Abstract

We introduce a new class of paraxial optical beams exhibiting discrete-like diffraction patterns reminiscent to those observed in periodic evanescently coupled waveguide lattices. It is demonstrated that such paraxial beams are analytically described in terms of generalized Bessel functions. Such effects are elucidated via pertinent examples.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  23. N. K. Efremdis, P. Zhang, Z. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, “Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. A81(5), 053817 (2010).
    [CrossRef]
  24. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35(23), 4045–4047 (2010).
    [CrossRef] [PubMed]
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2013

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A87(2), 022303 (2013).
[CrossRef]

2012

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the Correlation and Anticorrelation behavior of Path-entangled Photons in Glauber-Fock Oscillator Lattices,” Phys. Rev. A85(1), 013848 (2012).
[CrossRef]

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, P. Aleahmad, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of Bloch-like revivals in semi-infinite Glauber-Fock photonic lattices,” Opt. Lett.37(18), 3801–3803 (2012).
[CrossRef] [PubMed]

M. Bellec, G. M. Nikolopoulos, and S. Tzortzakis, “Faithful communication Hamiltonian in photonic lattices,” Opt. Lett.37(21), 4504–4506 (2012).
[CrossRef] [PubMed]

2011

S. Longhi, “Jaynes-Cummings photonic superlattices,” Opt. Lett.36(17), 3407–3409 (2011).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

2010

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch Oscillations of Path-Entangled Photons,” Phys. Rev. Lett.105(26), 263604 (2010).
[CrossRef] [PubMed]

N. K. Efremdis, P. Zhang, Z. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, “Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. A81(5), 053817 (2010).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35(23), 4045–4047 (2010).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35(23), 4045–4047 (2010).
[CrossRef] [PubMed]

2009

A. Rai and G. S. Agarwal, “Possibility of coherent phenomena such as Bloch oscillations with single photons via W states,” Phys. Rev. A79(5), 053849 (2009).
[CrossRef]

2008

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett.100(1), 013906 (2008).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Long-range interaction in waveguide lattices,” Phys. Rev. A77(4), 043804 (2008).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, “Second-order coupling in femtosecond-laser-written waveguide arrays,” Opt. Lett.33(22), 2689–2691 (2008).
[CrossRef] [PubMed]

2006

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual Observation of Zener Tunneling,” Phys. Rev. Lett.96(2), 023901 (2006).
[CrossRef] [PubMed]

2005

2003

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424(6950), 817–823 (2003).
[CrossRef] [PubMed]

1991

G. Dattoli, A. Torre, S. Lorenzzutta, and G. Maino, “Theory of generalized Bessel functions II,” Nuovo Cim.106(1), 21–51 (1991).
[CrossRef]

1990

G. Dattoli, L. Giannessi, L. Mezi, and A. Torre, “Theory of generalized Bessel functions,” Nuovo Cim.105(3), 327–348 (1990).
[CrossRef]

1965

Abouraddy, A. F.

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the Correlation and Anticorrelation behavior of Path-entangled Photons in Glauber-Fock Oscillator Lattices,” Phys. Rev. A85(1), 013848 (2012).
[CrossRef]

Agarwal, G. S.

A. Rai and G. S. Agarwal, “Possibility of coherent phenomena such as Bloch oscillations with single photons via W states,” Phys. Rev. A79(5), 053849 (2009).
[CrossRef]

Aleahmad, P.

Avidan, A.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett.100(1), 013906 (2008).
[CrossRef] [PubMed]

Bandres, M. A.

Bellec, M.

Bräuer, A.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual Observation of Zener Tunneling,” Phys. Rev. Lett.96(2), 023901 (2006).
[CrossRef] [PubMed]

Bromberg, Y.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch Oscillations of Path-Entangled Photons,” Phys. Rev. Lett.105(26), 263604 (2010).
[CrossRef] [PubMed]

Chen, Z.

