Abstract

An effective mechanism for dissipative soliton acceleration in nonlinear optical lattices under the presence of linear gain and nonlinear loss is presented. The key idea for soliton acceleration consists of the dynamical reduction of the amplitude of the effective potential experienced by the soliton so that its kinetic energy eventually increases. This is possible through the dependence of the effective potential amplitude on the soliton mass, which can be varied due to the presence of gain and loss mechanisms. In contrast to the case where either the linear or the nonlinear refractive index is spatially modulated, we show that when both indices are modulated with the same period we can have soliton acceleration and mass increasing as well as stable soliton propagation with constant non-oscillating velocity. The acceleration mechanism is shown to be very robust for a wide range of configurations.

© 2012 OSA

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2011 (5)

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

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).
[CrossRef]

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A83, 053617 (2011).
[CrossRef]

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A84, 013820 (2011).
[CrossRef]

2010 (4)

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E82, 056606 (2010).
[CrossRef]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A81, 013624 (2010).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

2009 (2)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev.3, 243–261 (2009).
[CrossRef]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).
[CrossRef] [PubMed]

2008 (3)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).
[CrossRef]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).
[CrossRef] [PubMed]

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).
[CrossRef]

2007 (4)

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32, 979–981 (2007).
[CrossRef] [PubMed]

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

2005 (2)

Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E72, 026606 (2005).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A72, 046610 (2005).

2004 (1)

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A70, 043604 (2004).
[CrossRef]

2003 (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003).
[CrossRef] [PubMed]

2001 (4)

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).
[CrossRef] [PubMed]

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett.86, 2353–2356 (2001).
[CrossRef] [PubMed]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).
[CrossRef]

2000 (1)

S. Flach, O. Yevtushenko, and Y. Zolotaryuk, “Directed current due to broken time-space symmetry,” Phys. Rev. Lett.84, 2358–2361 (2000).
[CrossRef] [PubMed]

1999 (1)

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).
[CrossRef]

1998 (1)

1993 (1)

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E47, 1375–1383 (1993).
[CrossRef]

1989 (1)

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).
[CrossRef]

1987 (3)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

B. A. Malomed, “Evolution of nonsoliton and ’quasi-classical’ wavetrains in nonlinear Schrödinger and Korteweg–De Vries equations with dissipative perturbations,” Physica D29, 155–172 (1987).
[CrossRef]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
[CrossRef]

1978 (1)

D. J. Kaup and A. C. Newell, “Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory,” Proc. R. Soc. London, Ser. A361, 413–446 (1978).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E82, 056606 (2010).
[CrossRef]

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).
[CrossRef]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).
[CrossRef]

Alexander, T. J.

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).
[CrossRef]

Assanto, G.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).
[CrossRef]

Baizakov, B. B.

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).
[CrossRef]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

Bishop, A. R.

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E47, 1375–1383 (1993).
[CrossRef]

Brauer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).
[CrossRef]

Brazhnyi, V. A.

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A70, 043604 (2004).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).
[CrossRef]

Burger, S.

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).
[CrossRef] [PubMed]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

Carretero-Gonzalez, R.

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A83, 053617 (2011).
[CrossRef]

Cataliotti, F. S.

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).
[CrossRef] [PubMed]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

Chacon, R.

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A83, 053617 (2011).
[CrossRef]

Chen, Z.

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).
[CrossRef]

Chiofalo, M. L.

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).
[CrossRef] [PubMed]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).
[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).
[CrossRef] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).
[CrossRef]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).
[CrossRef] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32, 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003).
[CrossRef] [PubMed]

Cisneros, L. A.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

da Luz, H. L. F.

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).
[CrossRef]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).
[CrossRef]

Darmanyan, S. A.

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).
[CrossRef]

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).
[CrossRef]

Durnin, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).
[CrossRef]

El-Ganainy, R.

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).
[CrossRef]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

Flach, S.

S. Flach, O. Yevtushenko, and Y. Zolotaryuk, “Directed current due to broken time-space symmetry,” Phys. Rev. Lett.84, 2358–2361 (2000).
[CrossRef] [PubMed]

Fort, C.

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).
[CrossRef] [PubMed]

Gammal, A.

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).
[CrossRef]

Garanovich, I. L.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. (in press), doi: .

Hizanidis, K.

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A84, 013820 (2011).
[CrossRef]

Inguscio, M.

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).
[CrossRef] [PubMed]

Kaminer, I.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef] [PubMed]

Kartashov, Y. V.

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

Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E72, 026606 (2005).
[CrossRef]

Kaup, D. J.

D. J. Kaup and A. C. Newell, “Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory,” Proc. R. Soc. London, Ser. A361, 413–446 (1978).
[CrossRef]

Kip, D.

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).
[CrossRef] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).
[CrossRef] [PubMed]

Kivshar, Y. S.

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).
[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).
[CrossRef]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. (in press), doi: .

Kominis, Y.

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A84, 013820 (2011).
[CrossRef]

Konotop, V. V.

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E82, 056606 (2010).
[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A70, 043604 (2004).
[CrossRef]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).
[CrossRef]

Kuzmiak, V.

