Abstract

We address two closely related problems: diffraction management and soliton dynamics in parity-time ( T) symmetric lattices with a quadratic frequency modulation. The normal, anomalous, or zero diffraction is possible for narrow beams with a broad band of spatial frequencies. The frequency band of nondiffraction beams can be enlarged by increasing the chirp rate of lattices. Counter-intuitively, the gain-loss component plays the same role as the real part of lattice on the suppression of diffraction, which leads to an effective reduction of critical lattice depth for nondiffraction beams. Additionally, we reveal the existence of a novel type of “bright” solitons in defocusing Kerr media modulated by chirped T lattices. We also demonstrate that lattice chirp can be utilized to suppress the instability of solitons. Our results expand the concept of T symmetry in both linear and nonlinear regimes, and may find interesting optical applications.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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  35. J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).
  36. H. Wang, S. Shi, X. Ren, X. Zhu, B. A. Malomed, D. Mihalache, and Y. He, “Two-dimensional solitons in triangular photonic lattices with parity-time symmetry,” Opt. Commun. 313, 139–145 (2015).
  37. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton control in chirped photonic lattices,” J. Opt. Soc. Am. B 22(7), 1356–1359 (2005).
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2015 (1)

H. Wang, S. Shi, X. Ren, X. Zhu, B. A. Malomed, D. Mihalache, and Y. He, “Two-dimensional solitons in triangular photonic lattices with parity-time symmetry,” Opt. Commun. 313, 139–145 (2015).

2014 (8)

J. Yang, “Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials,” Opt. Lett. 39(19), 5547–5550 (2014).
[Crossref] [PubMed]

J. Yang, “Partially PT symmetric optical potentials with all-real spectra and soliton families in multidimensions,” Opt. Lett. 39(5), 1133–1136 (2014).
[Crossref] [PubMed]

C. P. Jisha, L. Devassy, A. Alberucci, and V. C. Kuriakose, “Influence of the imaginary component of the photonic potential on the properties of solitons in PT-symmetric systems,” Phys. Rev. A 90, 043855 (2014).
[Crossref]

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89, 013812 (2014).
[Crossref]

C. Huang, F. Ye, Y. V. Kartashov, B. A. Malomed, and X. Chen, “PT symmetry in optics beyond the paraxial approximation,” Opt. Lett. 39(18), 5443–5446 (2014).
[Crossref]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity,” Opt. Lett. 39(19), 5641–5644 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).

2013 (3)

A. S. Rodrigues, K. Li, V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and C. M. Bender, “PT-symmetric double-well potentials revisited: Bifurcations, stability and dynamics,” Rom. Rep. Phys 65, 5–26 (2013).

R. Li, P. Li, and L. Li, “Asymmetric optical amplifier based on parity-time symmetry,” Proc. Romanian Acad. A 14, 121–126 (2013).

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

2012 (4)

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1C2), 1–79 (2012).
[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).
[Crossref]

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[Crossref]

2011 (4)

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).
[Crossref]

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Stability of solitons in PT-symmetric nonlinear potentials,” EPL-Europhys. Lett. 96(6), 064003 (2011).
[Crossref]

Z. Shi, X. Jiang, X. Zhu, and H. Li, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[Crossref]

H. Wang and J. Wang, “Defect solitons in parity-time periodic potentials,” Opt. Express 19(5), 4030–4035 (2011).
[Crossref] [PubMed]

2010 (2)

K. Zhou, Z. Guo, J. Wang, and S. Liu, “Defect modes in defective parity-time symmetric periodic complex potentials,” Opt. Lett. 35(17), 2928–2930 (2010).
[Crossref] [PubMed]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

2009 (1)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

2008 (3)

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[Crossref] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (2)

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of dynamic localization in periodically curved waveguide arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[Crossref]

2005 (3)

2002 (2)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[Crossref]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[Crossref] [PubMed]

1999 (1)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

1998 (1)

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

Abdullaev, F. K.

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).
[Crossref]

Achilleos, V.

