Abstract

Azimuthally modulated higher order rotationally symmetric Bessel-like optical patterns were generated by coherent superposition of two co-propagating Bessel beams – either in or out of phase. By changing the distance between the beam centers, a whole variety of transition states can be realized. As one prominent example, a 4-fold symmetry quadrupole-like photonic structure was optically inducted in an SBN crystal and nonlinear beam propagation in such a photonic wave-guiding structure is investigated in both self-focusing and self-defocusing regimes. The proposed device serves as an all-optical 2d 1 × 4 photonic interconnect.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]

2014 (2)

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

2013 (2)

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

A. Badalyan, R. Hovsepyan, P. Mantashyan, V. Mekhitaryan, and R. Drampyan, “Bessel standing wave technique for optical induction of complex refractive lattice structures in photorefractive materials,” J. Mod. Opt. 60, 617–628 (2013).
[Crossref]

2012 (1)

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14, 033018 (2012).
[Crossref]

2010 (2)

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[Crossref] [PubMed]

S. Huang, P. Zhang, X. Wang, and Z. Chen, “Observation of soliton interaction and planetlike orbiting in Bessel-like photonic lattices,” Opt. Lett. 35, 2284 (2010).
[Crossref] [PubMed]

2008 (2)

2007 (2)

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

T. I. Lakoba and J. Yang, “A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity,” J. Comput. Phys. 226, 1668–1692 (2007).
[Crossref]

2006 (2)

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of light localization in modulated Bessel optical lattices,” Opt. Express 14, 2825–2830 (2006).
[Crossref] [PubMed]

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

2005 (2)

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

2004 (2)

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[Crossref]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B Quantum Semiclass. Opt. 6, 444–447 (2004).
[Crossref]

2003 (3)

2001 (1)

J. C. Gutierrez-Vega, M. Iturbe-Castillo, G. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

2000 (1)

1996 (1)

1995 (1)

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

1988 (1)

1987 (1)

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

1986 (1)

F. P. Schäfer, “On some properties of axicons,” Appl. Phys. B 39, 1–8 (1986).
[Crossref]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003).

Anderson, D. Z.

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

Assanto, G.

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]

Badalyan, A.

A. Badalyan, R. Hovsepyan, P. Mantashyan, V. Mekhitaryan, and R. Drampyan, “Bessel standing wave technique for optical induction of complex refractive lattice structures in photorefractive materials,” J. Mod. Opt. 60, 617–628 (2013).
[Crossref]

Bersch, C.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

Boguslawski, M.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14, 033018 (2012).
[Crossref]

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[Crossref] [PubMed]

Bokic, B. M.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

Buse, K.

Carretero-Gonzalez, R.

Chattrapiban, N.

Chavez-Cerda, S.

J. C. Gutierrez-Vega, M. Iturbe-Castillo, G. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Chávez-Cerda, S.

Chen, X.

Chen, Z.

Christodoulides, D. N.

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]

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] [PubMed]

Cofield, D.

Cojocaru, C.

K. Staliunas, R. Herrero, C. Cojocaru, and J. Trull, “Nondiffractive propagation of light in photonic crystals,” in Proceedings of the 7th International Conference on Transparent Optical Networks, Ict.1, 281–283 (2005).

Denz, C.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14, 033018 (2012).
[Crossref]

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[Crossref] [PubMed]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

Desyatnikov, A. S.

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of light localization in modulated Bessel optical lattices,” Opt. Express 14, 2825–2830 (2006).
[Crossref] [PubMed]

Diebel, F.

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

Drampyan, R.

A. Badalyan, R. Hovsepyan, P. Mantashyan, V. Mekhitaryan, and R. Drampyan, “Bessel standing wave technique for optical induction of complex refractive lattice structures in photorefractive materials,” J. Mod. Opt. 60, 617–628 (2013).
[Crossref]

Durnin, J.

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

Eberly, J. H.

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

Efremidis, N. K.

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] [PubMed]

Egorov, A. A.

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[Crossref]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B Quantum Semiclass. Opt. 6, 444–447 (2004).
[Crossref]

Fischer, R.

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] [PubMed]

Friberg, A. T.

Gutierrez-Vega, J. C.

J. C. Gutierrez-Vega, M. Iturbe-Castillo, G. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Gutiérrez-Vega, J. C.

Herrero, R.

K. Staliunas, R. Herrero, C. Cojocaru, and J. Trull, “Nondiffractive propagation of light in photonic crystals,” in Proceedings of the 7th International Conference on Transparent Optical Networks, Ict.1, 281–283 (2005).

Hill, W. T.

Hovsepyan, R.

A. Badalyan, R. Hovsepyan, P. Mantashyan, V. Mekhitaryan, and R. Drampyan, “Bessel standing wave technique for optical induction of complex refractive lattice structures in photorefractive materials,” J. Mod. Opt. 60, 617–628 (2013).
[Crossref]

Huang, S.