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A70, 043604 (2004).
[CrossRef]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett.23, 1701–1703 (1998).
[CrossRef]

Li, B.

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).
[CrossRef]

Longhi, S.

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev.3, 243–261 (2009).
[CrossRef]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. (in press), doi: .

Maddaloni, P.

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

Makris, K. G.

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).
[CrossRef]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).
[CrossRef] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).
[CrossRef] [PubMed]

Malomed, B. A.

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. A81, 013624 (2010).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A72, 046610 (2005).

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).
[CrossRef]

B. A. Malomed, “Evolution of nonsoliton and ’quasi-classical’ wavetrains in nonlinear Schrödinger and Korteweg–De Vries equations with dissipative perturbations,” Physica D29, 155–172 (1987).
[CrossRef]

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

Minardi, F.

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).
[CrossRef] [PubMed]

Minzoni, A. A.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

Miri, M. A.

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).
[CrossRef]

Newell, A. C.

D. J. Kaup and A. C. Newell, “Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory,” Proc. R. Soc. London, Ser. A361, 413–446 (1978).
[CrossRef]

Ostrovskaya, E. A.

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).
[CrossRef]

Papagiannis, P.

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A84, 013820 (2011).
[CrossRef]

Peleg, O.

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).
[CrossRef] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).
[CrossRef] [PubMed]

Pertsch, T.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett.23, 1701–1703 (1998).
[CrossRef]

Peschel, U.

Polleti, D.

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).
[CrossRef]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

Rietmann, M.

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A83, 053617 (2011).
[CrossRef]

Ruter, C. E.

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).
[CrossRef] [PubMed]

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A81, 013624 (2010).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A72, 046610 (2005).

Salerno, M.

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E82, 056606 (2010).
[CrossRef]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).
[CrossRef]

Scharf, R.

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E47, 1375–1383 (1993).
[CrossRef]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

Segev, M.

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef] [PubMed]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).
[CrossRef] [PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).
[CrossRef]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).
[CrossRef] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

Shandarova, K.

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).
[CrossRef] [PubMed]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003).
[CrossRef] [PubMed]

Siviloglou, G. A.

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32, 979–981 (2007).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).
[CrossRef]

Skuse, B. D.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

Smerzi, A.

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett.86, 2353–2356 (2001).
[CrossRef] [PubMed]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

Smyth, N. F.

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).
[CrossRef]

Sukhorukov, A. A.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. (in press), doi: .

Tomio, L.

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).
[CrossRef]

Torner, L.

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

Tosi, M. P.

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).
[CrossRef] [PubMed]

Trombettoni, A.

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett.86, 2353–2356 (2001).
[CrossRef] [PubMed]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E72, 026606 (2005).
[CrossRef]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

Worthy, A. L

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

Yevtushenko, O.

S. Flach, O. Yevtushenko, and Y. Zolotaryuk, “Directed current due to broken time-space symmetry,” Phys. Rev. Lett.84, 2358–2361 (2000).
[CrossRef] [PubMed]

Yulin, A. V.

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E82, 056606 (2010).
[CrossRef]

Zolotaryuk, Y.

S. Flach, O. Yevtushenko, and Y. Zolotaryuk, “Directed current due to broken time-space symmetry,” Phys. Rev. Lett.84, 2358–2361 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Laser Photon. Rev. (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev.3, 243–261 (2009).
[CrossRef]

Nat. Photonics (1)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).
[CrossRef]

Nature (2)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).
[CrossRef]

Phys. Rev. A (8)

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A70, 043604 (2004).
[CrossRef]

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A83, 053617 (2011).
[CrossRef]

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A84, 013820 (2011).
[CrossRef]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).
[CrossRef]

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A72, 046610 (2005).

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A81, 013624 (2010).
[CrossRef]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).
[CrossRef]

Phys. Rev. E (3)

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E82, 056606 (2010).
[CrossRef]

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E47, 1375–1383 (1993).
[CrossRef]

Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E72, 026606 (2005).
[CrossRef]

Phys. Rev. Lett. (10)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).
[CrossRef] [PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).
[CrossRef] [PubMed]

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett.86, 2353–2356 (2001).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).
[CrossRef]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).
[CrossRef] [PubMed]

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).
[CrossRef]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).
[CrossRef] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef] [PubMed]

S. Flach, O. Yevtushenko, and Y. Zolotaryuk, “Directed current due to broken time-space symmetry,” Phys. Rev. Lett.84, 2358–2361 (2000).
[CrossRef] [PubMed]

Physica D (1)

B. A. Malomed, “Evolution of nonsoliton and ’quasi-classical’ wavetrains in nonlinear Schrödinger and Korteweg–De Vries equations with dissipative perturbations,” Physica D29, 155–172 (1987).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

D. J. Kaup and A. C. Newell, “Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory,” Proc. R. Soc. London, Ser. A361, 413–446 (1978).
[CrossRef]

Rev. Mod. Phys. (2)

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).
[CrossRef]

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

Science (1)

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).
[CrossRef] [PubMed]

Other (2)

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. (in press), doi: .

N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons, Lect. Notes Phys. (Springer, 2005), Vol. 661.

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