N. K. Efremdis, P. Zhang, Z. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, “Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. A81(5), 053817 (2010).
[CrossRef]

Christodoulides, D. N.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A87(2), 022303 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the Correlation and Anticorrelation behavior of Path-entangled Photons in Glauber-Fock Oscillator Lattices,” Phys. Rev. A85(1), 013848 (2012).
[CrossRef]

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, P. Aleahmad, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of Bloch-like revivals in semi-infinite Glauber-Fock photonic lattices,” Opt. Lett.37(18), 3801–3803 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

N. K. Efremdis, P. Zhang, Z. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, “Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. A81(5), 053817 (2010).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35(23), 4045–4047 (2010).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35(23), 4045–4047 (2010).
[CrossRef] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett.100(1), 013906 (2008).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Dattoli, G.

G. Dattoli, A. Torre, S. Lorenzzutta, and G. Maino, “Theory of generalized Bessel functions II,” Nuovo Cim.106(1), 21–51 (1991).
[CrossRef]

G. Dattoli, L. Giannessi, L. Mezi, and A. Torre, “Theory of generalized Bessel functions,” Nuovo Cim.105(3), 327–348 (1990).
[CrossRef]

Dreisow, F.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, “Second-order coupling in femtosecond-laser-written waveguide arrays,” Opt. Lett.33(22), 2689–2691 (2008).
[CrossRef] [PubMed]

Efremdis, N. K.

N. K. Efremdis, P. Zhang, Z. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, “Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. A81(5), 053817 (2010).
[CrossRef]

Efremidis, N. K.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35(23), 4045–4047 (2010).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett.35(23), 4045–4047 (2010).
[CrossRef] [PubMed]

Giannessi, L.

G. Dattoli, L. Giannessi, L. Mezi, and A. Torre, “Theory of generalized Bessel functions,” Nuovo Cim.105(3), 327–348 (1990).
[CrossRef]

Gutiérrez-Vega, J. C.

Heinrich, M.

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, “Second-order coupling in femtosecond-laser-written waveguide arrays,” Opt. Lett.33(22), 2689–2691 (2008).
[CrossRef] [PubMed]

Ismail, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Jones, A. L.

Kay, A.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

Keil, R.

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A87(2), 022303 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the Correlation and Anticorrelation behavior of Path-entangled Photons in Glauber-Fock Oscillator Lattices,” Phys. Rev. A85(1), 013848 (2012).
[CrossRef]

R. Keil, A. Perez-Leija, P. Aleahmad, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of Bloch-like revivals in semi-infinite Glauber-Fock photonic lattices,” Opt. Lett.37(18), 3801–3803 (2012).
[CrossRef] [PubMed]

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

Kip, D.

N. K. Efremdis, P. Zhang, Z. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, “Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. A81(5), 053817 (2010).
[CrossRef]

Kwek, L. C.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

Lahini, Y.

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch Oscillations of Path-Entangled Photons,” Phys. Rev. Lett.105(26), 263604 (2010).
[CrossRef] [PubMed]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett.100(1), 013906 (2008).
[CrossRef] [PubMed]

Lederer, F.

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Long-range interaction in waveguide lattices,” Phys. Rev. A77(4), 043804 (2008).
[CrossRef]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual Observation of Zener Tunneling,” Phys. Rev. Lett.96(2), 023901 (2006).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Lobino, M.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Longhi, S.

Lorenzzutta, S.

G. Dattoli, A. Torre, S. Lorenzzutta, and G. Maino, “Theory of generalized Bessel functions II,” Nuovo Cim.106(1), 21–51 (1991).
[CrossRef]

Maino, G.

G. Dattoli, A. Torre, S. Lorenzzutta, and G. Maino, “Theory of generalized Bessel functions II,” Nuovo Cim.106(1), 21–51 (1991).
[CrossRef]

Matsuda, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Matthews, J. C. F.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Mezi, L.