Imbrock, J.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

Iturbe-Castillo, M.

J. C. Gutierrez-Vega, M. Iturbe-Castillo, G. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

J. C. Gutiérrez-Vega, M. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[Crossref]

Joseph, J.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[Crossref] [PubMed]

Jovic, D. M.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[Crossref]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B Quantum Semiclass. Opt. 6, 444–447 (2004).
[Crossref]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[Crossref]

Kevrekidis, P. G.

Kivshar, Y. S.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of light localization in modulated Bessel optical lattices,” Opt. Express 14, 2825–2830 (2006).
[Crossref] [PubMed]

D. N. Neshev, E. Ostrovskaya, Y. S. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28, 710–712 (2003).
[Crossref] [PubMed]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003).

Kratzig, E.

Krolikowski, W.

Lakoba, T. I.

T. I. Lakoba and J. Yang, “A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity,” J. Comput. Phys. 226, 1668–1692 (2007).
[Crossref]

Law, K. J. H.

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]

Leykam, D.

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

Li, W.

Lopez-Aguayo, S.

Lou, C.

Malomed, B. A.

Mantashyan, P.

A. Badalyan, R. Hovsepyan, P. Mantashyan, V. Mekhitaryan, and R. Drampyan, “Bessel standing wave technique for optical induction of complex refractive lattice structures in photorefractive materials,” J. Mod. Opt. 60, 617–628 (2013).
[Crossref]

Mekhitaryan, V.

A. Badalyan, R. Hovsepyan, P. Mantashyan, V. Mekhitaryan, and R. Drampyan, “Bessel standing wave technique for optical induction of complex refractive lattice structures in photorefractive materials,” J. Mod. Opt. 60, 617–628 (2013).
[Crossref]

Miceli, J. J. J.

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

Neshev, D. N.

New, G.

J. C. Gutierrez-Vega, M. Iturbe-Castillo, G. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Ostrovskaya, E.

Pankrath, R.

Piper, A.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

Ramirez, G.

J. C. Gutierrez-Vega, M. Iturbe-Castillo, G. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Rodriguez-Dagnino, R. M.

J. C. Gutierrez-Vega, M. Iturbe-Castillo, G. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Rogers, E. A.

Rose, P.

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14, 033018 (2012).
[Crossref]

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[Crossref] [PubMed]

Roy, R.

Schäfer, F. P.

F. P. Schäfer, “On some properties of axicons,” Appl. Phys. B 39, 1–8 (1986).
[Crossref]

Segev, M.

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]

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] [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]

Song, D.

Staliunas, K.

K. Staliunas, R. Herrero, C. Cojocaru, and J. Trull, “Nondiffractive propagation of light in photonic crystals,” in Proceedings of the 7th International Conference on Transparent Optical Networks, Ict.1, 281–283 (2005).

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.

Susanto, H.

Tang, L.

D. Song, C. Lou, L. Tang, X. Wang, W. Li, X. Chen, K. J. H. Law, H. Susanto, P. G. Kevrekidis, J. Xu, and Z. Chen, “Self-trapping of optical vortices in waveguide lattices with a self-defocusing nonlinearity,” Opt. Express 16, 10110–10116 (2008).
[Crossref] [PubMed]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

Tepichin, E.

J. C. Gutierrez-Vega, M. Iturbe-Castillo, G. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Terhalle, B.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

Timotijevic, D. V.

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[Crossref]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B Quantum Semiclass. Opt. 6, 444–447 (2004).
[Crossref]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[Crossref]

Torruellas, W.

S. Trillo and W. Torruellas, Spatial Solitons (Springer Series in Optical Sciences, 2001).
[Crossref]

Träger, D.

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

Trillo, S.

S. Trillo and W. Torruellas, Spatial Solitons (Springer Series in Optical Sciences, 2001).
[Crossref]

Trull, J.

K. Staliunas, R. Herrero, C. Cojocaru, and J. Trull, “Nondiffractive propagation of light in photonic crystals,” in Proceedings of the 7th International Conference on Transparent Optical Networks, Ict.1, 281–283 (2005).

Turunen, J.

van Stevendaal, U.

Vasara, A.

Vysloukh, V. A.

Y. V. Kartashov, R. Carretero-Gonzalez, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10703–10710 (2005).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B Quantum Semiclass. Opt. 6, 444–447 (2004).
[Crossref]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[Crossref]

Wang, X.

Xavier, J.

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[Crossref] [PubMed]

Xu, J.

Yang, J.

T. I. Lakoba and J. Yang, “A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity,” J. Comput. Phys. 226, 1668–1692 (2007).
[Crossref]

Zhang, P.

Zozulya, A. A.