A. S. Rodrigues, K. Li, V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and C. M. Bender, “PT-symmetric double-well potentials revisited: Bifurcations, stability and dynamics,” Rom. Rep. Phys 65, 5–26 (2013).

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Alberucci, A.

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89, 013812 (2014).
[Crossref]

C. P. Jisha, L. Devassy, A. Alberucci, and V. C. Kuriakose, “Influence of the imaginary component of the photonic potential on the properties of solitons in PT-symmetric systems,” Phys. Rev. A 90, 043855 (2014).
[Crossref]

Almeida, V. R.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Assanto, G.

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89, 013812 (2014).
[Crossref]

Bender, C. M.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

A. S. Rodrigues, K. Li, V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and C. M. Bender, “PT-symmetric double-well potentials revisited: Bifurcations, stability and dynamics,” Rom. Rep. Phys 65, 5–26 (2013).

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[Crossref]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

Bersch, C.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Boettcher, S.

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Brazhnyi, V. A.

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89, 013812 (2014).
[Crossref]

Brody, D. C.

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[Crossref]

Chen, G.

J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).

Chen, W.

J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).

Chen, X.

Chen, Y.-F.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Chen, Z.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[Crossref]

Christodoulides, D. N.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[Crossref] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref] [PubMed]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref] [PubMed]

Cianci, E.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of dynamic localization in periodically curved waveguide arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Devassy, L.

C. P. Jisha, L. Devassy, A. Alberucci, and V. C. Kuriakose, “Influence of the imaginary component of the photonic potential on the properties of solitons in PT-symmetric systems,” Phys. Rev. A 90, 043855 (2014).
[Crossref]

Dreisow, F.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[Crossref] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref] [PubMed]

Fan, S.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Fegadolli, W. S.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Feng, L.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of dynamic localization in periodically curved waveguide arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Frantzeskakis, D. J.

A. S. Rodrigues, K. Li, V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and C. M. Bender, “PT-symmetric double-well potentials revisited: Bifurcations, stability and dynamics,” Rom. Rep. Phys 65, 5–26 (2013).

Garanovich, I. L.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1C2), 1–79 (2012).
[Crossref]

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[Crossref]

Ge, L.

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).
[Crossref]

Gianfreda, M.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Guo, A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Guo, Z.

He, Y.

H. Wang, S. Shi, X. Ren, X. Zhu, B. A. Malomed, D. Mihalache, and Y. He, “Two-dimensional solitons in triangular photonic lattices with parity-time symmetry,” Opt. Commun. 313, 139–145 (2015).

J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[Crossref]

Heinrich, M.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

Huang, C.

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref] [PubMed]

Jiang, X.

Z. Shi, X. Jiang, X. Zhu, and H. Li, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[Crossref]

Jisha, C. P.

C. P. Jisha, L. Devassy, A. Alberucci, and V. C. Kuriakose, “Influence of the imaginary component of the photonic potential on the properties of solitons in PT-symmetric systems,” Phys. Rev. A 90, 043855 (2014).
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C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89, 013812 (2014).
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Jones, H. F.

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
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Kartashov, Y.

Kartashov, Y. V.

C. Huang, F. Ye, Y. V. Kartashov, B. A. Malomed, and X. Chen, “PT symmetry in optics beyond the paraxial approximation,” Opt. Lett. 39(18), 5443–5446 (2014).
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Y. V. Kartashov, B. A. Malomed, and L. Torner, “Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity,” Opt. Lett. 39(19), 5641–5644 (2014).
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D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Stability of solitons in PT-symmetric nonlinear potentials,” EPL-Europhys. Lett. 96(6), 064003 (2011).
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F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton control in chirped photonic lattices,” J. Opt. Soc. Am. B 22(7), 1356–1359 (2005).
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Kevrekidis, P. G.

A. S. Rodrigues, K. Li, V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and C. M. Bender, “PT-symmetric double-well potentials revisited: Bifurcations, stability and dynamics,” Rom. Rep. Phys 65, 5–26 (2013).

