Abstract

As light localization becomes increasingly pronounced in photonic systems with less order, we investigate optically induced two-dimensional Fibonacci structures that are supposed to be among the most ordered realizations of deterministic aperiodic patterns. For the generation of corresponding refractive index structures, we implement a recently developed incremental induction method using nondiffracting Bessel beams as waveguide formation entities. Even though Fibonacci structures present slightly reduced order, we show that transverse light transport here is significantly hampered in comparison with discrete diffraction in a periodic lattice. Numerical simulations that support our experimental findings help to identify three cases of input waveguide configurations that significantly determine the initial propagation in a Fibonacci structure. These crucial starting conditions determine the character of light transport, yielding either localization or enhanced expansion. A diverse set of light transport scenarios is identified therein.

© 2016 Optical Society of America

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References

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    [Crossref]
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2015 (2)

2014 (3)

M. Renner and G. von Freymann, “Transverse mode localization in three-dimensional deterministic aperiodic structures,” Adv. Opt. Mater. 2, 226–230 (2014).
[Crossref]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Apodized structures for the integration of defect sites into photonic lattices,” Appl. Phys. Lett. 105, 111102 (2014).
[Crossref]

F. Diebel, P. Rose, M. Boguslawski, and C. Denz, “Optical induction scheme for assembling nondiffracting aperiodic Vogel spirals,” Appl. Phys. Lett. 104, 191101 (2014).
[Crossref]

2013 (1)

2012 (5)

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20, 27331–27343 (2012).
[Crossref]

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14, 33018 (2012).
[Crossref]

J. Trevino, S. F. Liew, H. Noh, H. Cao, and L. Dal Negro, “Geometrical structure, multifractal spectra and localized optical modes of aperiodic Vogel spirals,” Opt. Express 20, 3015–3033 (2012).
[Crossref]

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).
[Crossref]

M. Baake and U. Grimm, “Mathematical diffraction of aperiodic structures,” Chem. Soc. Rev. 41, 6821–6843 (2012).
[Crossref]

2011 (3)

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[Crossref]

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84, 13832 (2011).
[Crossref]

2009 (3)

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[Crossref]

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref]

A. Lagendijk, B. Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

2008 (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]

2007 (1)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

2006 (3)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
[Crossref]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).
[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]

2004 (1)

2003 (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref]

2002 (1)

R. Lifshitz, “The square Fibonacci tiling,” J. Alloys Compd. 342, 186–190 (2002).
[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,” Nature 404, 53–56 (2000).
[Crossref]

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]

1994 (1)

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref]

1992 (1)

H. Hiramoto and M. Kohmoto, “Electronic spectral and wavefunction properties of one-dimensional quasiperiodic systems: a scaling approach,” Int. J. Mod. Phys. B 6, 281–320 (1992).
[Crossref]

1991 (1)

R. A. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991).
[Crossref]

1988 (1)

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60, 1081–1084 (1988).
[Crossref]

1987 (1)

1986 (1)

P. St. J. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B 39, 231–246 (1986).
[Crossref]

1984 (2)

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett. 53, 1951–1953 (1984).
[Crossref]

D. Levine and P. J. Steinhardt, “Quasicrystals: a new class of ordered structures,” Phys. Rev. Lett. 53, 2477–2480 (1984).
[Crossref]

Ali, M. K.

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60, 1081–1084 (1988).
[Crossref]

Armijo, J.

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]

Baake, M.

M. Baake and U. Grimm, “Mathematical diffraction of aperiodic structures,” Chem. Soc. Rev. 41, 6821–6843 (2012).
[Crossref]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).
[Crossref]

Belic, M. R.

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[Crossref]

Blech, I.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett. 53, 1951–1953 (1984).
[Crossref]

Boguslawski, M.

F. Diebel, P. Rose, M. Boguslawski, and C. Denz, “Optical induction scheme for assembling nondiffracting aperiodic Vogel spirals,” Appl. Phys. Lett. 104, 191101 (2014).
[Crossref]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Apodized structures for the integration of defect sites into photonic lattices,” Appl. Phys. Lett. 105, 111102 (2014).
[Crossref]

M. Boguslawski, S. Brake, J. Armijo, F. Diebel, P. Rose, and C. Denz, “Analysis of transverse Anderson localization in refractive index structures with customized random potential,” Opt. Express 21, 31713 (2013).
[Crossref]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20, 27331–27343 (2012).
[Crossref]

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14, 33018 (2012).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84, 13832 (2011).
[Crossref]

S. Brake, M. Boguslawski, D. Leykam, A. S. Desyatnikov, and C. Denz, “Observation of transverse coherent backscattering in disordered photonic structures,” arXiv:1501.04458 (2015).

