Abstract

Rotational properties of counterpropagating mutually incoherent self-trapped vortex beams in optically induced fixed photonic lattices are investigated numerically. The rotation dynamics in these systems is defined by transport through tunneling between lattice sites. Different lattice structures are considered, such as hexagonal/trigonal and circular photonic lattices. Periodically increasing propagation distance, regular rotation of vortex filaments is observed for hexagonal photonic lattice. For circular photonic lattices with negative defect, we discover novel types of rotating beam structures that have no counterparts in the case without the lattice. Observed rotating structures are stable in the presence of noise.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]

2006 (4)

2005 (7)

A. Desyatnikov, D. Neshev, Y. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869 (2005).
[CrossRef] [PubMed]

F. Fedele, J. Yang, and Z. Chen, "Defect modes in one-dimensional photonic lattices," Opt. Lett. 30, 1506 (2005).
[CrossRef] [PubMed]

D. Jović, D. Arsenović, A. Strinić, M. Belić, and M. Petrović, "Counterpropagating optical vortices in photorefractive crystals," Opt. Express 13, 4379 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

S. Xiao and M. Qiu, "High-Q microcavities realized in a circular photonic crystal slab," Photonics and Nanostruct.Fundam. Appl. 3, 134 (2005).
[CrossRef]

O. Manela, G. Bartal, O. Cohen, J. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

2004 (8)

H. Martin, E. Eugenieva, Z. Chen, and D. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

J. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

E. Ostrovskaya and Y. Kivshar, "Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices," Opt. Express 12, 19 (2004).
[CrossRef] [PubMed]

M. Belić, M. Petrović, D. Jović, A. Strinić, D. Arsenović, K. Motzek, F. Kaiser, Ph. Jander, C. Denz, M. Tlidi, and P. Mandel, "Transverse modulational instabilities of counterpropagating solitons in photorefractive crystals," Opt. Express 12, 708 (2004).
[CrossRef] [PubMed]

A. Ferrando, M. Zacares, P. Fernandez, D. Binosi, and J. A. Monsoriu, "Vortex solitons in photonic crystal fibers," Opt. Express 12, 817 (2004).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, T. Carmon, and M. Segev, "Interactions between spatial screening solitons propagating in opposite directions," J. Opt. Soc. Am. B 21,1354 (2004).
[CrossRef]

O. Manela, O. Cohen, G. Bartal, J. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

2003 (6)

B. Baizakov, A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642 (2003).
[CrossRef]

J. Fleischer, T. Carmon, M. Segev, N. Efremidis, and D. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belić, C. Denz, and F. Kaiser, "Dynamic counterpropagating vector solitons in saturable self-focusing media," Phys. Rev. E. 68, 066611 (2003).
[CrossRef]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

J. Yang and Z. Musslimani, "Fundamental and vortex solitons in a two-dimensional optical lattice," Opt. Lett. 28, 2094 (2003).
[CrossRef] [PubMed]

2002 (4)

A. Desyatnikov and Y. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

O. Cohen, S. Lan, T. Carmon, J. Giordmaine, and M. Segev, "Spatial vector solitons consisting of counterpropagating fields," Opt. Lett. 27, 2013 (2002).
[CrossRef]

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E. 66, 046602 (2002).
[CrossRef]

O. Cohen, R. Uzdin, T. Carmon, J. Fleischer, M. Segev, and S. Odulov, "Collisions between optical spatial solitons propagating in opposite directions," Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

1993 (1)

M. Haelterman, A. Sheppard, and A. Snyder, "Bimodal counterpropagating spatial solitary-waves," Opt. Commun. 103, 145 (1993).
[CrossRef]

Alexander, T. J.

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Arsenovic, D.

Baizakov, B.

B. Baizakov, A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642 (2003).
[CrossRef]

Bartal, G.

O. Manela, G. Bartal, O. Cohen, J. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

J. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Belic, M.

Binosi, D.

Buljan, H.