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Kivshar, Y. S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1C2), 1–79 (2012).
[Crossref]

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[Crossref]

Konotop, V. V.

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).
[Crossref]

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Stability of solitons in PT-symmetric nonlinear potentials,” EPL-Europhys. Lett. 96(6), 064003 (2011).
[Crossref]

Krolikowski, W.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

Kuriakose, V. C.

C. P. Jisha, L. Devassy, A. Alberucci, and V. C. Kuriakose, “Influence of the imaginary component of the photonic potential on the properties of solitons in PT-symmetric systems,” Phys. Rev. A 90, 043855 (2014).
[Crossref]

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of dynamic localization in periodically curved waveguide arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Lei, F.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Li, H.

Z. Shi, X. Jiang, X. Zhu, and H. Li, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[Crossref]

Li, K.

A. S. Rodrigues, K. Li, V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and C. M. Bender, “PT-symmetric double-well potentials revisited: Bifurcations, stability and dynamics,” Rom. Rep. Phys 65, 5–26 (2013).

Li, L.

R. Li, P. Li, and L. Li, “Asymmetric optical amplifier based on parity-time symmetry,” Proc. Romanian Acad. A 14, 121–126 (2013).

Li, P.

R. Li, P. Li, and L. Li, “Asymmetric optical amplifier based on parity-time symmetry,” Proc. Romanian Acad. A 14, 121–126 (2013).

Li, R.

R. Li, P. Li, and L. Li, “Asymmetric optical amplifier based on parity-time symmetry,” Proc. Romanian Acad. A 14, 121–126 (2013).

Liu, J.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[Crossref]

Liu, S.

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of dynamic localization in periodically curved waveguide arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Long, G. L.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Longhi, S.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1C2), 1–79 (2012).
[Crossref]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of dynamic localization in periodically curved waveguide arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Lu, M.-H.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Lv, J.

J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[Crossref] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref] [PubMed]

Malomed, B. A.

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of dynamic localization in periodically curved waveguide arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref] [PubMed]

Mihalache, D.

H. Wang, S. Shi, X. Ren, X. Zhu, B. A. Malomed, D. Mihalache, and Y. He, “Two-dimensional solitons in triangular photonic lattices with parity-time symmetry,” Opt. Commun. 313, 139–145 (2015).

J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[Crossref]

Min, Y.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref] [PubMed]

Minovich, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

Miri, M.-A.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Mitchell, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

Monifi, F.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Morandotti, R.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[Crossref] [PubMed]

Neshev, D.

Neshev, D. N.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

Nixon, S.

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).
[Crossref]

Nolte, S.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

Nori, F.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Oliveira, J. E. B.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Onishchukov, G.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Ozdemir, S. K.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Peng, B.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Pertsch, T.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Peschel, U.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of dynamic localization in periodically curved waveguide arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Regensburger, A.

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Ren, X.

H. Wang, S. Shi, X. Ren, X. Zhu, B. A. Malomed, D. Mihalache, and Y. He, “Two-dimensional solitons in triangular photonic lattices with parity-time symmetry,” Opt. Commun. 313, 139–145 (2015).

Rodrigues, A. S.

A. S. Rodrigues, K. Li, V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and C. M. Bender, “PT-symmetric double-well potentials revisited: Bifurcations, stability and dynamics,” Rom. Rep. Phys 65, 5–26 (2013).

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Salamo, G. J.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Scherer, A.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Shi, S.

H. Wang, S. Shi, X. Ren, X. Zhu, B. A. Malomed, D. Mihalache, and Y. He, “Two-dimensional solitons in triangular photonic lattices with parity-time symmetry,” Opt. Commun. 313, 139–145 (2015).

Shi, Z.

Z. Shi, X. Jiang, X. Zhu, and H. Li, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[Crossref]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

Siviloglou, G. A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Sohler, W.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref] [PubMed]

Stegeman, G. I.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref] [PubMed]

Su, Z.