Boriskina, S. V.

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).
[Crossref]

Brake, S.

M. Boguslawski, S. Brake, J. Armijo, F. Diebel, P. Rose, and C. Denz, “Analysis of transverse Anderson localization in refractive index structures with customized random potential,” Opt. Express 21, 31713 (2013).
[Crossref]

S. Brake, M. Boguslawski, D. Leykam, A. S. Desyatnikov, and C. Denz, “Observation of transverse coherent backscattering in disordered photonic structures,” arXiv:1501.04458 (2015).

Burghoff, J.

Cahn, J. W.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett. 53, 1951–1953 (1984).
[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,” Nature 404, 53–56 (2000).
[Crossref]

Cao, H.

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]

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]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref]

Dal Negro, L.

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).
[Crossref]

J. Trevino, S. F. Liew, H. Noh, H. Cao, and L. Dal Negro, “Geometrical structure, multifractal spectra and localized optical modes of aperiodic Vogel spirals,” Opt. Express 20, 3015–3033 (2012).
[Crossref]

Davidson, N.

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref]

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,” Nature 404, 53–56 (2000).
[Crossref]

Denz, C.

F. Diebel, P. Rose, M. Boguslawski, and C. Denz, “Optical induction scheme for assembling nondiffracting aperiodic Vogel spirals,” Appl. Phys. Lett. 104, 191101 (2014).
[Crossref]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Apodized structures for the integration of defect sites into photonic lattices,” Appl. Phys. Lett. 105, 111102 (2014).
[Crossref]

M. Boguslawski, S. Brake, J. Armijo, F. Diebel, P. Rose, and C. Denz, “Analysis of transverse Anderson localization in refractive index structures with customized random potential,” Opt. Express 21, 31713 (2013).
[Crossref]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20, 27331–27343 (2012).
[Crossref]

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14, 33018 (2012).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84, 13832 (2011).
[Crossref]

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[Crossref]

S. Brake, M. Boguslawski, D. Leykam, A. S. Desyatnikov, and C. Denz, “Observation of transverse coherent backscattering in disordered photonic structures,” arXiv:1501.04458 (2015).

Desyatnikov, A. S.

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]

S. Brake, M. Boguslawski, D. Leykam, A. S. Desyatnikov, and C. Denz, “Observation of transverse coherent backscattering in disordered photonic structures,” arXiv:1501.04458 (2015).

Diebel, F.

F. Diebel, P. Rose, M. Boguslawski, and C. Denz, “Optical induction scheme for assembling nondiffracting aperiodic Vogel spirals,” Appl. Phys. Lett. 104, 191101 (2014).
[Crossref]

M. Boguslawski, S. Brake, J. Armijo, F. Diebel, P. Rose, and C. Denz, “Analysis of transverse Anderson localization in refractive index structures with customized random potential,” Opt. Express 21, 31713 (2013).
[Crossref]

Durnin, J.

Ewbank, M. D.

R. A. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991).
[Crossref]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Fleischer, J. W.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).
[Crossref]

Florescu, M.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[Crossref]

Freedman, B.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).
[Crossref]

Gellermann, W.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref]

Gratias, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett. 53, 1951–1953 (1984).
[Crossref]

Grimm, U.

M. Baake and U. Grimm, “Mathematical diffraction of aperiodic structures,” Chem. Soc. Rev. 41, 6821–6843 (2012).
[Crossref]

Grujic, D. Ž.

Gumbs, G.

G. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60, 1081–1084 (1988).
[Crossref]

Harrison, M. T.

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,” Nature 404, 53–56 (2000).
[Crossref]

Hiramoto, H.

H. Hiramoto and M. Kohmoto, “Electronic spectral and wavefunction properties of one-dimensional quasiperiodic systems: a scaling approach,” Int. J. Mod. Phys. B 6, 281–320 (1992).
[Crossref]

Jelenkovic, B. M.

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Jovic, D. M.

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[Crossref]

Jovic Savic, D. M.

Kelberer, A.

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Apodized structures for the integration of defect sites into photonic lattices,” Appl. Phys. Lett. 105, 111102 (2014).
[Crossref]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20, 27331–27343 (2012).
[Crossref]

Kivshar, Y. S.

