," Phys. Rev. E 73, 026601 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, "Matter-wave solitons in nonlinear optical lattices," Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Salerno, M.

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in a low-dimensional periodic potential," Phys. Rev. A 70, 053613 (2004).
[CrossRef]

Sarger, L.

Schreiber, T.

Segev, M.

Shandarov, V.

Silberberg, Y.

Steinvurzel, P.

Stepic, M.

Stoychev, K. T.

M. T. Primatarowa, K. T. Stoychev, and R. S. Kamburova, "Interaction of solitons with extended nonlinear defects," Phys. Rev. E 72, 036608 (2005).
[CrossRef]

Sukhorukov, A. A.

Szameit, A.

Telpel, J.

Torner, L.

L. Torner and Y. V. Kartashov, "Light bullets in optical tandems," Opt. Lett. 34, 1129 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index," Opt. Lett. 33, 2173 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity," Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Three-dimensional spatiotemporal solitons in nonlocal nonlinear media," Phys. Rev. E 73, 025601 (2006).
[CrossRef]

F. Ye, Y. V. Kartashov, and L. Torner, "Asymmetric matter-wave solitons at nonlinear interfaces," Phys. Rev. A 74, 063616 (2006).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, "Spatiotemporal optical solitons," J. Opt. B 7, R53 (2005).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice," Phys. Rev. E 70, 055603 (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, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, "Tandem light bullets," 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, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

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

Torres, P. J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, "Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities," Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

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, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Tünnermann, A.

Turitsyn, S. K.

A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Energy localization in nonlinear fiber arrays: Collapse-effect compressor," Phys. Rev. Lett. 75, 73 (1995).
[CrossRef] [PubMed]

A. B. Aceves, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Multidimensional solitons in fiber arrays," Opt. Lett. 19,329 (1994).
[CrossRef] [PubMed]

Valiulis, G.

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius, and A. Piskarskas, "Observation of temporal solitons in second-harmonic generation with titled pulses," Phys. Rev. Lett. 81, 570 (1998).
[CrossRef]

Vekslerchik, V.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, "Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities," Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wieman, C. E.

J. L. Roberts, N. R. Claussen, J. P. Burke, C. H. Greene, E. A. Cornell, and C. E. Wieman, "Resonant magnetic field control of elastic scattering in cold 85Rb," Phys. Rev. Lett. 81, 5109 (1998).
[CrossRef]

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, "Spatiotemporal optical solitons," J. Opt. B 7, R53 (2005).
[CrossRef]

Wise, F. W.

X. Liu, L. J. Qian, and F. W. Wise, "Generation of optical spatiotemporal solitons," Phys. Rev. Lett. 82, 4361 (1999).
[CrossRef]

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," Phys. Rev. E 66, 046619 (2002).
[CrossRef]

Ye, F.

F. Ye, Y. V. Kartashov, and L. Torner, "Asymmetric matter-wave solitons at nonlinear interfaces," Phys. Rev. A 74, 063616 (2006).
[CrossRef]

Zhang, R.

Zoubir, A.

J. Opt. B

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, "Spatiotemporal optical solitons," J. Opt. B 7, R53 (2005).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. A

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, "Solitary waves under the competition of linear and nonlinear periodic potentials," J. Phys. A 40, 14151 (2007).
[CrossRef]

Opt. Commun.

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

Opt. Express

Opt. Lett.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity," Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index," Opt. Lett. 33, 2173 (2008).
[CrossRef] [PubMed]

P. D. Rasmussen, F. H. Bennet, D. N. Neshev, A. A. Sukhorukov, C. R. Rosberg, W. Krolikowski, O. Bang, and Y. Kivshar, "Observation of two-dimensional nonlocal gap solitons," Opt. Lett. 34, 295 (2009).
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A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830 (2005).
[CrossRef] [PubMed]

