Abstract

We introduce a universal method to optically induce multiperiodic photonic complex superstructures bearing two-dimensional (2D) refractive index modulations over several centimeters of elongation. These superstructures result from the accomplished superposition of 2D fundamental periodic structures. To find the specific sets of fundamentals, we combine particular spatial frequencies of the respective Fourier series expansions, which enables us to use nondiffracting beams in the experiment showing periodic 2D intensity modulation in order to successively develop the desired multiperiodic structures. We present the generation of 2D photonic staircase, hexagonal wire mesh and ratchet structures, whose succeeded generation is confirmed by phase resolving methods using digital-holographic techniques to detect the induced refractive index pattern.

© 2012 OSA

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2012 (3)

D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A85, 031801(R) (2012).
[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]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Photonic ratchet superlattices by optical multiplexing,” Opt. Lett.37, 797–799 (2012).
[CrossRef] [PubMed]

2011 (4)

J. Becker, P. Rose, M. Boguslawski, and C. Denz, “Systematic approach to complex periodic vortex and helix lattices,” Opt. Express19, 9848–9862 (2011).
[CrossRef] [PubMed]

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett.106, 083902 (2011).
[CrossRef] [PubMed]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
[CrossRef]

M. Heinrich, R. Keil, F. Dreisow, A. Tünnermann, A. Szameit, and S. Nolte, “Nonlinear discrete optics in femtosecond laser-written photonic lattices,” Appl. Phys. B104, 469–480 (2011).
[CrossRef]

2010 (5)

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett.105, 143902 (2010).
[CrossRef]

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B81, 075012 (2010).
[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]

S. Longhi, “Photonic analog of Zitterbewegung in binary waveguide arrays,” Opt. Lett.35, 235–237 (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, 2284–2286 (2010).
[CrossRef] [PubMed]

2009 (5)

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional superlattice solitons,” Opt. Lett.34, 3701–3703 (2009).
[CrossRef] [PubMed]

T. Salger, S. Kling, T. Hecking, C. Geckeler, L. Morales-Molina, and M. Weitz, “Directed transport of atoms in a Hamiltonian quantum ratchet,” Science326, 1241–1243 (2009).
[CrossRef] [PubMed]

P. Hänggi and F. Marchesoni, “Artificial Brownian motors: Controlling transport on the nanoscale,” Rev. Mod. Phys.81, 387–442 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Optics52, 63–148 (2009).
[CrossRef]

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A79, 053852 (2009).
[CrossRef]

2008 (3)

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of multivortex solitons in photonic lattices,” Phys. Rev. Lett.101, 013903 (2008).
[CrossRef] [PubMed]

P. Rose, B. Terhalle, J. Imbrock, and C. Denz, “Optically induced photonic superlattices by holographic multiplexing,” J. Phys. D: Appl. Phys.41, 224004 (2008).
[CrossRef]

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt.47, A52–A61 (2008).
[CrossRef] [PubMed]

2007 (4)

T. J. Alexander, A. S. Desyatnikov, and Y. S. Kivshar, “Multivortex solitons in triangular photonic lattices,” Opt. Lett.32, 1293–1295 (2007).
[CrossRef] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6, 183–191 (2007).
[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. B86, 399–405 (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]

2006 (3)

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. 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]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature440, 1166–1169 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Y. S. Kivshar, “Two-dimensional self-trapped nonlinear photonic lattices,” Opt. Express14, 2851–2863 (2006).
[CrossRef] [PubMed]

2005 (1)

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

2004 (4)

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. E70, 065602(R) (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett.93, 093904 (2004).
[CrossRef] [PubMed]

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett.29, 44–46 (2004).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, “Two-dimensional higher-band vortex lattice solitons,” Opt. Lett.29, 2049–2051 (2004).
[CrossRef] [PubMed]

2003 (4)

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

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett.91, 263902 (2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422, 147–150 (2003).
[CrossRef] [PubMed]

Z. Bouchal, “Nondiffracting optical beams: Physical properties, experiments, and applications,” Czech. J. Phys.53, 537–578 (2003).
[CrossRef]

2000 (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404, 53–56 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998).
[CrossRef]

1991 (3)

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett.67, 2295–2298 (1991).
[CrossRef] [PubMed]

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, and S. H. Lee “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett.16, 1774–1776 (1991).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun.85, 171–176 (1991).
[CrossRef]

1988 (1)

1987 (1)

1980 (1)

Alexander, T. J.

Bandres, M. A.

