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Peculiarities of localization in the presence of surface interaction in the crystal characterized by the jump change in Kerr nonlinearity

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Abstract

We propose the new model of nonlinearity describing a sharp change in Kerr nonlinearity coefficients in dependence on the field amplitude. The excitation interaction with surface is taken into account. Three new types of surface states localized near the surface separated the linear medium and the crystal with proposed type of nonlinearity, are found in exact analytical forms. One type of the surface states exists in the crystal characterized by positive (self-focusing) nonlinearity and two types of the surface states exist in the crystals characterized by negative (defocusing) nonlinearity. The structure of nonlinear surface states, peculiarities of the surface domain formation and power flow redistributions were analyzed in dependence on intensity of interaction between excitations and surface.

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References

  1. V.K. Fedyanin, D. Mihalache, Z. Phys. B 47, 167 (1982)

    Article  ADS  Google Scholar 

  2. D. Mikhalake, V.K. Fedyanin, Theor. Math. Phys. 54, 443 (1983)

    Article  Google Scholar 

  3. U. Langbein, F. Lederer, H.E. Ponath, Opt. Commun. 53, 417 (1985)

    Article  ADS  Google Scholar 

  4. K.M. Leung, Phys. Rev. A 31, 1189 (1985)

    Article  ADS  Google Scholar 

  5. N.N. Ahmediev, V.I. Korneev, U.V. Kuzmenko, J. Exp. Theor. Phys. 88, 107 (1985)

    Google Scholar 

  6. D. Mihalache, M. Bertolotti, C. Sibilia, Prog. Opt. 27, 229 (1989)

    ADS  Google Scholar 

  7. D. Mihalache, G.I. Stegeman, C.T. Seaton, E.M. Wright, R. Zanoni, A.D. Boardman, T. Twardowski, Opt. Lett. 12, 187 (1987)