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, T. Carmon, and M. Segev, "Interactions between spatial screening solitons propagating in opposite directions," J. Opt. Soc. Am. B 21,1354 (2004).
[CrossRef]

J. Fleischer, T. Carmon, M. Segev, N. Efremidis, and D. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. Fleischer, M. Segev, and S. Odulov, "Collisions between optical spatial solitons propagating in opposite directions," Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

O. Cohen, S. Lan, T. Carmon, J. Giordmaine, and M. Segev, "Spatial vector solitons consisting of counterpropagating fields," Opt. Lett. 27, 2013 (2002).
[CrossRef]

Chen, Z.

F. Fedele, J. Yang, and Z. Chen, "Defect modes in one-dimensional photonic lattices," Opt. Lett. 30, 1506 (2005).
[CrossRef] [PubMed]

H. Martin, E. Eugenieva, Z. Chen, and D. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Christodoulides, D.

H. Martin, E. Eugenieva, Z. Chen, and D. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

J. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

J. Fleischer, T. Carmon, M. Segev, N. Efremidis, and D. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E. 66, 046602 (2002).
[CrossRef]

Ciattoni, A.

Cohen, O.

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

O. Manela, G. Bartal, O. Cohen, J. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, T. Carmon, and M. Segev, "Interactions between spatial screening solitons propagating in opposite directions," J. Opt. Soc. Am. B 21,1354 (2004).
[CrossRef]

O. Manela, O. Cohen, G. Bartal, J. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

J. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. Fleischer, M. Segev, and S. Odulov, "Collisions between optical spatial solitons propagating in opposite directions," Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

O. Cohen, S. Lan, T. Carmon, J. Giordmaine, and M. Segev, "Spatial vector solitons consisting of counterpropagating fields," Opt. Lett. 27, 2013 (2002).
[CrossRef]

DelRe, E.

Denz, C.

Desyatnikov, A.

A. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Y. Kivshar, "Two-dimensional self-trapped nonlinear photonic lattices," Opt. Express 14, 2851 (2006).
[CrossRef] [PubMed]

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

A. Desyatnikov, D. Neshev, Y. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869 (2005).
[CrossRef] [PubMed]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belić, C. Denz, and F. Kaiser, "Dynamic counterpropagating vector solitons in saturable self-focusing media," Phys. Rev. E. 68, 066611 (2003).
[CrossRef]

A. Desyatnikov and Y. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Dreischuh, A.

Efremidis, N.

J. Fleischer, T. Carmon, M. Segev, N. Efremidis, and D. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E. 66, 046602 (2002).
[CrossRef]

Eugenieva, E.

H. Martin, E. Eugenieva, Z. Chen, and D. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Fedele, F.

Fernandez, P.

Ferrando, A.

Fischer, R.

Fleischer, J.

O. Manela, G. Bartal, O. Cohen, J. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

J. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

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

J. Fleischer, T. Carmon, M. Segev, N. Efremidis, and D. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. Fleischer, M. Segev, and S. Odulov, "Collisions between optical spatial solitons propagating in opposite directions," Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E. 66, 046602 (2002).
[CrossRef]

Giordmaine, J.

Haelterman, M.

M. Haelterman, A. Sheppard, and A. Snyder, "Bimodal counterpropagating spatial solitary-waves," Opt. Commun. 103, 145 (1993).
[CrossRef]

Hudock, J.

J. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Jägers, J.

Jander, Ph.

Jovic, D.

Kaiser, F.

Kartashov, Y.

Kivshar, Y.

Kivshar, Y. S.

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Krolikowski, W.

Lan, S.

Lederer, F.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

Makasyuk, I.

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Malomed, A.

B. Baizakov, A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642 (2003).
[CrossRef]

Mandel, P.

Manela, O.

O. Manela, G. Bartal, O. Cohen, J. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, T. Carmon, and M. Segev, "Interactions between spatial screening solitons propagating in opposite directions," J. Opt. Soc. Am. B 21,1354 (2004).
[CrossRef]

J. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Martin, H.