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]

Kohmoto, M.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref]

H. Hiramoto and M. Kohmoto, “Electronic spectral and wavefunction properties of one-dimensional quasiperiodic systems: a scaling approach,” Int. J. Mod. Phys. B 6, 281–320 (1992).
[Crossref]

Kraus, Y. E.

M. Verbin, O. Zilberberg, Y. Lahini, Y. E. Kraus, and Y. Silberberg, “Topological pumping over a photonic Fibonacci quasicrystal,” Phys. Rev. B 91, 064201 (2015).
[Crossref]

Krolikowski, W.

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]

Lagendijk, A.

A. Lagendijk, B. Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

Lahini, Y.

M. Verbin, O. Zilberberg, Y. Lahini, Y. E. Kraus, and Y. Silberberg, “Topological pumping over a photonic Fibonacci quasicrystal,” Phys. Rev. B 91, 064201 (2015).
[Crossref]

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref]

Lederer, F.

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

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]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468–470 (2004).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref]

Levi, L.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref]

Levine, D.

D. Levine and P. J. Steinhardt, “Quasicrystals: a new class of ordered structures,” Phys. Rev. Lett. 53, 2477–2480 (1984).
[Crossref]

Leykam, D.

S. Brake, M. Boguslawski, D. Leykam, A. S. Desyatnikov, and C. Denz, “Observation of transverse coherent backscattering in disordered photonic structures,” arXiv:1501.04458 (2015).

Liew, S. F.

Lifshitz, R.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).
[Crossref]

R. Lifshitz, “The square Fibonacci tiling,” J. Alloys Compd. 342, 186–190 (2002).
[Crossref]

Liu, Z. Y.

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]

Lucic, N. M.

Maciá, E.

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Morandotti, R.

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref]

Neshev, D. N.

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]

Neurgaonkar, R. R.

R. A. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991).
[Crossref]

Noh, H.

Nolte, S.

Pantelic, D. V.

Pertsch, T.

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]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468–470 (2004).
[Crossref]

Peschel, U.

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]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, “Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,” Opt. Lett. 29, 468–470 (2004).
[Crossref]

Piper, A.

Pozzi, F.

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref]

Pugatch, R.

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref]

Rechtsman, M.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref]

Renner, M.

M. Renner and G. von Freymann, “Transverse mode localization in three-dimensional deterministic aperiodic structures,” Adv. Opt. Mater. 2, 226–230 (2014).
[Crossref]

Rose, P.

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Apodized structures for the integration of defect sites into photonic lattices,” Appl. Phys. Lett. 105, 111102 (2014).
[Crossref]

F. Diebel, P. Rose, M. Boguslawski, and C. Denz, “Optical induction scheme for assembling nondiffracting aperiodic Vogel spirals,” Appl. Phys. Lett. 104, 191101 (2014).
[Crossref]

M. Boguslawski, S. Brake, J. Armijo, F. Diebel, P. Rose, and C. Denz, “Analysis of transverse Anderson localization in refractive index structures with customized random potential,” Opt. Express 21, 31713 (2013).
[Crossref]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Multiplexing complex two-dimensional photonic superlattices,” Opt. Express 20, 27331–27343 (2012).
[Crossref]

P. Rose, M. Boguslawski, and C. Denz, “Nonlinear lattice structures based on families of complex nondiffracting beams,” New J. Phys. 14, 33018 (2012).
[Crossref]

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84, 13832 (2011).
[Crossref]

Schwartz, T.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

Segev, M.

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref]

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]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).
[Crossref]

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,” Nature 404, 53–56 (2000).
[Crossref]

Shechtman, D.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett. 53, 1951–1953 (1984).
[Crossref]

Silberberg, Y.

M. Verbin, O. Zilberberg, Y. Lahini, Y. E. Kraus, and Y. Silberberg, “Topological pumping over a photonic Fibonacci quasicrystal,” Phys. Rev. B 91, 064201 (2015).
[Crossref]

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref]

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

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref]

Sorel, M.

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref]

St. J. Russell, P.

P. St. J. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B 39, 231–246 (1986).
[Crossref]

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]

Steinhardt, P. J.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[Crossref]

D. Levine and P. J. Steinhardt, “Quasicrystals: a new class of ordered structures,” Phys. Rev. Lett. 53, 2477–2480 (1984).
[Crossref]

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]

Sutherland, B.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref]

Taylor, P. C.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref]

Tiggelen, B.

