Abstract

We investigate the generation and stability of light bullets (LBs) in Laguerre–Gauss (LG) optical lattices, in which both linear and nonlinear changes in the refractive index are spatially modulated. We demonstrate that the linear and nonlinear contributions considerably affect the bullet shape and its range of stability; at the same time the nonlinear modulation depth, through the propagation constant, affects the width of the stability domain. We find that the energy of stable space-time solitons increases with the increase in the modulation depth. We discover that the behavior of LBs in LG optical lattices is substantially different from the behavior in the more familiar Bessel lattices.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  36. L. Dong, F. Ye, and H. Wang, “Suppression of azimuthal instability of ring vortex solitons,” New J. Phys. 11, 073026 (2009).
    [CrossRef]
  37. J. Zheng and L. Dong, “Multipeaked fundamental and vortex solitons in azimuthally modulated Bessel lattices,” J. Opt. Soc. Am. B 28, 780–786 (2011).
    [CrossRef]
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    [CrossRef]

2013 (1)

Y. Kominis, “Bright, dark, antidark, and kink solitons in media with periodically alternating sign of nonlinearity,” Phys. Rev. A 87, 063849 (2013).
[CrossRef]

2012 (1)

2011 (4)

2010 (1)

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81, 013624 (2010).
[CrossRef]

2009 (4)

2008 (2)

2007 (2)

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, 12145–12150 (2007).
[CrossRef]

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]

2006 (5)

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, 2151–2157 (2006).
[CrossRef]

Y. Kominis, “Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures,” Phys. Rev. E 73, 066619 (2006).
[CrossRef]

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

2005 (5)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (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]

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, 4314–4324 (2005).
[CrossRef]

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, 2138–2143 (2005).
[CrossRef]

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef]

2004 (1)

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 (3)

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated x-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[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]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

2002 (2)

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, 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]

2001 (1)

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

2000 (1)

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, 4462–4465 (2000).
[CrossRef]

1999 (1)

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[CrossRef]

1998 (3)

H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

P. D. 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, 570–573 (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, 5109–5112 (1998).
[CrossRef]

1992 (1)

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]

Bennet, F. H.

Bjarklev, A.

Blömer, D.

Bludov, Y. V.

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

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, 5109–5112 (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]

Caironi, D.

P. D. 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, 570–573 (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, 277–281 (2001).
[CrossRef]

Chen, F.

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

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, 5109–5112 (1998).
[CrossRef]

Conti, C.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated x-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[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, 5109–5112 (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(R) (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]

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]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

Danielius, R.

P. D. 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, 570–573 (1998).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef]

Di Trapani, P.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated x-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Dong, L.

J. Zheng and L. Dong, “Multipeaked fundamental and vortex solitons in azimuthally modulated Bessel lattices,” J. Opt. Soc. Am. B 28, 780–786 (2011).
[CrossRef]

L. Dong, F. Ye, and H. Wang, “Suppression of azimuthal instability of ring vortex solitons,” New J. Phys. 11, 073026 (2009).
[CrossRef]

Dreisow, F.

Drummond, P. D.

H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

Dubietis, A.

P. D. 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, 570–573 (1998).
[CrossRef]

Edmundson, D. E.

Efremidis, N. K.

K. Hizanidis, Y. Kominis, and N. K. Efremidis, “Interlaced linear-nonlinear optical waveguide arrays,” Opt. Express 16, 18296–18311 (2008).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

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, 4462–4465 (2000).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

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, 5109–5112 (1998).
[CrossRef]

He, H.

H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[CrossRef]

Hizanidis, K.

Hu, B.

Jedrkiewicz, O.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated x-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

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, 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, 4462–4465 (2000).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[CrossRef]

L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1141 (2009).
[CrossRef]

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17, 11328–11334 (2009).
[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, “Three-dimensional spatiotemporal solitons in nonlocal nonlinear media,” 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, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (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]

Kip, D.