J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).

Sukhorukov, A. A.

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1C2), 1–79 (2012).
[Crossref]

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[Crossref]

Szameit, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tuennermann, and Y. S. Kivshar, “Diffraction control in periodically curved two-dimensional waveguide arrays,” Opt. Express 15(15), 9737–9747 (2007).
[Crossref] [PubMed]

Torner, L.

Tuennermann, A.

Tünnermann, A.

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

Volatier-Ravat, M.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Vysloukh, V.

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton control in chirped photonic lattices,” J. Opt. Soc. Am. B 22(7), 1356–1359 (2005).
[Crossref]

Wang, H.

H. Wang, S. Shi, X. Ren, X. Zhu, B. A. Malomed, D. Mihalache, and Y. He, “Two-dimensional solitons in triangular photonic lattices with parity-time symmetry,” Opt. Commun. 313, 139–145 (2015).

H. Wang and J. Wang, “Defect solitons in parity-time periodic potentials,” Opt. Express 19(5), 4030–4035 (2011).
[Crossref] [PubMed]

Wang, J.

Xie, J.

J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).

Xu, Y.-L.

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Yang, J.

Yang, L.

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Ye, F.

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Zezyulin, D. A.

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).
[Crossref]

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Stability of solitons in PT-symmetric nonlinear potentials,” EPL-Europhys. Lett. 96(6), 064003 (2011).
[Crossref]

Zhou, K.

Zhu, X.

H. Wang, S. Shi, X. Ren, X. Zhu, B. A. Malomed, D. Mihalache, and Y. He, “Two-dimensional solitons in triangular photonic lattices with parity-time symmetry,” Opt. Commun. 313, 139–145 (2015).

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[Crossref]

Z. Shi, X. Jiang, X. Zhu, and H. Li, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[Crossref]

EPL-Europhys. Lett. (1)

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Stability of solitons in PT-symmetric nonlinear potentials,” EPL-Europhys. Lett. 96(6), 064003 (2011).
[Crossref]

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

Nat. Mater. (1)

L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12, 108–113 (2013).
[Crossref]

Nat. Phys. (2)

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010).
[Crossref]

Nature (1)

A. Regensburger, C. Bersch, M.-A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488, 167–171 (2012).
[Crossref] [PubMed]

Opt. Commun. (2)

J. Xie, Z. Su, W. Chen, G. Chen, J. Lv, D. Mihalache, and Y. He, “Defect solitons in two-dimensional photonic lattices with parity-time symmetry,” Opt. Commun. 335, 146–152 (2014).

H. Wang, S. Shi, X. Ren, X. Zhu, B. A. Malomed, D. Mihalache, and Y. He, “Two-dimensional solitons in triangular photonic lattices with parity-time symmetry,” Opt. Commun. 313, 139–145 (2015).

Opt. Express (3)

Opt. Lett. (5)

Phys. Rep. (1)

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. 518(1C2), 1–79 (2012).
[Crossref]

Phys. Rev. A (8)

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012).
[Crossref]

C. P. Jisha, L. Devassy, A. Alberucci, and V. C. Kuriakose, “Influence of the imaginary component of the photonic potential on the properties of solitons in PT-symmetric systems,” Phys. Rev. A 90, 043855 (2014).
[Crossref]

C. P. Jisha, A. Alberucci, V. A. Brazhnyi, and G. Assanto, “Nonlocal gap solitons in PT-symmetric periodic potentials with defocusing nonlinearity,” Phys. Rev. A 89, 013812 (2014).
[Crossref]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).
[Crossref]

Z. Shi, X. Jiang, X. Zhu, and H. Li, “Bright spatial solitons in defocusing Kerr media with PT-symmetric potentials,” Phys. Rev. A 84, 053855 (2011).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Dynamics of surface solitons at the edge of chirped optical lattices,” Phys. Rev. A 76, 013831 (2007).
[Crossref]

A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78, 031801 (2008).
[Crossref]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).
[Crossref]