L. Torner and Y. V. Kartashov, "Light bullets in optical tandems," Opt. Lett. 34, 1129 (2009).
[CrossRef] [PubMed]

A. B. Aceves and C. De Angelis, "Spatiotemporal pulse dynamics in a periodic nonlinear waveguide," Opt. Lett. 18, 110 (1993).
[CrossRef] [PubMed]

A. B. Aceves, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, "Multidimensional solitons in fiber arrays," Opt. Lett. 19,329 (1994).
[CrossRef] [PubMed]

D. E. Edmundson and R. H. Enns, "Robust bistable light bullets," Opt. Lett. 17, 586 (1992).
[CrossRef] [PubMed]

Y. Silberberg, "Collapse of optical pulses," Opt. Lett. 15, 1282(1990).
[CrossRef] [PubMed]

Phys. Lett. A

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, "Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices," Phys. Lett. A 367, 149 (2007).
[CrossRef]

Phys. Rev. A

Y. V. Bludov and V. V. Konotop, "Localized modes in arrays of boson-fermion mixtures," Phys. Rev. A 74, 043616 (2006).
[CrossRef]

F. Ye, Y. V. Kartashov, and L. Torner, "Asymmetric matter-wave solitons at nonlinear interfaces," Phys. Rev. A 74, 063616 (2006).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in a low-dimensional periodic potential," Phys. Rev. A 70, 053613 (2004).
[CrossRef]

Phys. Rev. E

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice," Phys. Rev. E 70, 055603 (2004).
[CrossRef]

M. T. Primatarowa, K. T. Stoychev, and R. S. Kamburova, "Interaction of solitons with extended nonlinear defects," Phys. Rev. E 72, 036608 (2005).
[CrossRef]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, "Collapse arrest and soliton stabilization in nonlocal nonlinear media," 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, "Three-dimensional spatiotemporal solitons in nonlocal nonlinear media," Phys. Rev. E 73, 025601 (2006).
[CrossRef]

A. Desyatnikov, A. Maimistov, and B. Malomed, "Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity," Phys. Rev. E 61, 3107 (2000).
[CrossRef]

H. Sakaguchi and B. A. Malomed, "Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity," Phys. Rev. E 73, 026601 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, "Matter-wave solitons in nonlinear optical lattices," Phys. Rev. E 72, 046610 (2005).
[CrossRef]

M. Öster, M. Johansson, and A. Eriksson, "Enhanced mobility of strongly localized modes in waveguide arrays by inversion of stability," Phys. Rev. E 67, 056606 (2003).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

(a),(c) Spatial field distributions at τ=0, and (b),(d) temporal field distributions at r=0 in light bullets corresponding to b=0.02 (top row) and b=18 (bottom row) at p=3, σ=0.9.

Fig. 2.
Fig. 2.

(a) Energy versus propagation constant and (b) Hamiltonian versus energy for light bullets for p=12 at σ=0.0 (1), 0.5 (2), and 0.7 (3). Real part of perturbation growth rate versus b for p=12 at (c) σ=0.5 and (d) σ=0.7. Critical energy and δb=b cr-b co (e) versus σ at p=12 and (f) versus p at σ=0.6.

Fig. 3.
Fig. 3.

Isosurface plots showing propagation dynamics of perturbed light bullets corresponding to (a) b=10, (b) b=12, and (c) b=8. Left column shows input patterns at ξ=0, while right column shows output patters at (a) ξ=0.8, (b) ξ=1, and (c) ξ=300. In all cases p=12, σ=0.7.

Equations (6)

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iqξ=12(2qη2+2qξ2)+β2 2qτ2 [1σR(η,ζ)]q2qpR(η,ζ)q.
U= q2dηdζdτ,
H=12 [q2βqτ2] (1σR)q42pRq2dηdζdτ,
Lξ=eξ2i[r×(q*qqq*)]dηdζdτ.
i δ u=12(2ur2+1urrk2ur2+2uτ2)+bupRu(1σR)w2(2u+υ),
i δ υ=12(2υr2+1rυrk2υr2+2υτ2)bυ+pRυ+(1σR)w2(2υ+u).

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