    Article  ADS  Google Scholar 

  8. D. Mihalache, R.G. Nazmitdinov, V.K. Fedyanin, Phys. Elem. Part. Atom. Nucl. 20, 198 (1989)

    Google Scholar 

  9. A.B. Aceves, J.V. Moloney, A.C. Newell, Phys. Rev. A 39, 1809 (1989)

    Article  ADS  Google Scholar 

  10. A.B. Aceves, J.V. Moloney, A.C. Newell, Phys. Rev. A 39, 1828 (1989)

    Article  ADS  Google Scholar 

  11. A.D. Boardman, M.M. Shabat, R.F. Wallis, J. Phys. D: Appl. Phys. 24, 1702 (1991)

    Article  ADS  Google Scholar 

  12. I.E. Dikshtein, S.A. Nikitov, D.S. Nikitov, Phys. Solid State 40, 1710 (1998)

    Article  ADS  Google Scholar 

  13. F. Kh. Abdullaev, B.B. Baizakov, B.A. Umarov, Opt. Commun. 156, 341 (1998)

    Article  ADS  Google Scholar 

  14. B. Alfassi, C. Rotschild, O. Manela, M. Segev, D.N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007)

    Article  ADS  Google Scholar 

  15. B.A. Malomed, D. Mihalache, Rom. J. Phys. 64, 106 (2019)

    Google Scholar 

  16. O. Takayama, A.A. Bogdanov, A.V. Lavrinenko, J. Phys.: Condens. Matter 29, 463001 (2017)

    ADS  Google Scholar 

  17. Y.-D. Wu, Prog. Electromagnet. Res. M 43, 71 (2015)

    Article  Google Scholar 

  18. W. Liu, C. Yang, M. Liu, W. Yu, Y. Zhang, M. Lei, Z. Wei, Europhys. Lett. 118, 34004 (2017)

    Article  ADS  Google Scholar 

  19. Y. Jia, Y. Liao, L. Wu, Y. Shan, X. Dai, H. Cai, Y. Xiang, D. Fan, Nanoscale 7, 4515 (2019)

    Article  Google Scholar 

  20. C. Ironside,Semiconductor Integrated Optics for Switching Light (Morgan & Claypool Publishers, Bristol, UK, 2017)

  21. A. Goodarzi, M. Ghanaatshoar, M. Mozafari, Sci. Rep. 8, 15340 (2018)

    Article  ADS  Google Scholar 

  22. S.V. Suchkov, A.A. Sukhorukov, J. Huang, S.V. Dmitriev, C. Lee, Yu.S. Kivshar, Laser Photon. Rev. 10, 177 (2016)

    Article  ADS  Google Scholar 

  23. H. Kishikawa, N. Goto, Opt. Eng. 46, 044602 (2007)

    Article  ADS  Google Scholar 

  24. I. Armstrong, I. Andonovic, A. Kelly, J. Opt. Netw. 3, 882 (2004)

    Article  Google Scholar 

  25. E.C. Jarque, V.A. Malyshev, Opt. Commun. 142, 66 (1997)

    Article  ADS  Google Scholar 

  26. A. Schuzgen, N. Peyghambarian, S. Hughes, Phys. Stat. Sol. B 206, 125 (1999)

    Article  ADS  Google Scholar 

  27. P.I. Khadzhi, L.V. Fedorov, Tech. Phys. Lett. 61, 110 (1991)

    Google Scholar 

  28. P.I. Hadji, G.D. Shibarshina, A.Kh. Rotaru,Optical Bistability in a System of Coherent Excitons and Biexcitons in Semiconductors (Chisinau, Shtiintsa, 1988)

  29. D.N. Christodoulides, M.I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995)

    Article  ADS  Google Scholar 

  30. B. Zhu, T. Zhang, H. Ma, Z. Yan, X. Yang, X. Li, W. Shao, C. Lou, X. Ren, J. Xu, J. Tian, J. Opt. Soc. Am. B 27, 1381 (2010)

