Skip to main content
Log in

Counterpropagating optical solitons in \({\mathcal {PT}}\)-symmetric photonic lattices

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

We investigate numerically solitonic solutions for the system of two optical beams propagating in opposite directions in a parity-time (\({\mathcal {PT}}\)) symmetric photonic lattice by using modified Petviashvili’s method. Our system supports \({\mathcal {PT}}\)-symmetric fundamental solitons. We propagate such solitons and investigate their basic characteristics. We report symmetry breaking (or split-up) transition between counterpropagating beams in \({\mathcal {PT}}\)-symmetric photonic lattices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Abdullaev, F.K., Kartashov, Y.V., Konotop, V.V., Zezyulin, D.A.: Solitons in \({\cal {PT}}\)-symmetric nonlinear lattices. Phys. Rev. A 83, 041805 (2011)

    Article  ADS  Google Scholar 

  • Achilleos, V., Kevrekidis, P.G., Frantzeskakis, D.J., Carretero-González, R.: Dark solitons and vortices in \({\cal {PT}}\)-symmetric nonlinear media: from spontaneous symmetry breaking to nonlinear \({\cal PT}\)phase transitions. Phys. Rev. A 86, 013808 (2012)

    Article  ADS  Google Scholar 

  • Alexeeva, N.V., Barashenkov, I.V., Sukhorukov, A.A., Kivshar, Y.S.: Optical solitons in \({\cal {PT}}\)-symmetric nonlinear couplers with gain and loss. Phys. Rev. A 85, 063837 (2012)

    Article  ADS  Google Scholar 

  • Barashenkov, I.V., Suchkov, S.V., Sukhorukov, A.A., Dmitriev, S.V., Kivshar, Y.S.: Breathers in \({\cal {PT}}\)-symmetric optical couplers. Phys. Rev. A 86, 053809 (2012)

    Article  ADS  Google Scholar 

  • Bender, C.M., Boettcher, S.: Real spectra in non-Hermitian Hamiltonians having \({\cal {PT}}\) symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Bender, C.M.: Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947–1018 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  • Bender, C.M., Brody, D.C., Jones, H.F.: Complex extension of quantum mechanics. Phys. Rev. Lett. 89, 270401 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Guo, A., Salamo, G.J., Duchesne, D., Morandotti, R., Volatier-Ravat, M., Aimez, V., Siviloglou, G.A., Christodoulides, D.N.: Observation of \({\cal {PT}}\) symmetry-breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009)

    Article  ADS  Google Scholar 

  • He, Y., Zhu, X., Mihalache, D., Liu, J., Chen, Z.: Lattice solitons in \({\cal {PT}}\)-symmetric mixed linear-nonlinear optical lattices. Phys. Rev. A 85, 013831 (2012)

    Article  ADS  Google Scholar 

  • Jović, D., Prvanović, S., Jovanović, R., Petrović, M.: Gaussian-induced rotation in periodic photonic lattices. Opt. Lett. 32, 1857–1859 (2007)

    Article  ADS  Google Scholar 

  • Kivshar, Y.S., Agrawal, G.: Optical Solitons: From Fibers to Photonic Crystals. Academic, San Diego (2003)

    Google Scholar 

  • Makris, K.G., El-Ganainy, R., Christodoulides, D.N., Musslimani, Z.H.: Beam dynamics in \({\cal {PT}}\)-symmetric optical lattices. Phys. Rev. Lett. 100, 103904 (2008)

    Article  ADS  Google Scholar 

  • Makris, K.G., El-Ganainy, R., Christodoulides, D.N., Musslimani, Z.H.: \({\cal {PT}}\)-symmetric optical lattices. Phys. Rev. A 81, 063807 (2010)

    Article  ADS  Google Scholar 

  • Musslimani, Z.H., Makris, K.G., El-Ganainy, R., Christodoulides, D.N.: Optical solitons in \({\cal {PT}}\)-periodic potentials. Phys. Rev. Lett 100, 030402 (2008)

    Article  ADS  MATH  Google Scholar 

  • Nixon, S., Ge, L., Yang, J.: Stability analysis for solitons in \({\cal {PT}}\)-symmetric optical lattices. Phys. Rev. A 85, 023822 (2012)

    Article  ADS  Google Scholar 

  • Petrović, M., Jović, D., Belić, M., Schröder, J., Jander, Ph, Denz, C.: Two dimensional counterpropagating spatial solitons in photorefractive crystals. Phys. Rev. Lett. 95, 053901 (2005)

    Article  ADS  Google Scholar 

  • Petrović, M.S., Belić, M.R., Denz, C., Kivshar, YuS: Counterpropagating optical beams and solitons. Laser Photonics Rev. 5, 214–233 (2011)

    Article  Google Scholar 

  • Petviashvili, V.I.: Equation of an extraordinary soliton. Fizika Plazmy 2, 469–472 (1976a)

    ADS  Google Scholar 

  • Petviashvili, V.I.: Equation of an extraordinary soliton. Sov. J. Plasma Phys. 2, 257–258 (1976b)

    ADS  Google Scholar 

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

    Article  Google Scholar 

  • Shi, Z., Jiang, X., Zhu, X., Li, H.: Bright spatial solitons in defocusing Kerr media with \({\cal {PT}}\)-symmetric potentials. Phys. Rev. A 84, 053855 (2011)

    Article  ADS  Google Scholar 

  • Wimmer, M., Regensburger, A., Miri, M., Bersch, C., Christodoulides, D.N., Peschel, U.: Observation of optical solitons in \({\cal {PT}}\)-symmetric lattices. Nat. Commun. 6, 7782 (2015)

    Article  ADS  Google Scholar 

  • Zhong, W.P., Belić, M.R., Huang, T.: Two-dimensional accessible solitons in \({\cal {PT}}\)-symmetric potentials. Nonlinear Dyn. 70, 2027–2034 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work has been supported by the Ministry of Science of the Republic of Serbia under Projects OI 171033, 171006 and III 45016, and by the NPRP 6-021-1-005 Project of the Qatar National Research Fund (a member of Qatar Foundation).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Aleksandra Strinić.

Additional information

This article is part of the Topical Collection on Advances in the Science of Light.

Guest Edited by Jelena Radovanovic, Milutin Stepic, Mikhail Sumetsky, Mauro Pereira and Dragan Indjin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stojanović, S., Strinić, A. & Petrović, M. Counterpropagating optical solitons in \({\mathcal {PT}}\)-symmetric photonic lattices. Opt Quant Electron 48, 343 (2016). https://doi.org/10.1007/s11082-016-0605-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-016-0605-z

Keywords

Navigation