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]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature440, 1166–1169 (2006).
[CrossRef] [PubMed]

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

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, “Two-dimensional higher-band vortex lattice solitons,” Opt. Lett.29, 2049–2051 (2004).
[CrossRef] [PubMed]

Becker, J.

Belic, M. R.

D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A85, 031801(R) (2012).
[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. B86, 399–405 (2007).
[CrossRef]

Boguslawski, M.

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Photonic ratchet superlattices by optical multiplexing,” Opt. Lett.37, 797–799 (2012).
[CrossRef] [PubMed]

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. Becker, P. Rose, M. Boguslawski, and C. Denz, “Systematic approach to complex periodic vortex and helix lattices,” Opt. Express19, 9848–9862 (2011).
[CrossRef] [PubMed]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
[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]

Bouchal, Z.

Z. Bouchal, “Nondiffracting optical beams: Physical properties, experiments, and applications,” Czech. J. Phys.53, 537–578 (2003).
[CrossRef]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404, 53–56 (2000).
[CrossRef] [PubMed]

Campos, J.

Chan, C. T.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998).
[CrossRef]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998).
[CrossRef]

Chávez-Cerda, S.

Chen, Z.

Christodoulides, D. N.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature440, 1166–1169 (2006).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422, 147–150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett.13, 794–796 (1988).
[CrossRef] [PubMed]

Cohen, O.

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

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, “Two-dimensional higher-band vortex lattice solitons,” Opt. Lett.29, 2049–2051 (2004).
[CrossRef] [PubMed]

Costantino, P.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett.91, 263902 (2003).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404, 53–56 (2000).
[CrossRef] [PubMed]

Denz, C.

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

D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A85, 031801(R) (2012).
[CrossRef]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Photonic ratchet superlattices by optical multiplexing,” Opt. Lett.37, 797–799 (2012).
[CrossRef] [PubMed]

J. Becker, P. Rose, M. Boguslawski, and C. Denz, “Systematic approach to complex periodic vortex and helix lattices,” Opt. Express19, 9848–9862 (2011).
[CrossRef] [PubMed]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
[CrossRef]

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett.106, 083902 (2011).
[CrossRef] [PubMed]

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R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett.91, 263902 (2003).
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B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett.106, 083902 (2011).
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T. Salger, S. Kling, T. Hecking, C. Geckeler, L. Morales-Molina, and M. Weitz, “Directed transport of atoms in a Hamiltonian quantum ratchet,” Science326, 1241–1243 (2009).
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B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett.106, 083902 (2011).
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B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of multivortex solitons in photonic lattices,” Phys. Rev. Lett.101, 013903 (2008).
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B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature440, 1166–1169 (2006).
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P. Hänggi and F. Marchesoni, “Artificial Brownian motors: Controlling transport on the nanoscale,” Rev. Mod. Phys.81, 387–442 (2009).
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F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A79, 053852 (2009).
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T. Salger, S. Kling, T. Hecking, C. Geckeler, L. Morales-Molina, and M. Weitz, “Directed transport of atoms in a Hamiltonian quantum ratchet,” Science326, 1241–1243 (2009).
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B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett.106, 083902 (2011).
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B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of multivortex solitons in photonic lattices,” Phys. Rev. Lett.101, 013903 (2008).
[CrossRef] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. 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. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Y. S. Kivshar, “Two-dimensional self-trapped nonlinear photonic lattices,” Opt. Express14, 2851–2863 (2006).
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M. Heinrich, R. Keil, F. Dreisow, A. Tünnermann, A. Szameit, and S. Nolte, “Nonlinear discrete optics in femtosecond laser-written photonic lattices,” Appl. Phys. B104, 469–480 (2011).
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M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional superlattice solitons,” Opt. Lett.34, 3701–3703 (2009).
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R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett.91, 263902 (2003).
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T. Salger, S. Kling, T. Hecking, C. Geckeler, L. Morales-Molina, and M. Weitz, “Directed transport of atoms in a Hamiltonian quantum ratchet,” Science326, 1241–1243 (2009).
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R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett.91, 263902 (2003).
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G. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, “Observation of second-band vortex solitons in 2D photonic lattices,” Phys. Rev. Lett.95, 053904 (2005).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, “Two-dimensional higher-band vortex lattice solitons,” Opt. Lett.29, 2049–2051 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422, 147–150 (2003).
[CrossRef] [PubMed]

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404, 53–56 (2000).
[CrossRef] [PubMed]

Sukhorukov, A. A.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. 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]

Szameit, A.