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

Adv. Mater. (1)

J. Xavier, M. Boguslawski, P. Rose, J. Joseph, and C. Denz, “Reconfigurable optically induced quasicrystallographic three-dimensional complex nonlinear photonic lattice structures,” Adv. Mater. 22, 356–360 (2010).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (2)

F. P. Schäfer, “On some properties of axicons,” Appl. Phys. B 39, 1–8 (1986).
[Crossref]

B. Terhalle, A. S. Desyatnikov, C. Bersch, D. Träger, L. Tang, J. Imbrock, Y. S. Kivshar, and C. Denz, “Anisotropic photonic lattices and discrete solitons in photorefractive media,” Appl. Phys. B 86, 399–405 (2007).
[Crossref]

Appl. Phys. Lett. (2)

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102, 101101 (2013).
[Crossref]

F. Diebel, D. Leykam, M. Boguslawski, P. Rose, C. Denz, and A. S. Desyatnikov, “All-optical switching in optically induced nonlinear waveguide couplers,” Appl. Phys. Lett. 104, 261111 (2014).
[Crossref]

J. Comput. Phys. (1)

T. I. Lakoba and J. Yang, “A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity,” J. Comput. Phys. 226, 1668–1692 (2007).
[Crossref]

J. Mod. Opt. (1)

A. Badalyan, R. Hovsepyan, P. Mantashyan, V. Mekhitaryan, and R. Drampyan, “Bessel standing wave technique for optical induction of complex refractive lattice structures in photorefractive materials,” J. Mod. Opt. 60, 617–628 (2013).
[Crossref]

J. Opt. B Quantum Semiclass. Opt. (1)

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B Quantum Semiclass. Opt. 6, 444–447 (2004).
[Crossref]

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

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] [PubMed]

New J. Phys. (1)

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14, 033018 (2012).
[Crossref]

Opt. Commun. (1)

J. C. Gutierrez-Vega, M. Iturbe-Castillo, G. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, and G. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

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 (2)

F. Diebel, B. M. Bokić, M. Boguslawski, A. Piper, D. V. Timotijević, D. M. Jović, and C. Denz, “Control of Airy-beam self-acceleration by photonic lattices,” Phys. Rev. A 90, 033802 (2014).
[Crossref]

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520 (1995).
[Crossref] [PubMed]

Phys. Rev. E (1)

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, “Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices,” Phys. Rev. E 70, 065602 (2004).
[Crossref]

Phys. Rev. Lett. (3)

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

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96, 083904 (2006).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable ring-profile vortex solitons in Bessel optical lattices,” Phys. Rev. Lett. 94, 043902 (2005).
[Crossref] [PubMed]

Other (3)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003).

S. Trillo and W. Torruellas, Spatial Solitons (Springer Series in Optical Sciences, 2001).
[Crossref]

K. Staliunas, R. Herrero, C. Cojocaru, and J. Trull, “Nondiffractive propagation of light in photonic crystals,” in Proceedings of the 7th International Conference on Transparent Optical Networks, Ict.1, 281–283 (2005).

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Figures (5)

Fig. 1
Fig. 1 Experimental setup and Bessel beam characterization. The inset shows the experimentally realized single Bessel beam at the front and back face of the homogeneous SBN crystal, as well as a cross-section through the recorded 3d intensity volume and the spacial spectrum in Fourier space.
Fig. 2
Fig. 2 Intensity patterns obtained by coherent superposition of two nondiffracting Bessel beams for different transverse displacement d (in units of Bessel structure size g). (top row) Calculated intensity pattern, (middle row) experimentally recorded intensity profiles in real space. (bottom row) Experimentally recorded field distributions in Fourier space. The phase is encoded in the color, the brightness is given by the intensity. For (a)–(d) both Bessel beams are in phase, for (e) beams are π out of phase.
Fig. 3
Fig. 3 Intensity distribution for Mathieu beams with different order m and ellipticity ε that are almost identical to the resulting pattern in Fig. 2.
Fig. 4
Fig. 4 Linear guiding and localization by 2d azimuthally modulated waveguide structure. (a) Input and output beam for homogenous crystal. (b),(c) Guided intensity at the output for a weakly induced focusing structure, (c),(h) for strong focusing structure. (d),(i) Guided intensity at the output for a weakly induced defocusing structure, (e),(j) for strong defocusing structure.
Fig. 5
Fig. 5 Nonlinear off-center soliton formation in azimuthally modulated Bessel-like structure. (a) Experimentally realized probe beam at the input (soliton profile is calculated numerically) and (b) induction beam. (c)–(e) Experimentally observed soliton formation for increasing probe beam intensity. (f)–(h) Corresponding numerical simulations.

Equations (2)

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

i A z + 1 2 2 A + 1 2 k 0 2 w 0 2 Δ n 2 ( I ) A = 0 ,
2 ϕ + ln ( 1 + I ) ϕ = E ext x ln ( 1 + I ) + k B T e ( 2 ln ( 1 + I ) + ( ln ( 1 + I ) ) 2 ) ,

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