Advertisement

Spatial Solitons in Nonlinear Photonic Crystal Fibers

  • José R. Salgueiro
  • Albert Ferrando
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

This chapter aims to review the most relevant results on solitons in nonlinear solid-core photonic crystal fibers since their introduction about fifteen years ago. These include fundamental solitons and vortices, as well as vector systems of two fundamental, vortex or mixed components. Also other related systems as solitons in double-core photonic crystal fibers will be reviewed. The presentation will describe the mode families as well as their stability properties. The work is intended to be a comprehensive document on the field and provide a fast update to the reader as well as the necessary sources for a further detailed documentation.

Keywords

Photonic crystal fibers Spatial solitons Vortices Vector solitons Discrete symmetry Nonlinear modes 

Notes

Acknowledgements

This work was supported by the MINECO (Government of Spain) under Grants TEC2014-53727-C2-1-R and FIS2014-61984-EXP, as well as by Xunta de Galicia under grant GPC2015/019.

References

  1. 1.
    Akhmediev, N.N., Ankiewicz, A.: Solitons: Nonlinear Pulses and Beams. Chapman and Hall, Cornwall (1997)zbMATHGoogle Scholar
  2. 2.
    Baizakov, B.B., Malomed, B.A., Salerno, M.: Multidimensional solitons in periodic potentials. Europhys. Lett. 63(5), 642 (2003)ADSCrossRefzbMATHGoogle Scholar
  3. 3.
    Bennet, F., Farnell, J.: Waveguide arrays in selectively infiltrated photonic crystal fibres. Opt. Commun. 283(20), 4069–4073 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    Betlej, A., Suntsov, S., Makris, K.G., Jankovic, L., Christodoulides, D.N., Stegeman, G.I., Fini, J., Bise, R.T., DiGiovanni, D.J.: All-optical switching and multifrequency generation in a dual-core photonic crystal fiber. Opt. Lett. 31(10), 1480–1482 (2006)ADSCrossRefGoogle Scholar
  5. 5.
    Brtka, M., Gammal, A., Malomed, B.A.: Hidden vorticity in binary Bose-Einstein condensates. Phys. Rev. A 82, 053,610 (2010)Google Scholar
  6. 6.
    Chen, M.Y., Zhou, J.: Mode converter based on mode coupling in an asymmetric dual-core photonic crystal fibre. Abbreviation Title J. Opt. A: Pure Appl. Opt. 10(11), 115,304 (2008)Google Scholar
  7. 7.
    Christodoulides, D.N., Eugenieva, E.D.: Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays. Phys. Rev. Lett. 87(23), 233,901 (2001)CrossRefGoogle Scholar
  8. 8.
    Desyatnikov, A.S., Dennis, M.R., Ferrando, A.: All-optical discrete vortex switch. Phys. Rev. A 83, 063,822 (2011)Google Scholar
  9. 9.
    Diebel, F., Leykam, D., Boguslawski, M., Rose, P., Denz, C., Desyatnikov, A.S.: All-optical switching in optically induced nonlinear waveguide couplers. Appl. Phys. Lett. 104(26), 261,111 (2014)Google Scholar
  10. 10.
    Ferrando, A.: Discrete-symmetry vortices as angular Bloch modesloch modes. Phys. Rev. E 72(3), 036,612 (2005)Google Scholar
  11. 11.
    Ferrando, A., Silvestre, E., Andrés, P., Miret, J.J., Andrés, M.V.: Designing the properties of dispersion-flattened photonic crystal fibers. Opt. Express 9(13), 687 (2001)ADSCrossRefGoogle Scholar
  12. 12.
    Ferrando, A., Silvestre, E., Miret, J.J., Andrés, P.: Vector description of high-order modes in photonic crystal fibers. J. Opt. Soc. Am. 17, 1333–1340 (2000)ADSCrossRefGoogle Scholar