A. Lagendijk, B. Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

Timotijevic, D. V.

Torquato, S.

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[Crossref]

Trevino, J.

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]

Tünnermann, A.

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,” Nature 404, 53–56 (2000).
[Crossref]

Vasiljevic, J. M.

Vazquez, R. A.

R. A. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991).
[Crossref]

Verbin, M.

M. Verbin, O. Zilberberg, Y. Lahini, Y. E. Kraus, and Y. Silberberg, “Topological pumping over a photonic Fibonacci quasicrystal,” Phys. Rev. B 91, 064201 (2015).
[Crossref]

von Freymann, G.

M. Renner and G. von Freymann, “Transverse mode localization in three-dimensional deterministic aperiodic structures,” Adv. Opt. Mater. 2, 226–230 (2014).
[Crossref]

Wiersma, D. S.

A. Lagendijk, B. Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

Will, M.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Zilberberg, O.

M. Verbin, O. Zilberberg, Y. Lahini, Y. E. Kraus, and Y. Silberberg, “Topological pumping over a photonic Fibonacci quasicrystal,” Phys. Rev. B 91, 064201 (2015).
[Crossref]

Adv. Opt. Mater. (1)

M. Renner and G. von Freymann, “Transverse mode localization in three-dimensional deterministic aperiodic structures,” Adv. Opt. Mater. 2, 226–230 (2014).
[Crossref]

Appl. Phys. B (1)

P. St. J. Russell, “Optics of Floquet-Bloch waves in dielectric gratings,” Appl. Phys. B 39, 231–246 (1986).
[Crossref]

Appl. Phys. Lett. (2)

F. Diebel, P. Rose, M. Boguslawski, and C. Denz, “Optical induction scheme for assembling nondiffracting aperiodic Vogel spirals,” Appl. Phys. Lett. 104, 191101 (2014).
[Crossref]

M. Boguslawski, A. Kelberer, P. Rose, and C. Denz, “Apodized structures for the integration of defect sites into photonic lattices,” Appl. Phys. Lett. 105, 111102 (2014).
[Crossref]

Chem. Soc. Rev. (1)

M. Baake and U. Grimm, “Mathematical diffraction of aperiodic structures,” Chem. Soc. Rev. 41, 6821–6843 (2012).
[Crossref]

Int. J. Mod. Phys. B (1)

H. Hiramoto and M. Kohmoto, “Electronic spectral and wavefunction properties of one-dimensional quasiperiodic systems: a scaling approach,” Int. J. Mod. Phys. B 6, 281–320 (1992).
[Crossref]

J. Alloys Compd. (1)

R. Lifshitz, “The square Fibonacci tiling,” J. Alloys Compd. 342, 186–190 (2002).
[Crossref]

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

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

Laser Photon. Rev. (1)

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).
[Crossref]

Nature (4)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).
[Crossref]

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,” Nature 404, 53–56 (2000).
[Crossref]

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, 33018 (2012).
[Crossref]

Opt. Commun. (1)

R. A. Vazquez, M. D. Ewbank, and R. R. Neurgaonkar, “Photorefractive properties of doped strontium-barium niobate,” Opt. Commun. 80, 253–258 (1991).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

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)

M. Boguslawski, P. Rose, and C. Denz, “Increasing the structural variety of discrete nondiffracting wave fields,” Phys. Rev. A 84, 13832 (2011).
[Crossref]

D. M. Jović, M. R. Belić, and C. Denz, “Transverse localization of light in nonlinear photonic lattices with dimensionality crossover,” Phys. Rev. A 84, 043811 (2011).
[Crossref]

Phys. Rev. B (2)

M. Florescu, S. Torquato, and P. J. Steinhardt, “Complete band gaps in two-dimensional photonic quasicrystals,” Phys. Rev. B 80, 155112 (2009).
[Crossref]

M. Verbin, O. Zilberberg, Y. Lahini, Y. E. Kraus, and Y. Silberberg, “Topological pumping over a photonic Fibonacci quasicrystal,” Phys. Rev. B 91, 064201 (2015).
[Crossref]

Phys. Rev. Lett. (7)

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]

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, “Metallic phase with long-range orientational order and no translational symmetry,” Phys. Rev. Lett. 53, 1951–1953 (1984).
[Crossref]

D. Levine and P. J. Steinhardt, “Quasicrystals: a new class of ordered structures,” Phys. Rev. Lett. 53, 2477–2480 (1984).
[Crossref]