Phys. Rev. E (1)

I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, “Broadband diffraction management and self-collimation of white light in photonic lattices,” Phys. Rev. E 74, 066609 (2006).
[Crossref]

Phys. Rev. Lett. (10)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759 (1999).
[Crossref]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, “Observation of dynamic localization in periodically curved waveguide arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85, 1863–1866 (2000).
[Crossref] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80, 5243–5246 (1998).
[Crossref]

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002).
[Crossref]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).
[Crossref] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
[Crossref] [PubMed]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009).
[Crossref] [PubMed]

Proc. Romanian Acad. A (1)

R. Li, P. Li, and L. Li, “Asymmetric optical amplifier based on parity-time symmetry,” Proc. Romanian Acad. A 14, 121–126 (2013).

Rom. Rep. Phys (1)

A. S. Rodrigues, K. Li, V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, and C. M. Bender, “PT-symmetric double-well potentials revisited: Bifurcations, stability and dynamics,” Rom. Rep. Phys 65, 5–26 (2013).

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Figures (5)

Fig. 1
Fig. 1 (a) Spatial spectra of chirped T lattices. Dispersion relation at α = 0.1 (b) and 0.3 (c). (d) Critical lattice depth versus lattice frequency. Threshold depth at Ω = 2 are marked by circles. (e) Critical lattice depth versus k at W0 = 0.5,Ω = 1.8, and α = 0.3. Ω = 2 except for (d, e). In all panels, V0 = 1, solid curves stand for W0 = 0.5 and dashed ones denote W0 = 0.
Fig. 2
Fig. 2 Beam propagations in linear media. (a) Unchirped T lattice with α = 0. (b) Chirped T lattice with α = 0.3. (c) Chirped real lattice with p = 4.65, (d) Chirped real lattice with p = 3.1. V0 = 1, W0 = 0.5, p = 2.1 in (a, b) and V0 = 1, W0 = 0, α = 0.3 in (c, d). In all panels Ω = 2.
Fig. 3
Fig. 3 (a) U − b curves of solitons in lattices with α = 0.3,W0 = 0.5 (upper) and 0 (lower). (b) Profiles of solitons marked in (a). (c) Propagation constant cutoff versus lattice chirp rate. (d) Dependence of soliton width on power. (e, f) Propagation examples of solitons at b = 0.53 and 4 marked in (c). White noises are added into the initial inputs. In all panels p = 2, V0 = 1, Ω = 2. W0 = 0.5 except for (a). Focusing medium.
Fig. 4
Fig. 4 (a) Ub curves of solitons. Profiles of solitons at b = 0.1 and 0.4 in lattices with α = 0 (b) and 0.3 (c). (d) Dependence of soliton width on power. In all panels p = 2, V0 = 1, W0 = 0.5, Ω = 2. Defocusing media.
Fig. 5
Fig. 5 (a) Instability growth rate versus propagation constant. (b) Unstable propagation of soliton at b = 0.1 in a unchirped T lattice. Stable propagation of solitons at b = 0.1 (c) and 0.5 (d) in a chirped lattice with α = 0.3. In all panels p = 2, V0 = 1, W0 = 0.5, Ω = 2. Defocusing media.

Equations (5)

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

i q z = 1 2 2 q x 2 σ | q | 2 q p R ( x ) q ,
R k ( k ) = 1 2 ( V 0 + W 0 ) ( 3 α Ω ) 1 / 3 Ai [ ( 3 α Ω ) 1 / 3 ( Ω k ) ] ,
i d q k d z = 1 2 k 2 q k p R k ( k k ) q k ( k ) d k ,
b ( k ) = 1 2 k 2 + 2 p R k ( 0 ) + 2 p R k ( 2 k ) .
i [ i p W 0 W i σ Im ( w 2 ) L ^ σ Re ( w 2 ) L ^ + σ Re ( w 2 ) i p W 0 W + i σ Im ( w 2 ) ] [ u v ] = λ [ u v ] ,

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