  13. 13.
    Ferrando, A., Silvestre, E., Miret, J.J., Andrés, P., Andrés, M.V.: Full-vector analysis of a realistic photonic crystal fiber. Opt. Lett. 24(5), 276 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    Ferrando, A., Zacarés, M., Andrés, P., Fernández de Córdoba, P., Monsoriu, J.A.: Nodal solitons and the nonlinear breaking of discrete symmetry. Opt. Express 13(4), 1072 (2005)ADSCrossRefGoogle Scholar
  15. 15.
    Ferrando, A., Zacarés, M., Fernández de Córdoba, P., Binosi, D., Monsoriu, J.A.: Spatial soliton formation in photonic crystal fibers. Opt. Express 11(5), 452–459 (2003)ADSCrossRefGoogle Scholar
  16. 16.
    Ferrando, A., Zacarés, M., Fernández de Córdoba, P., Binosi, D., Monsoriu, J.A.: Vortex solitons in photonic crystal fibers. Opt. Express 12(5), 817–822 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    Ferrando, A., Zacarés, M., García-March, M.A.: Vorticity cutoff in nonlinear photonic crystals. Phys. Rev. Lett. 95, 043,901 (2005)Google Scholar
  18. 18.
    Fleischer, J.W., Bartal, G., Cohen, O., Manela, O., Segev, M., Hudock, J., Christodoulides, D.N.: Observation of vortex-ring “discrete” solitons in 2D photonic lattices. Phys. Rev. Lett. 92, 123,904 (2004)Google Scholar
  19. 19.
    Fleischer, J.W., Segev, M., Efremidis, N.K., Christodoulides, D.N.: Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature 422(6928), 147–150 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    García-March, M.A., Ferrando, A., Zacarés, M., Vijande, J., Carr, L.D.: Angular pseudomomentum theory for the generalized nonlinear Schrödinger equation in discrete rotational symmetry media. Physica D 238(15), 1432–1438 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Gubeskys, A., Malomed, B.A.: Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices. Phys. Rev. A 76, 043,623 (2007)Google Scholar
  22. 22.
    Hamermesh, M.: Group Theory and its Application to Physical Problems. Addison-Wesley, Reading, Massachusetts (1964)zbMATHGoogle Scholar
  23. 23.
    Izdebskaya, Y.V., Rebling, J., Desyatnikov, A.S., Kivshar, Y.S.: Observation of vector solitons with hidden vorticity. Opt. Lett. 37(5), 767–769 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    Joannopoulos, J.D., Johnson, S.G., Winn, J.N., Meade, R.D.: Photonic Crystals: Molding the Flow of Light, 2nd edn. Princeton University Press, Princeton (2008)zbMATHGoogle Scholar
  25. 25.
    Kartashov, Y.V., Ferrando, A., Egorov, A.A., Torner, L.: Soliton topology versus discrete symmetry in optical lattices. Phys. Rev. Lett 95(12), 123,902 (2005)Google Scholar
  26. 26.
    Kim, H., Kim, J., Paek, U.C., Lee, B.H., Kim, K.T.: Tunable photonic crystal fiber coupler based on a side-polishing technique. Opt. Lett. 29(11), 1194–1196 (2004)ADSCrossRefGoogle Scholar
  27. 27.
    Kivshar, Y.S., Agrawal, G.P.: Optical Solitons: From Fibers to Photonic Crystals. Academic Press, San Diego (2003)Google Scholar
  28. 28.
    Knight, J.C.: Photonic crystal fibres. Nature 424, 847–851 (2003)ADSCrossRefGoogle Scholar
  29. 29.