G. Dattoli, L. Giannessi, L. Mezi, and A. Torre, “Theory of generalized Bessel functions,” Nuovo Cim.105(3), 327–348 (1990).
[CrossRef]

Michaelis, D.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual Observation of Zener Tunneling,” Phys. Rev. Lett.96(2), 023901 (2006).
[CrossRef] [PubMed]

Morandotti, R.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett.100(1), 013906 (2008).
[CrossRef] [PubMed]

Moya-Cessa, H.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A87(2), 022303 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the Correlation and Anticorrelation behavior of Path-entangled Photons in Glauber-Fock Oscillator Lattices,” Phys. Rev. A85(1), 013848 (2012).
[CrossRef]

R. Keil, A. Perez-Leija, P. Aleahmad, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of Bloch-like revivals in semi-infinite Glauber-Fock photonic lattices,” Opt. Lett.37(18), 3801–3803 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

Nikolopoulos, G. M.

Nolte, S.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

R. Keil, A. Perez-Leija, P. Aleahmad, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of Bloch-like revivals in semi-infinite Glauber-Fock photonic lattices,” Opt. Lett.37(18), 3801–3803 (2012).
[CrossRef] [PubMed]

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Long-range interaction in waveguide lattices,” Phys. Rev. A77(4), 043804 (2008).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, “Second-order coupling in femtosecond-laser-written waveguide arrays,” Opt. Lett.33(22), 2689–2691 (2008).
[CrossRef] [PubMed]

OBrien, J. L.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Perez-Leija, A.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A87(2), 022303 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the Correlation and Anticorrelation behavior of Path-entangled Photons in Glauber-Fock Oscillator Lattices,” Phys. Rev. A85(1), 013848 (2012).
[CrossRef]

R. Keil, A. Perez-Leija, P. Aleahmad, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of Bloch-like revivals in semi-infinite Glauber-Fock photonic lattices,” Opt. Lett.37(18), 3801–3803 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

Pertsch, T.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, “Second-order coupling in femtosecond-laser-written waveguide arrays,” Opt. Lett.33(22), 2689–2691 (2008).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Long-range interaction in waveguide lattices,” Phys. Rev. A77(4), 043804 (2008).
[CrossRef]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual Observation of Zener Tunneling,” Phys. Rev. Lett.96(2), 023901 (2006).
[CrossRef] [PubMed]

Peruzzo, A.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Peschel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual Observation of Zener Tunneling,” Phys. Rev. Lett.96(2), 023901 (2006).
[CrossRef] [PubMed]

Politi, A.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Poulios, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Pozzi, F.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett.100(1), 013906 (2008).
[CrossRef] [PubMed]

Rai, A.

A. Rai and G. S. Agarwal, “Possibility of coherent phenomena such as Bloch oscillations with single photons via W states,” Phys. Rev. A79(5), 053849 (2009).
[CrossRef]

Rodríguez-Lara, B. M.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

Ruter, C. E.

N. K. Efremdis, P. Zhang, Z. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, “Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. A81(5), 053817 (2010).
[CrossRef]

Silberberg, Y.

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch Oscillations of Path-Entangled Photons,” Phys. Rev. Lett.105(26), 263604 (2010).
[CrossRef] [PubMed]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett.100(1), 013906 (2008).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Sorel, M.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett.100(1), 013906 (2008).
[CrossRef] [PubMed]

Streppel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual Observation of Zener Tunneling,” Phys. Rev. Lett.96(2), 023901 (2006).
[CrossRef] [PubMed]

Szameit, A.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A87(2), 022303 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the Correlation and Anticorrelation behavior of Path-entangled Photons in Glauber-Fock Oscillator Lattices,” Phys. Rev. A85(1), 013848 (2012).
[CrossRef]

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, P. Aleahmad, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Observation of Bloch-like revivals in semi-infinite Glauber-Fock photonic lattices,” Opt. Lett.37(18), 3801–3803 (2012).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Long-range interaction in waveguide lattices,” Phys. Rev. A77(4), 043804 (2008).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, “Second-order coupling in femtosecond-laser-written waveguide arrays,” Opt. Lett.33(22), 2689–2691 (2008).
[CrossRef] [PubMed]

Thompson, M. G.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Torre, A.