    Article  ADS  Google Scholar 

  31. Z. Luo, F. Liu, Y. Xu, H. Liu, T. Zhang, J. Xu, J. Tian, Opt. Express 21, 15075 (2013)

    Article  ADS  Google Scholar 

  32. L. Chun-yang, J. Ying, S. De, M. Yi-ning, Y. Ji-kai, C. Wei-jun, Chin. J. Lumin. 39, 1572 (2018)

    Article  Google Scholar 

  33. S.E. Savotchenko, J. Exp. Theor. Phys. Lett. 109, 744 (2019)

    Article  Google Scholar 

  34. S.E. Savotchenko, J. Exp. Theor. Phys. 129, 159 (2019)

    Article  ADS  Google Scholar 

  35. S.E. Savotchenko, Opt. Spectrosc. 127, 159 (2019)

    Article  ADS  Google Scholar 

  36. S.E. Savotchenko, Solid State Commun. 296, 32 (2019)

    Article  ADS  Google Scholar 

  37. S.E. Savotchenko, Quantum Electron. 49, 850 (2019)

    Article  ADS  Google Scholar 

  38. S.E. Savotchenko, Opt. Spectrosc. 128, 345 (2020)

    Article  ADS  Google Scholar 

  39. S.E. Savotchenko, Opt. Commun. 465, 125597 (2020)

    Article  Google Scholar 

  40. N.N. Beletsky, E.A. Hasan, Phys. Solid State 36, 647 (1994)

    Google Scholar 

  41. K.D. Lyakhomskaya, P.I. Hadji, Tech. Phys. 70, 86 (2000)

    Google Scholar 

  42. A.E. Kaplan, IEEE J. Quantum Electron. 21, 1538 (1985)

    Article  ADS  Google Scholar 

  43. R.H. Enns, S.S. Rangnekar, A.E. Kaplan, Phys. Rev. A 36, 1270 (1987)

    Article  ADS  Google Scholar 

  44. S.E. Savotchenko, Romanian J. Phys. 65, 202 (2020)

    Google Scholar 

  45. V.E. Wood, E.D. Evans, R.P. Kenan, Opt. Commun. 69, 156 (1988)

    Article  ADS  Google Scholar 

  46. S. Gatz, J. Herrmann, J. Opt. Soc. Am. B 8, 2296 (1991)

    Article  ADS  Google Scholar 

  47. J. Herrmann, J. Opt. Soc. Am. B 8, 1507 (1991)

    Article  ADS  Google Scholar 

  48. S. Bian, J. Frejlich, K.H. Ringhofer, Phys. Rev. Lett. 78, 4035 (1997)

    Article  ADS  Google Scholar 

  49. J.M. Christian, G.S. McDonald, P. Chamorro-Posada, J. Opt. Soc. Am. B 26, 2323 (2009)

    Article  ADS  Google Scholar 

  50. D.V. Valovik, J. Commun. Technol. Electron. 56, 1311 (2011)

    Article  Google Scholar 

  51. L.V. Fedorov, K.D. Ljahomskaja, Tech. Phys. Lett. 23, 915 (1997)

    Article  ADS  Google Scholar 

  52. K. Zhan, H. Tian, X. Li, X. Xu, Z. Jiao, Y. Jia, Sci. Rep. 6, 32990 (2016)

    Article  ADS  Google Scholar 

  53. D.V. Valovik, Appl. Math. Model. 53, 296 (2018)

    Article  MathSciNet  Google Scholar 

  54. D.V. Raschetova, S.V. Tikhov, D.V. Valovik, Lobachevskii, J. Math. 39, 1108 (2018)

    Google Scholar 

  55. V. Kursseva, S. Tikhov, D. Valovik, J. Nonlinear Opt. Phys. Mater. 28, 1950009 (2019)

    Article  ADS  Google Scholar 

  56. O.V. Korovai, P.I. Khadzhi, Phys. Solid State 50, 1116 (2008)

    Article  Google Scholar 

  57. O.V. Korovai, Phys. Solid State 57, 1456 (2015)

    Article  ADS  Google Scholar 

  58. S.E. Savotchenko, Russ. Phys. J. 62, 1 (2019)

    Article  Google Scholar 

  59. S.E. Savotchenko, Surf. Interfaces 15, 191 (2019)

    Article  Google Scholar 

  60. T.A. Laine, inElectromagnetic Wave Propagation in Nonlinear Kerr Media (Royal Institute of Technology (KTH), Department of Physics, Stockholm, Sweden, 2000)

  61. Yu.S. Kivshar, G.P. Agrawal,Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

  62. M. Čada, M. Qasymeh, J. Pištora, inWave Propagation Theories and Applications (IntechOpen, 2013)

  63. Yu.S. Kivshar, A.M. Kosevich, O.A. Chubykalo, Phys. Lett. A 125, 35 (1987)

    Article  ADS  Google Scholar 

  64. Yu.S. Kivshar, A.M. Kosevich, O.A. Chubykalo, Phys. Rev. A 41, 1677 (1990)

    Article  ADS  Google Scholar 

  65. M.M. Bogdan, I.V. Gerasimchuk, A.S. Kovalev, Low Temp. Phys. 23, 197 (1997)

    Article  Google Scholar 

  66. I.V. Gerasimchuk, A.S. Kovalev, Low Temp. Phys. 26, 586 (2000)

    Article  ADS  Google Scholar 

  67. A.A. Sukhorukov, Yu.S. Kivshar, J. Opt. Soc. Am. B 19, 772 (2002)

    Article  ADS  Google Scholar 

  68. S.E. Savotchenko, Russ. Phys. J. 47, 556 (2004)

    Article  Google Scholar 

  69. Y.V. Kartashov, B.A. Malomed, L. Torner, Rev. Mod. Phys. 83, 247 (2011)

    Article  ADS  Google Scholar 

  70. S.E. Savotchenko, Condens. Matter Interphases 19, 291 (2017)

    Google Scholar 

  71. S.E. Savotchenko, Commun. Nonlinear Sci. Numer. Simul. 63, 171 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  72. S.E. Savotchenko, Tech. Phys. 62, 1772 (2017)

    Article  Google Scholar 

  73. S.E. Savotchenko, Pramana – J. Phys. 93, 77 (2019)

    Article  ADS  Google Scholar 

  74. D.V. Valovik, J. Nonlinear Opt. Phys. Mater. 25, 1650051 (2016)

    Article  ADS  Google Scholar 

  75. N.B. Ali, Chin. J. Phys. 55, 2384 (2017)

    Article  Google Scholar 

  76. Surface Waves: New Trends and Developments, edited by F. Ebrahimi (IntechOpen, 2018)

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  1. Belgorod State Technological University named after V.G. Shukhov 308012, Kostukova St. 46, Belgorod, Russia

    Sergey E. Savotchenko

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Savotchenko, S.E. Peculiarities of localization in the presence of surface interaction in the crystal characterized by the jump change in Kerr nonlinearity. Eur. Phys. J. B 93, 182 (2020). https://doi.org/10.1140/epjb/e2020-10316-x

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