Kivshar, Y.

Kivshar, Y. S.

Kominis, Y.

Y. Kominis, “Bright, dark, antidark, and kink solitons in media with periodically alternating sign of nonlinearity,” Phys. Rev. A 87, 063849 (2013).
[CrossRef]

Y. Kominis and K. Hizanidis, “Power dependent soliton location and stability in complex photonic structures,” Opt. Express 16, 12124–12138 (2008).
[CrossRef]

K. Hizanidis, Y. Kominis, and N. K. Efremidis, “Interlaced linear-nonlinear optical waveguide arrays,” Opt. Express 16, 18296–18311 (2008).
[CrossRef]

Y. Kominis, “Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures,” Phys. Rev. E 73, 066619 (2006).
[CrossRef]

Konotop, V. V.

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(R) (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]

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]

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, 4462–4465 (2000).
[CrossRef]

Liu, X.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[CrossRef]

Malomed, B. A.

H. Sakaguchi and B. A. Malomed, “Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity,” Opt. Lett. 37, 1035–1037 (2012).
[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and A. Roeksabutr, “Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type,” Opt. Express 19, 17834–17851 (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81, 013624 (2010).
[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(R) (2006).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (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]

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]

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(R) (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]

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]

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(R) (2006).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (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]

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]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

Neshev, D. N.

Nolte, S.

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]

Piskarskas, A.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated x-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

P. D. 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, 570–573 (1998).
[CrossRef]

Qian, L. J.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[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, 5109–5112 (1998).
[CrossRef]

Roeksabutr, A.

Rosberg, C. R.

Runde, D.

Rüter, C. E.

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, “Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity,” Opt. Lett. 37, 1035–1037 (2012).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81, 013624 (2010).
[CrossRef]

Sarger, L.

Schreiber, T.

Segev, M.

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, 4314–4324 (2005).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

Shandarov, V.

Stepic, M.

Sukhorukov, A. A.

Szameit, A.

Torner, L.

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[CrossRef]

L. Torner and Y. V. Kartashov, “Light bullets in optical tandems,” Opt. Lett. 34, 1129–1141 (2009).
[CrossRef]

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17, 11328–11334 (2009).
[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, “Three-dimensional spatiotemporal solitons in nonlocal nonlinear media,” 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, “Stable spatiotemporal solitons in Bessel optical lattices,” Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (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]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (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]

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (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]

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]

Trapani, P. D.

P. D. 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, 570–573 (1998).
[CrossRef]

Trillo, S.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated x-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Trull, J.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated x-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

Tünnermann, A.

Valiulis, G.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated x-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

P. D. 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, 570–573 (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]

Wang, H.

L. Dong, F. Ye, and H. Wang, “Suppression of azimuthal instability of ring vortex solitons,” New J. Phys. 11, 073026 (2009).
[CrossRef]

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, 5109–5112 (1998).
[CrossRef]

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).
[CrossRef]

Wise, F. W.

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (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]

Yang, J.

J. Yang, “Transversely stable soliton trains in photonic lattices,” Phys. Rev. A 84, 033840 (2011).
[CrossRef]

Ye, F.

L. Dong, F. Ye, and H. Wang, “Suppression of azimuthal instability of ring vortex solitons,” New J. Phys. 11, 073026 (2009).
[CrossRef]

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17, 11328–11334 (2009).
[CrossRef]

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

Zheng, J.

Zoubir, A.