G. Dattoli, A. Torre, S. Lorenzzutta, and G. Maino, “Theory of generalized Bessel functions II,” Nuovo Cim.106(1), 21–51 (1991).
[CrossRef]

G. Dattoli, L. Giannessi, L. Mezi, and A. Torre, “Theory of generalized Bessel functions,” Nuovo Cim.105(3), 327–348 (1990).
[CrossRef]

Trompeter, H.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual Observation of Zener Tunneling,” Phys. Rev. Lett.96(2), 023901 (2006).
[CrossRef] [PubMed]

Tünnermann, A.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Long-range interaction in waveguide lattices,” Phys. Rev. A77(4), 043804 (2008).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, and A. Tünnermann, “Second-order coupling in femtosecond-laser-written waveguide arrays,” Opt. Lett.33(22), 2689–2691 (2008).
[CrossRef] [PubMed]

Tzortzakis, S.

Wörhoff, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Zeuner, J. M.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

Zhang, P.

N. K. Efremdis, P. Zhang, Z. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, “Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. A81(5), 053817 (2010).
[CrossRef]

Zhou, X. Q.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424(6950), 817–823 (2003).
[CrossRef] [PubMed]

Nuovo Cim.

G. Dattoli, L. Giannessi, L. Mezi, and A. Torre, “Theory of generalized Bessel functions,” Nuovo Cim.105(3), 327–348 (1990).
[CrossRef]

G. Dattoli, A. Torre, S. Lorenzzutta, and G. Maino, “Theory of generalized Bessel functions II,” Nuovo Cim.106(1), 21–51 (1991).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L. C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. N. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A87(1), 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A87(2), 022303 (2013).
[CrossRef]

A. Rai and G. S. Agarwal, “Possibility of coherent phenomena such as Bloch oscillations with single photons via W states,” Phys. Rev. A79(5), 053849 (2009).
[CrossRef]

A. Perez-Leija, R. Keil, A. Szameit, A. F. Abouraddy, H. Moya-Cessa, and D. N. Christodoulides, “Tailoring the Correlation and Anticorrelation behavior of Path-entangled Photons in Glauber-Fock Oscillator Lattices,” Phys. Rev. A85(1), 013848 (2012).
[CrossRef]

A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Long-range interaction in waveguide lattices,” Phys. Rev. A77(4), 043804 (2008).
[CrossRef]

N. K. Efremdis, P. Zhang, Z. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, “Wave propagation in waveguide arrays with alternating positive and negative couplings,” Phys. Rev. A81(5), 053817 (2010).
[CrossRef]

Phys. Rev. Lett.

J. M. Zeuner, N. K. Efremidis, R. Keil, F. Dreisow, D. N. Christodoulides, A. Tünnermann, S. Nolte, and A. Szameit, “Optical Analogues for massless Dirac particles and conical diffraction in one dimension,” Phys. Rev. Lett.109(2), 023602 (2012).
[CrossRef] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson Localization and Nonlinearity in One-Dimensional Disordered Photonic Lattices,” Phys. Rev. Lett.100(1), 013906 (2008).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch Oscillations of Path-Entangled Photons,” Phys. Rev. Lett.105(26), 263604 (2010).
[CrossRef] [PubMed]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, “Visual Observation of Zener Tunneling,” Phys. Rev. Lett.96(2), 023901 (2006).
[CrossRef] [PubMed]

R. Keil, A. Perez-Leija, F. Dreisow, M. Heinrich, H. Moya-Cessa, S. Nolte, D. N. Christodoulides, and A. Szameit, “Classical Analogue of Displaced Fock States and Quantum Correlations in Glauber-Fock Photonic Lattices,” Phys. Rev. Lett.107(10), 103601 (2011).
[CrossRef] [PubMed]

Science

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X. Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum Walks of Correlated Photons,” Science329(5998), 1500–1503 (2010).
[CrossRef] [PubMed]

Other

J. C. F. Matthews, K. Poulios, J. D. A. Meinecke, A. Politi, A. Peruzzo, N. Ismail, K. Wörhoff, M. G. Thompson, and J. L. O'Brien, “Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions,” Preprint: arXiv:1106.1166.