    Lagsgaard, J., Bang, O., Bjarklev, A.: Photonic crystal fiber design for broadband directional coupling. Opt. Lett. 29(21), 2473–2475 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    Lederer, F., Stegeman, G.I., Christodoulides, D.N., Assanto, G., Segev, M., Silberberg, Y.: Discrete solitons in optics. Phys. Rep. 463(1–3), 1–126 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    Leykam, D., Malomed, B., Desyatnikov, A.S.: Composite vortices in nonlinear circular waveguide arrays. J. Opt. B: Quantum Semiclassical Opt. 15(4), 044,016 (2013)Google Scholar
  32. 32.
    Li, P., Zhao, J., Liu, S., Gan, X., Peng, T., Jiao, X.: Dynamic behaviors of optical vortices in dual-core photonic crystal fibers. Opt. Commun. 285(9), 2355–2359 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    Malmberg, J.N., Carlsson, A.H., Anderson, D., Lisak, M., Ostrovskaya, E.A., Kivshar, Y.S.: Vector solitons in (\(2+1\)) dimensions. Opt. Lett. 25(9), 643–645 (2000)Google Scholar
  34. 34.
    Malomed, B.A., Kevrekidis, P.G.: Discrete vortex solitons. Phys. Rev. E 64, 026,601 (2001)CrossRefGoogle Scholar
  35. 35.
    Minardi, S., Eilenberger, F., Kartashov, Y.V., Szameit, A., Röpke, U., Kobelke, J., Schuster, K., Bartelt, H., Nolte, S., Torner, L., Lederer, F., Tünnermann, A., Pertsch, T.: Three-dimensional light bullets in arrays of waveguides. Phys. Rev. Lett. 105(26), 263,901 (2010)Google Scholar
  36. 36.
    Mingaleev, S.F., Kivshar, Y.S., Sammut, R.A.: Long-range interaction and nonlinear localized modes in photonic crystal waveguides. Phys. Rev. E 62(4), 5777–5782 (2000)ADSCrossRefGoogle Scholar
  37. 37.
    Neshev, D.N., Alexander, T.J., Ostrovskaya, E.A., Kivshar, Y.S.: Observation of discrete vortex solitons in optically induced photonic lattices. Phys. Rev. Lett. 92(12), 123,903 (2004)Google Scholar
  38. 38.
    Ostrovskaya, E.A., Kivshar, Y.S.: Matter-wave gap vortices in optical lattices. Phys. Rev. Lett. 93, 160,405 (2004)Google Scholar
  39. 39.
    Pelinovsky, D.E.: Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations. Proc. R. Soc. Lond. Ser. A 461, 783–812 (2005)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Pelinovsky, D.E., Kivshar, Y.S.: Stability criterion for multicomponent solitary waves. Phys. Rev. E 62, 8668–8676 (2000)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Pelinovsky, D.E., Yang, J.: Internal oscillations and radiation damping vector solitons. Stud. Appl. Math. 105, 245–267 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Rosberg, C.R., Bennet, F.H., Neshev, D.N., Rasmussen, P.D., Bang, O., Krolikowski, W., Bjarklev, A., Kivshar, Y.S.: Tunable diffraction and self-defocusing in liquid-filled photonic crystal fibers. Opt. Express 15(19), 12145–12150 (2007)ADSCrossRefGoogle Scholar
  43. 43.
    Russell, P.: Photonic crystal fibers. Science 299, 358–362 (2003)ADSCrossRefGoogle Scholar
  44. 44.
    Russell, P.: Photonic crystal fibers: A historical account. IEEE LEOS Newsl. 21, 11–15 (2007)Google Scholar
  45. 45.
    Russell, P.S.: Photonic-crystal fibers. J. Lightwave Technol. 24(12), 4729–4749 (2006)ADSCrossRefGoogle Scholar
  46. 46.
    Saitoh, K., Sato, Y., Koshiba, M.: Coupling characteristics of dual-core photonic crystal fiber couplers. Opt. Express 11(24), 3188–3195 (2003)ADSCrossRefGoogle Scholar
  47. 47.
    Salgueiro, J.R.: Vector–vortex solitons in nonlinear photonic crystal fibers. J. Opt. 18(7), 074,004 (2016)Google Scholar