H. Martin, E. Eugenieva, Z. Chen, and D. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Monsoriu, J. A.

Motzek, K.

Musslimani, Z.

Neshev, D.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

A. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Y. Kivshar, "Two-dimensional self-trapped nonlinear photonic lattices," Opt. Express 14, 2851 (2006).
[CrossRef] [PubMed]

A. Desyatnikov, D. Neshev, Y. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869 (2005).
[CrossRef] [PubMed]

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

Odulov, S.

O. Cohen, R. Uzdin, T. Carmon, J. Fleischer, M. Segev, and S. Odulov, "Collisions between optical spatial solitons propagating in opposite directions," Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

Ostrovskaya, E.

Ostrovskaya, E. A.

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Palange, E.

Pertsch, T.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

Peschel, U.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

Petrovic, M.

Prvanovic, S.

Qiu, M.

S. Xiao and M. Qiu, "High-Q microcavities realized in a circular photonic crystal slab," Photonics and Nanostruct.Fundam. Appl. 3, 134 (2005).
[CrossRef]

Rizza, C.

Rotschild, C.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, T. Carmon, and M. Segev, "Interactions between spatial screening solitons propagating in opposite directions," J. Opt. Soc. Am. B 21,1354 (2004).
[CrossRef]

Sagemerten, N.

Salerno, M.

B. Baizakov, A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642 (2003).
[CrossRef]

Sears, S.

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E. 66, 046602 (2002).
[CrossRef]

Segev, M.

O. Manela, G. Bartal, O. Cohen, J. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, T. Carmon, and M. Segev, "Interactions between spatial screening solitons propagating in opposite directions," J. Opt. Soc. Am. B 21,1354 (2004).
[CrossRef]

J. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

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

J. Fleischer, T. Carmon, M. Segev, N. Efremidis, and D. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. Fleischer, M. Segev, and S. Odulov, "Collisions between optical spatial solitons propagating in opposite directions," Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E. 66, 046602 (2002).
[CrossRef]

O. Cohen, S. Lan, T. Carmon, J. Giordmaine, and M. Segev, "Spatial vector solitons consisting of counterpropagating fields," Opt. Lett. 27, 2013 (2002).
[CrossRef]

Sheppard, A.

M. Haelterman, A. Sheppard, and A. Snyder, "Bimodal counterpropagating spatial solitary-waves," Opt. Commun. 103, 145 (1993).
[CrossRef]

Snyder, A.

M. Haelterman, A. Sheppard, and A. Snyder, "Bimodal counterpropagating spatial solitary-waves," Opt. Commun. 103, 145 (1993).
[CrossRef]

Strinic, A.

Sukhorukov, A.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

Terhalle, B.

Tlidi, M.

Träger, D.

Trompeter, H.

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

Uzdin, R.

O. Cohen, R. Uzdin, T. Carmon, J. Fleischer, M. Segev, and S. Odulov, "Collisions between optical spatial solitons propagating in opposite directions," Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

Xiao, S.

S. Xiao and M. Qiu, "High-Q microcavities realized in a circular photonic crystal slab," Photonics and Nanostruct.Fundam. Appl. 3, 134 (2005).
[CrossRef]

Yang, J.

Zacares, M.

Europhys. Lett. (1)

B. Baizakov, A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642 (2003).
[CrossRef]

Fundam. Appl. (1)

S. Xiao and M. Qiu, "High-Q microcavities realized in a circular photonic crystal slab," Photonics and Nanostruct.Fundam. Appl. 3, 134 (2005).
[CrossRef]

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

Nature (1)

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

Opt. Commun. (1)

M. Haelterman, A. Sheppard, and A. Snyder, "Bimodal counterpropagating spatial solitary-waves," Opt. Commun. 103, 145 (1993).
[CrossRef]

Opt. Express (6)

Opt. Lett. (7)

Phys. Rev. E. (2)

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belić, C. Denz, and F. Kaiser, "Dynamic counterpropagating vector solitons in saturable self-focusing media," Phys. Rev. E. 68, 066611 (2003).
[CrossRef]