J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (Roberts, 2005).

H. Moya-Cessa and F. Soto-Eguibar, Differential Equations: An Operational Approach (Rinton Press, 2011).

C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge, 2005).

W. H. Louisell, Quantum and Statistical Properties of Radiation (Wiley, 1973).

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Figures (4)

Fig. 1
Fig. 1

Transverse view of an array of evanescently coupled single mode waveguides. κ 1 is the coupling strength between nearest neighbors whereas κ 2 represents the couplings between next-nearest neighbors.

Fig. 2
Fig. 2

(a) and (c) depict the intensity evolution of the initial fields ψ( x,0 )=exp( x 2 / 2 σ 2 ) J 3 ( αx ) and ψ( x,0 )=exp( x 2 / 2 σ 2 ) J 6 ( αx ) , respectively. The parameters used are α=1 and σ= 10 3 . (b) and (d) show the corresponding initial field profile.

Fig. 3
Fig. 3

Theoretical comparison of light propagation through free space for the initial field profile ψ( x,0 )=exp( x 2 / 2 σ 2 ) J 0 ( αx ) (a-c), and in a periodic photonic lattice of 30 elements, under a single site excitation (d-f). Figs. (a, d) depict the initial field distributions, (b, e) the normalized intensity evolution, and (c, f) the intensity profiles at the output. The parameters used for the paraxial beams are α=1 and σ= 10 3 . For the waveguide array we assumed coupling coefficients κ 1 =1 c m 1 and κ 2 =0.1 c m 1 .

Fig. 4
Fig. 4

(a) Intensity propagation of the field ψ( x,0 )=exp( x 2 / 2 σ 2 ) J 0 ( αx ) and (b) the absolute square of the Gaussian envelope exp( x 2 / 2 σ 2 ) , the parameters used are the same as in Fig. (3). In this case, we found that FWHM=3mm , whereas l=3.3cm .

Equations (13)

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

i d E m dZ + κ 1 ( E m+1 + E m1 )+ κ 2 ( E m+2 + E m2 )=0,
E m ( Z )= l= i ml J m2l ( 2 κ 1 Z ) J l ( 2 κ 2 Z ) ,
E m ( Z )= i m J m ( 2 κ 1 Z,2 κ 2 Z;i ).
J m ( x,y;1 )= 1 2π π π exp[ i( xsin( ϕ )+ysin( 2ϕ )mϕ ) ] dϕ,
2m J m ( x,y;r )=x[ J m1 ( x,y;r )+ J m+1 ( x,y;r )]+2y( rJ m2 ( x,y;r )+ 1 r J m2 ( x,y;r ) ),
T(x,y;r,t) = m= t m J m ( x,y; r ) =exp( x 2 ( t 1 t )+ y 2 ( r t 2 1 r t 2 ) ).
i ψ ξ = 1 2 2 ψ s 2 ,
ψ( s,ξ )= F( wu )G( u )exp( i ξ 2 w 2 )exp( isw ) dudw.
ψ( s,ξ )=exp( g 1 s 2 i g 2 ) F( v )exp( ( i ξ 2 + g 3 ) v 2 )exp( isv exp( i2 g 2 ) )dv,
ψ( s,ξ )= 1 2π exp( g 1 ( ξ ) s 2 i g 2 ( ξ ) ) π π exp( inϕ+iAsin( ϕ )+iB sin 2 ( ϕ ) ) dϕ,
ψ( s,ξ )=exp( g 1 ( ξ ) s 2 i( g 2 ( ξ ) B 2 ) ) m= ( i ) m J n+2m ( A ) J m ( B/2 ) .
exp( iξ p ^ 2 2 )exp( isv )= k=0 ( iξ /2 ) k k! ( i s ) 2k exp( isv )=exp( iξ v 2 2 )exp( isv )
ψ( s,ξ )=exp( g 1 s 2 i g 2 ) F( v )exp( ( i ξ 2 + g 3 ) v 2 )exp( isv exp( i2 g 2 ) )dv.

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