  48. 48.
    Salgueiro, J.R., Kivshar, Y.S.: Single- and double-vortex vector solitons in self-focusing nonlinear media. Phys. Rev. E 70, 056,613 (2004)Google Scholar
  49. 49.
    Salgueiro, J.R., Kivshar, Y.S.: Nonlinear dual-core photonic crystal fiber couplers. Opt. Lett. 30(14), 1858–1860 (2005)ADSCrossRefGoogle Scholar
  50. 50.
    Salgueiro, J.R., Kivshar, Y.S.: Optical vortex solitons and soliton clusters in photonic crystal fibres. Eur. Phys. J.-Spec. Top. 173, 281–288 (2009)CrossRefGoogle Scholar
  51. 51.
    Salgueiro, J.R., Kivshar, Y.S., Pelinovski, D.E., Simón, V., Michinel, H.: Spatial vector solitons in nonlinear photonic crystal fibers. Stud. Appl. Math. 115, 157–171 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Salgueiro, J.R., Michinel, H., Ferrando, A., Kivshar, Y.S.: Switching and instabilities of optical vortices in nonlinear dual-core photonic crystal fibre couplers. J. Eur. Opt. Soc. Rapid 1, 06,014 (2006)Google Scholar
  53. 53.
    Salgueiro, J.R., Olivieri, D., Michinel, H.: Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers. Opt. Quantum Electron. 39, 239–260 (2007)CrossRefGoogle Scholar
  54. 54.
    Salgueiro, J.R., Santos, F.: Nonlinear vortex modes in dual-core photonic crystal fiber couplers. J. Opt. Soc. Am. B 26(12), 2301–2307 (2009)ADSCrossRefGoogle Scholar
  55. 55.
    Szameit, A., Burghoff, J., Pertsch, T., Nolte, S., Tünnermann, A., Lederer, F.: Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica. Opt. Express 14(13), 6055 (2006)ADSCrossRefGoogle Scholar
  56. 56.
    Tombelaine, V., Labruyère, A., Kobelke, J., Schuster, K., Reichel, V., Leproux, P., Couderc, V., Jamier, R., Bartelt, H.: Nonlinear photonic crystal fiber with a structured multi-component glass core for four-wave mixing and supercontinuum generation. Opt. Express 17(18), 15392–15401 (2009)ADSCrossRefGoogle Scholar
  57. 57.
    Udem, T., Holzwarth, R., Hansch, T.W.: Optical frequency metrology. Nature 416(6877), 233–237 (2002)ADSCrossRefGoogle Scholar
  58. 58.
    Wu, D.K.C., Kuhlmey, B.T., Eggleton, B.J.: Ultrasensitive photonic crystal fiber refractive index sensor. Opt. Lett. 34(3), 322–324 (2009)ADSCrossRefGoogle Scholar
  59. 59.
    Xie, P., Zhang, Z.Q., Zhang, X.: Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasiperiodic photonic crystals. Phys. Rev. E 67, 026,607 (2003)Google Scholar
  60. 60.
    Yang, J., Pelinovsky, D.E.: Stable vortex and dipole vector solitons in a saturable nonlinear medium. Phys. Rev. E 67, 016,608 (2003)Google Scholar
  61. 61.
    Yeh, P., Yariv, A., Marom, E.: Theory of Bragg fiber. J. Opt. Soc. Am. 68(9), 1196–1201 (1978)ADSCrossRefGoogle Scholar
  62. 62.
    Zervas, M.N., Codemard, C.A.: High power fiber lasers: A review. IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241 (2014)CrossRefGoogle Scholar
  63. 63.
    Zhang, L., Yang, C.: Polarization splitter based on photonic crystal fibers. Opt. Express 11(9), 1015–1020 (2003)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Departamento de Física AplicadaUniversidade de Vigo, Escola de Enxeñaría Aeronáutica e do EspazoOurenseSpain
  2. 2.Departament d’Òptica, Interdisciplinary Modeling Group InterTechUniversitat de ValènciaBurjassot (València)Spain

Personalised recommendations