M. Heinrich, R. Keil, F. Dreisow, A. Tünnermann, A. Szameit, and S. Nolte, “Nonlinear discrete optics in femtosecond laser-written photonic lattices,” Appl. Phys. B104, 469–480 (2011).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett.105, 143902 (2010).
[CrossRef]

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional superlattice solitons,” Opt. Lett.34, 3701–3703 (2009).
[CrossRef] [PubMed]

Taketomi, Y.

Tang, L.

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. B86, 399–405 (2007).
[CrossRef]

Terhalle, B.

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett.106, 083902 (2011).
[CrossRef] [PubMed]

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of multivortex solitons in photonic lattices,” Phys. Rev. Lett.101, 013903 (2008).
[CrossRef] [PubMed]

P. Rose, B. Terhalle, J. Imbrock, and C. Denz, “Optically induced photonic superlattices by holographic multiplexing,” J. Phys. D: Appl. Phys.41, 224004 (2008).
[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. B86, 399–405 (2007).
[CrossRef]

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Y. S. Kivshar, “Two-dimensional self-trapped nonlinear photonic lattices,” Opt. Express14, 2851–2863 (2006).
[CrossRef] [PubMed]

Torner, L.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional superlattice solitons,” Opt. Lett.34, 3701–3703 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Optics52, 63–148 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett.93, 093904 (2004).
[CrossRef] [PubMed]

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. E70, 065602(R) (2004).
[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. B86, 399–405 (2007).
[CrossRef]

A. S. Desyatnikov, N. Sagemerten, R. Fischer, B. Terhalle, D. Träger, D. N. Neshev, A. Dreischuh, C. Denz, W. Krolikowski, and Y. S. Kivshar, “Two-dimensional self-trapped nonlinear photonic lattices,” Opt. Express14, 2851–2863 (2006).
[CrossRef] [PubMed]

Trompeter, H.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. 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]

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun.85, 171–176 (1991).
[CrossRef]

Tünnermann, A.

M. Heinrich, R. Keil, F. Dreisow, A. Tünnermann, A. Szameit, and S. Nolte, “Nonlinear discrete optics in femtosecond laser-written photonic lattices,” Appl. Phys. B104, 469–480 (2011).
[CrossRef]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett.105, 143902 (2010).
[CrossRef]

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional superlattice solitons,” Opt. Lett.34, 3701–3703 (2009).
[CrossRef] [PubMed]

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404, 53–56 (2000).
[CrossRef] [PubMed]

von Bally, G.

Vysloukh, V. A.

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional superlattice solitons,” Opt. Lett.34, 3701–3703 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Optics52, 63–148 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett.93, 093904 (2004).
[CrossRef] [PubMed]

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. E70, 065602(R) (2004).
[CrossRef]

Wang, X.

Weitz, M.

T. Salger, S. Kling, T. Hecking, C. Geckeler, L. Morales-Molina, and M. Weitz, “Directed transport of atoms in a Hamiltonian quantum ratchet,” Science326, 1241–1243 (2009).
[CrossRef] [PubMed]

Wiersma, D.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett.91, 263902 (2003).
[CrossRef]

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]

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett.67, 2295–2298 (1991).
[CrossRef] [PubMed]

Ye, F.

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A79, 053852 (2009).
[CrossRef]

Yzuel, M. J.

Zhang, P.

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. (2)

Appl. Phys. B (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. B86, 399–405 (2007).
[CrossRef]

M. Heinrich, R. Keil, F. Dreisow, A. Tünnermann, A. Szameit, and S. Nolte, “Nonlinear discrete optics in femtosecond laser-written photonic lattices,” Appl. Phys. B104, 469–480 (2011).
[CrossRef]

Czech. J. Phys. (1)

Z. Bouchal, “Nondiffracting optical beams: Physical properties, experiments, and applications,” Czech. J. Phys.53, 537–578 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys. D: Appl. Phys. (1)

P. Rose, B. Terhalle, J. Imbrock, and C. Denz, “Optically induced photonic superlattices by holographic multiplexing,” J. Phys. D: Appl. Phys.41, 224004 (2008).
[CrossRef]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater.6, 183–191 (2007).
[CrossRef] [PubMed]

Nature (4)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature404, 53–56 (2000).
[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]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature422, 147–150 (2003).
[CrossRef] [PubMed]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature440, 1166–1169 (2006).
[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)

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun.85, 171–176 (1991).
[CrossRef]

Opt. Express (2)

Opt. Lett. (10)

S. Longhi, “Photonic analog of Zitterbewegung in binary waveguide arrays,” Opt. Lett.35, 235–237 (2010).
[CrossRef] [PubMed]