J. Opt. B (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147–150 (2003).
[CrossRef]

New J. Phys. (1)

L. Dong, F. Ye, and H. Wang, “Suppression of azimuthal instability of ring vortex solitons,” New J. Phys. 11, 073026 (2009).
[CrossRef]

Opt. Commun. (1)

L. Torner, S. Carrasco, J. P. Torres, L.-C. Crasovan, and D. Mihalache, “Tandem light bullets,” Opt. Commun. 199, 277–281 (2001).
[CrossRef]

Opt. Express (7)

Opt. Lett. (4)

Phys. Rev. A (5)

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

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

Y. Kominis, “Bright, dark, antidark, and kink solitons in media with periodically alternating sign of nonlinearity,” Phys. Rev. A 87, 063849 (2013).
[CrossRef]

J. Yang, “Transversely stable soliton trains in photonic lattices,” Phys. Rev. A 84, 033840 (2011).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81, 013624 (2010).
[CrossRef]

Phys. Rev. E (6)

Y. Kominis, “Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures,” Phys. Rev. E 73, 066619 (2006).
[CrossRef]

H. He and P. D. Drummond, “Theory of multidimensional parametric band-gap simultons,” Phys. Rev. E 58, 5025–5046 (1998).
[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]

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]

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(R) (2006).
[CrossRef]

Phys. Rev. Lett. (9)

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]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated x-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[CrossRef]

P. D. 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, 570–573 (1998).
[CrossRef]

X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82, 4631–4634 (1999).
[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]

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, 5109–5112 (1998).
[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, 4462–4465 (2000).
[CrossRef]

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]

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef]

Rev. Mod. Phys. (1)

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

LG optical lattices in xy plane for different m=2, 3, 4, from left to right; here n=2 (top row), n=1 (bottom row), w0=1, and q=0.

Fig. 2.
Fig. 2.

(a), (c) Spatial field distributions of light bullets at τ=0. (b), (d) Temporal field distributions at r=0. The corresponding parameters are: b=2.52 (top row), b=8.55 (bottom row). Other parameters: p=0.5, σ=0.3, q=0, m=3, and n=2.

Fig. 3.
Fig. 3.

(a) Energy versus propagation constant and (b) Hamiltonian versus energy for light bullets with p=15 and for different σ=0, 1, 1.2. (c) Real part of the perturbation growth rate versus b for different perturbation indices k=0, 1, 2 and for p=15 and σ=0.65. (d) The same as (c) but for σ=1.25. (e) The width of the stability domain δb=bcrbco versus σ, and (f) versus p. Other parameters are as in Fig. 2.

Fig. 4.
Fig. 4.

Intensity distribution of 3D LBs in the xy plane (top row) and phase distribution (bottom row) at z=2 and τ=1, with q=0.5, n=2, and m=2, 3, 4 from left to right. Other parameters are as in Fig. 2.

Fig. 5.
Fig. 5.

Isosurface plots showing propagation dynamics of light bullets (top row) and intensity distribution (bottom row) at distances z=50, 100, 150, with n=1, m=2, and q=0.6; other parameters are as in Fig. 2.

Fig. 6.
Fig. 6.

Same as Fig. 5, but for m=4.

Fig. 7.
Fig. 7.

Isosurface plots showing propagation dynamics of light bullets (top row) and intensity distribution (bottom row) at z=50 and m=3, without (a), (c) and with a white noise of variance 0.08 added to the input (b), (d). Here q=0; other parameters are as in Fig. 2.

Equations (7)

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

iuz=12(2ux2+2uy2)+β22uτ2+[σV(x,y)1]|u|2upV(x,y)u,
V(x,y)=(cosmθ+iqsinmθ)Lnm(r2/w02)er2/w02,
Lnm(r2/w02)=[Γ(m+n+1)/n!Γ(m+1)]F(n,m+1,r2/w02),
U=|u|2dxdydτ,
H=12[|u|2β|uτ|2(1σR)|u|42pR|u|2]dxdydτ.
u=[w+qexp(ikφ+δz)+v*exp(ikφ+δ*z)]exp(ibz),
iδq=12(2qr2+1rqrk2qr2+2qτ2)+bqprq(1σr)w2(2q+v)iδv=+12(2vr2+1rurk2vr2+2vt2)bv+pRv+(1σR)w2(2v+u).

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