N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E. 66, 046602 (2002).
[CrossRef]

Phys. Rev. Lett. (10)

J. Fleischer, T. Carmon, M. Segev, N. Efremidis, and D. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

H. Martin, E. Eugenieva, Z. Chen, and D. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

J. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

O. Manela, G. Bartal, O. Cohen, J. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95, 053904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

A. Desyatnikov and Y. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. Fleischer, M. Segev, and S. Odulov, "Collisions between optical spatial solitons propagating in opposite directions," Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

Other (3)

M. Petrović (unpublished).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," in Progress in Optics, E. Wolf, ed., (Elsevier, Amstredam, 2005), Vol 47, pp. 219-319.

Supplementary Material (12)

» Media 1: MOV (1340 KB)     
» Media 2: MOV (1941 KB)     
» Media 3: MOV (1820 KB)     
» Media 4: MOV (1173 KB)     
» Media 5: MOV (1640 KB)     
» Media 6: MOV (1146 KB)     
» Media 7: MOV (1807 KB)     
» Media 8: MOV (2423 KB)     
» Media 9: MOV (1226 KB)     
» Media 10: MOV (2289 KB)     
» Media 11: MOV (2183 KB)     
» Media 12: MOV (2286 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Local and nonlocal rotation in triagonal lattice for various propagation distances: for propagation distances between these values chaotic behavior is observed (not shown). Movies of the intensity distribution of the forward field at its output face: (a) (1341 KB), (b) (1942 KB), (c) (1821 KB). Parameters: Γ=17, lattice spacing d=28 µm, FWHM of lattice beams 12.7 µm, input FWHM of vortices 26.2 µm, maximum lattice intensity Ig=5Id , |F0 |2=|BL |2=5Id . All movies start after stable rotation is established (transient dynamics are not shown).

Fig. 2.
Fig. 2.

First circle for different odd-fold symmetric circular optically induced photonic lattices with negative defect.

Fig. 3.
Fig. 3.

Typical behavior in the parameter plane of CP vortices in sevenfold symmetric circular optically induced photonic lattice with negative defect. Input vortices have the opposite topological charge ±1. Insets list the possible outcomes from vortex collisions. For larger values of Γ and L there is a nonpropagating region. Parameters: lattice spacing 30 µm, FWHM of lattice beams 12.7 µm, input FWHM of vortices 16.4 µm, maximum lattice intensity Ig=5Id , maximum input vortices intensity |F0 |2=|BL |2=5Id .

Fig. 4.
Fig. 4.

Characteristic examples shown in Fig. 3. Movies of the intensity distribution of the forward beam at its output face: (a) the rotating quadrupole (1173 KB), (b) the rotating-breathing tripole (1640 KB), (c) the dipole-like rotating structure (1147 KB), (d) the irregular rotating structure (1808 KB) and (e) unstable structure (2423 KB). Parameters Γ and L are given in the figures.

Fig. 5.
Fig. 5.

Rotating tripole, forward field, phase-intensity noise is 3%. Movies of the intensity distribution for: (a) threefold symmetric CPL, Γ=13.8, L=2LD=8 mm, input FWHM of vortices 16.4 µm (1226 KB), (b) fivefold symmetric CPL, Γ=11, L=2.5LD , input FWHM of vortices 19.6 µm (2290 KB) (c) sevenfold symmetric CPL, Γ=12.5, L=2LD , input FWHM of vortices 16.4 µm (2184 KB), (d) ninefold symmetric CPL, Γ=11, L=2.5LD , input FWHM of vortices 18 µm (2286 KB). Ratio between distance of two neighboring Gaussians in the first circle of lattices in different circular geometries and FWHM of that Gaussians is 2.05. Other parameters: Ig=5Id, |F0|2=|BL|2=5Id .

Equations (2)

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

i z F = Δ F + Γ E F , i z B = Δ B + Γ E B ,
τ t E + E = I + I g 1 + I + I g ,

Metrics