M. Heinrich, Y. V. Kartashov, L. P. R. Ramirez, A. Szameit, F. Dreisow, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, “Observation of two-dimensional superlattice solitons,” Opt. Lett.34, 3701–3703 (2009).
[CrossRef] [PubMed]

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, and S. H. Lee “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett.16, 1774–1776 (1991).
[CrossRef] [PubMed]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Photonic ratchet superlattices by optical multiplexing,” Opt. Lett.37, 797–799 (2012).
[CrossRef] [PubMed]

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett.29, 44–46 (2004).
[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, 2284–2286 (2010).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, “Two-dimensional higher-band vortex lattice solitons,” Opt. Lett.29, 2049–2051 (2004).
[CrossRef] [PubMed]

T. J. Alexander, A. S. Desyatnikov, and Y. S. Kivshar, “Multivortex solitons in triangular photonic lattices,” Opt. Lett.32, 1293–1295 (2007).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett.13, 794–796 (1988).
[CrossRef] [PubMed]

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

Phys. Rev. A (3)

F. Ye, D. Mihalache, and B. Hu, “Elliptic vortices in composite Mathieu lattices,” Phys. Rev. A79, 053852 (2009).
[CrossRef]

D. M. Jović, M. R. Belić, and C. Denz, “Anderson localization of light at the interface between linear and nonlinear dielectric media with an optically induced photonic lattice,” Phys. Rev. A85, 031801(R) (2012).
[CrossRef]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A84, 013832 (2011).
[CrossRef]

Phys. Rev. B (1)

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B81, 075012 (2010).
[CrossRef]

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. E70, 065602(R) (2004).
[CrossRef]

Phys. Rev. Lett. (9)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary solitons in bessel optical lattices,” Phys. Rev. Lett.93, 093904 (2004).
[CrossRef] [PubMed]

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett.91, 263902 (2003).
[CrossRef]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. 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]

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. S. Kivshar, “Observation of multivortex solitons in photonic lattices,” Phys. Rev. Lett.101, 013903 (2008).
[CrossRef] [PubMed]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett.80, 956–959 (1998).
[CrossRef]

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

E. Yablonovitch, T. J. Gmitter, and K. M. Leung, “Photonic band structure: The face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett.67, 2295–2298 (1991).
[CrossRef] [PubMed]

F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, and A. Szameit, “Classical simulation of relativistic Zitterbewegung in photonic lattices,” Phys. Rev. Lett.105, 143902 (2010).
[CrossRef]

B. Terhalle, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, C. Denz, and Y. S. Kivshar, “Dynamic diffraction and interband transitions in two-dimensional photonic lattices,” Phys. Rev. Lett.106, 083902 (2011).
[CrossRef] [PubMed]

Prog. Optics (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Prog. Optics52, 63–148 (2009).
[CrossRef]

Rev. Mod. Phys. (1)

P. Hänggi and F. Marchesoni, “Artificial Brownian motors: Controlling transport on the nanoscale,” Rev. Mod. Phys.81, 387–442 (2009).
[CrossRef]

Science (1)

T. Salger, S. Kling, T. Hecking, C. Geckeler, L. Morales-Molina, and M. Weitz, “Directed transport of atoms in a Hamiltonian quantum ratchet,” Science326, 1241–1243 (2009).
[CrossRef] [PubMed]

Other (1)

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Supplementary Material (4)

» Media 1: AVI (6020 KB)     
» Media 2: AVI (5837 KB)     
» Media 3: AVI (6200 KB)     
» Media 4: AVI (1131 KB)     

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Figures (6)

Fig. 1
Fig. 1

Schematics describing a multiperiodic 2D staircase lattice; (a): surface plot of the effective intensity calculated by series expansion up to an order of ten, (b): presentation of the relevant spatial frequencies, (c) periodic square lattice as the basis structure of each expansion term.

Fig. 2
Fig. 2

Schematics describing a multiperiodic 2D wire mesh lattice; (a): surface plot of the effective intensity calculated by series expansion up to an order of ten, (b): presentation of the relevant spatial frequencies, (c) periodic hexagonal lattice as the basis structure of each expansion term.

Fig. 3
Fig. 3

Schematics describing a multiperiodic 2D ratchet lattice; (a): surface plot of the effective intensity calculated by series expansion up to an order of ten, (b): presentation of the relevant spatial frequencies, (c) periodic square lattice as the basis structure of each expansion term.