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. Gumbs and M. K. Ali, “Dynamical maps, Cantor spectra, and localization for Fibonacci and related quasiperiodic lattices,” Phys. Rev. Lett. 60, 1081–1084 (1988).
[Crossref]

Y. Lahini, R. Pugatch, F. Pozzi, M. Sorel, R. Morandotti, N. Davidson, and Y. Silberberg, “Observation of a localization transition in quasiperiodic photonic lattices,” Phys. Rev. Lett. 103, 013901 (2009).
[Crossref]

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72, 633–636 (1994).
[Crossref]

Phys. Today (1)

A. Lagendijk, B. Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62(8), 24–29 (2009).
[Crossref]

Rep. Prog. Phys. (1)

E. Maciá, “The role of aperiodic order in science and technology,” Rep. Prog. Phys. 69, 397–441 (2006).
[Crossref]

Science (1)

L. Levi, M. Rechtsman, B. Freedman, T. Schwartz, and M. Segev, “Disorder-enhanced transport in photonic quasicrystals,” Science 332, 1541–1544 (2011).
[Crossref]

Other (2)

S. Brake, M. Boguslawski, D. Leykam, A. S. Desyatnikov, and C. Denz, “Observation of transverse coherent backscattering in disordered photonic structures,” arXiv:1501.04458 (2015).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

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Figures (7)

Fig. 1.
Fig. 1. (a) Fibonacci lattice with Gaussian beam sites (underlying Fibonacci words indicated alongside). (b) Spatial spectrum S ( k x , k y ) according to lattice shown in (a). (c) Measured effective intensity with Bessel beam lattice sites taken by multiple-shot illumination at the back face of the crystal. Bottom right quadrant shows according numerical simulation. (d) Experimental output for plane-wave probing (contours indicate waveguide positions). (e) Plot of (orange) spectrum S ( k t ) along the direction denoted in (b) and of (black) the ideal spectrum for an extended aperiodic Fibonacci lattice with δ -function lattice sites.
Fig. 2.
Fig. 2. Experimental setup for induction of Fibonacci lattices with incoherent Bessel beams. (A/P)SLM, (amplitude/phase) spatial light modulator; Cam, CCD camera; λ / 2 , half-wave plate; LED, background illumination; (R)P, (rotatable) polarizer; SBN, strontium barium niobate crystal; lenses and pin hole not labeled.
Fig. 3.
Fig. 3. Light propagation in aperiodic Fibonacci photonic lattices. Intensity distributions at the exit face of the crystal experimentally observed (first row) and numerically calculated (second row) for input probe beam size w 0 = 14    μm . Columns correspond to input beam positions 1 to 5, as shown in (k).
Fig. 4.
Fig. 4. Three cases of input waveguide configuration. Computed images show intensity distributions of (top row) single-, (middle row) double-, and (bottom row) quad-waveguide input for particular propagation distances as indicated in the upper right corner and marked in Fig. 5(b). Filled circles mark the position of the input waveguide.
Fig. 5.
Fig. 5. Development of beam widths with propagation distance. (a) Absolute beam widths ω eff of individual on-site probing scenarios and mean of beam width ω mean . (b) Relative beam widths ω eff / ω mean . Labels in (b) identify images in Fig. 4.
Fig. 6.
Fig. 6. Experimental images for a periodic photonic square lattice. (a) Effective intensity, (b) plane-wave, and (c) single-site probing output.
Fig. 7.
Fig. 7. Comparison of effective beam width development in a Fibonacci lattice against periodic and homogeneous medium cases. (a) Beam widths ω eff versus propagation distance z : (orange) mean beam width ω mean , and (gray) individual beam width; beam width in (dashed black) a periodic lattice and (dotted black) a homogeneous medium. Dashed vertical line at z = 20    mm indicates experimental propagation distance. Intensity distributions at z = 70    mm in (b) averaged Fibonacci intensity, (c) periodic square lattice, and (d) homogeneous medium, each for w 0 = 14    μm .

Equations (3)

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S 0 = A , S 1 = AB , S 2 = ABA , S 3 = ABAAB , S 4 = ABAABABA .
{ 2 i k z + Δ k n e 2 r 33 ( x Φ sc ) } A ( r⃗ ) = 0
P ( z ) = | E ( x , y , z ) | 4 d x d y ( | E ( x , y , z ) | 2 d x d y ) 2

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