Fig. 4
Fig. 4

Schematic of experimental setup to optically induce and analyze spatial refractive index modulations of photorefractive crystals. Green colored light path represents the lattice inducing part, the probing part is colored in red. A/PSLM: amplitude/phase spatial light modulator, BS: beam splitter, D/FSC: direct/Fourier space camera, L: lens, λ/2: half-wave retardation plate, M: mirror, MO: microscope objective, P: polarizer, PH: pinhole, SBN: cerium-doped strontium barium niobate. Camera picture presents a typical recorded intensity pattern, magnification shows details of interference fringes.

Fig. 5
Fig. 5

Analysis results of probing experiments using propagating plane wave of perpendicular incidence to crystal surface to characterize generated 2D photonic superlattices: (a)–(c) staircase structure, (d)–(f) wire mesh structure, (g)–(i) ratchet structure. Direction of c axis is illustrated in (g) and (i), respectively. Scale bar for all real space pictures is appended in (h). Left column present intensity, middle column phase distribution of the plane probe wave in real space. Insets of left column pictures illustrate far field diffraction spectrum. Refractive index landscapes are depicted as surface plots in right column. Animated plots for photonic staircase ( Media 1), wire mesh ( Media 2) as well as ratchet structure ( Media 3) are available online.

Fig. 6
Fig. 6

Time development of the rectangularly modulated refractive index structure. The detailed illumination times are (a) t1 = 20 s, (b) t2 = 80 s, (c) t3 = 140 s, (d) t4 = 200 s. Respective insets present corresponding intensity distributions in far field. The temporal development of the staircase structure can be found online as a video file ( Media 4).

Equations (14)

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

M ( r ) = m = 1 10 a m I ( k m j r ) .
Π 2 D ( r ) = m = 1 10 1 2 m 1 [ 2 + sin ( k m 1 r ) + sin ( k m 2 r ) ] ,
k m j = ( 2 m 1 ) 2 π g 1 e j = k m e j with j = 1 , 2 , e 1 = ( 1 , 1 ) , e 2 = ( 1 , 1 ) .
[ 2 + sin ( 2 ϕ 1 ) + sin ( 2 ϕ 2 ) ] = 1 2 [ 4 + e i ( 2 ϕ 1 π / 2 ) + e i ( 2 ϕ 1 π / 2 ) + e i ( 2 ϕ 2 π / 2 ) + e i ( 2 ϕ 2 π / 2 ) ] = 1 2 | e i ( ϕ 1 π / 4 ) + e i ( ϕ 1 π / 4 ) + i e i ( ϕ 2 π / 4 ) + i e i ( ϕ 2 π / 4 ) | 2 ,
Π 2 D ( r ) = m = 1 10 1 2 ( 2 m 1 ) | Ψ 4 , 1 ( r , k m ) | 2
X 2 D ( r ) = m = 1 10 1 m [ 3 2 + cos ( k m 1 r ) + cos ( k m 2 r ) + cos ( k m 3 r ) ] .
k m j = m 2 π g 1 e j = k m e j with j = 1 , 2 , 3 and e 1 = ( cos ( π / 6 ) , sin ( π / 6 ) ) , e 2 = ( 0 , 1 ) , e 3 = ( cos ( π / 6 ) , sin ( π / 6 ) ) .
[ 3 2 + cos ( ϕ 1 ) + cos ( ϕ 2 ) + cos ( ϕ 3 ) ] = 1 2 [ 3 + e i ϕ 1 + e i ϕ 1 + e i ϕ 2 + e i ϕ 2 + e i ϕ 3 + e i ϕ 3 ] .
| Ψ 3 , 0 ( r , k m ) | 2 = | e i φ 1 ( r , k m ) + e i φ 2 ( r , k m ) + e i φ 3 ( r , k m ) | 2 = 3 + e i ( φ 1 φ 2 ) + e i ( φ 1 φ 2 ) + e i ( φ 1 φ 3 ) + e i ( φ 1 φ 3 ) + e i ( φ 2 φ 3 ) + e i ( φ 2 φ 3 )
X 2 D ( r ) = m = 1 10 1 2 m | Ψ 3 , 0 ( r , k m ) | 2
Λ 2 D ( r ) = m = 1 10 1 m [ 2 + sin ( k m 1 r ) + sin ( k m 2 r ) ] .
k m j = m 2 π g 1 e j = k m e j with j = 1 , 2 , e 1 = ( 1 , 1 ) , e 2 = ( 1 , 1 ) .
Λ 2 D ( r ) = m = 1 10 1 2 m | Ψ 4 , 1 ( r , k m ) | 2 ,
Δ n w ( t ) = Δ n sat [ 1 e t / τ w ] , Δ n e ( t ) = Δ n 0 e t / τ e ,

Metrics