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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V.K. Fedyanin, D. Mihalache, Z. Phys. B 47, 167 (1982)
D. Mikhalake, V.K. Fedyanin, Theor. Math. Phys. 54, 443 (1983)
U. Langbein, F. Lederer, H.E. Ponath, Opt. Commun. 53, 417 (1985)
K.M. Leung, Phys. Rev. A 31, 1189 (1985)
N.N. Ahmediev, V.I. Korneev, U.V. Kuzmenko, J. Exp. Theor. Phys. 88, 107 (1985)
D. Mihalache, M. Bertolotti, C. Sibilia, Prog. Opt. 27, 229 (1989)
D. Mihalache, G.I. Stegeman, C.T. Seaton, E.M. Wright, R. Zanoni, A.D. Boardman, T. Twardowski, Opt. Lett. 12, 187 (1987)
D. Mihalache, R.G. Nazmitdinov, V.K. Fedyanin, Phys. Elem. Part. Atom. Nucl. 20, 198 (1989)
A.B. Aceves, J.V. Moloney, A.C. Newell, Phys. Rev. A 39, 1809 (1989)
A.B. Aceves, J.V. Moloney, A.C. Newell, Phys. Rev. A 39, 1828 (1989)
A.D. Boardman, M.M. Shabat, R.F. Wallis, J. Phys. D: Appl. Phys. 24, 1702 (1991)
I.E. Dikshtein, S.A. Nikitov, D.S. Nikitov, Phys. Solid State 40, 1710 (1998)
F. Kh. Abdullaev, B.B. Baizakov, B.A. Umarov, Opt. Commun. 156, 341 (1998)
B. Alfassi, C. Rotschild, O. Manela, M. Segev, D.N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007)
B.A. Malomed, D. Mihalache, Rom. J. Phys. 64, 106 (2019)
O. Takayama, A.A. Bogdanov, A.V. Lavrinenko, J. Phys.: Condens. Matter 29, 463001 (2017)
Y.-D. Wu, Prog. Electromagnet. Res. M 43, 71 (2015)
W. Liu, C. Yang, M. Liu, W. Yu, Y. Zhang, M. Lei, Z. Wei, Europhys. Lett. 118, 34004 (2017)
Y. Jia, Y. Liao, L. Wu, Y. Shan, X. Dai, H. Cai, Y. Xiang, D. Fan, Nanoscale 7, 4515 (2019)
C. Ironside,Semiconductor Integrated Optics for Switching Light (Morgan & Claypool Publishers, Bristol, UK, 2017)
A. Goodarzi, M. Ghanaatshoar, M. Mozafari, Sci. Rep. 8, 15340 (2018)
S.V. Suchkov, A.A. Sukhorukov, J. Huang, S.V. Dmitriev, C. Lee, Yu.S. Kivshar, Laser Photon. Rev. 10, 177 (2016)
H. Kishikawa, N. Goto, Opt. Eng. 46, 044602 (2007)
I. Armstrong, I. Andonovic, A. Kelly, J. Opt. Netw. 3, 882 (2004)
E.C. Jarque, V.A. Malyshev, Opt. Commun. 142, 66 (1997)
A. Schuzgen, N. Peyghambarian, S. Hughes, Phys. Stat. Sol. B 206, 125 (1999)
P.I. Khadzhi, L.V. Fedorov, Tech. Phys. Lett. 61, 110 (1991)
P.I. Hadji, G.D. Shibarshina, A.Kh. Rotaru,Optical Bistability in a System of Coherent Excitons and Biexcitons in Semiconductors (Chisinau, Shtiintsa, 1988)
D.N. Christodoulides, M.I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995)
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)
Z. Luo, F. Liu, Y. Xu, H. Liu, T. Zhang, J. Xu, J. Tian, Opt. Express 21, 15075 (2013)
L. Chun-yang, J. Ying, S. De, M. Yi-ning, Y. Ji-kai, C. Wei-jun, Chin. J. Lumin. 39, 1572 (2018)
S.E. Savotchenko, J. Exp. Theor. Phys. Lett. 109, 744 (2019)
S.E. Savotchenko, J. Exp. Theor. Phys. 129, 159 (2019)
S.E. Savotchenko, Opt. Spectrosc. 127, 159 (2019)
S.E. Savotchenko, Solid State Commun. 296, 32 (2019)
S.E. Savotchenko, Quantum Electron. 49, 850 (2019)
S.E. Savotchenko, Opt. Spectrosc. 128, 345 (2020)
S.E. Savotchenko, Opt. Commun. 465, 125597 (2020)
N.N. Beletsky, E.A. Hasan, Phys. Solid State 36, 647 (1994)
K.D. Lyakhomskaya, P.I. Hadji, Tech. Phys. 70, 86 (2000)
A.E. Kaplan, IEEE J. Quantum Electron. 21, 1538 (1985)
R.H. Enns, S.S. Rangnekar, A.E. Kaplan, Phys. Rev. A 36, 1270 (1987)
S.E. Savotchenko, Romanian J. Phys. 65, 202 (2020)
V.E. Wood, E.D. Evans, R.P. Kenan, Opt. Commun. 69, 156 (1988)
S. Gatz, J. Herrmann, J. Opt. Soc. Am. B 8, 2296 (1991)
J. Herrmann, J. Opt. Soc. Am. B 8, 1507 (1991)
S. Bian, J. Frejlich, K.H. Ringhofer, Phys. Rev. Lett. 78, 4035 (1997)
J.M. Christian, G.S. McDonald, P. Chamorro-Posada, J. Opt. Soc. Am. B 26, 2323 (2009)
D.V. Valovik, J. Commun. Technol. Electron. 56, 1311 (2011)
L.V. Fedorov, K.D. Ljahomskaja, Tech. Phys. Lett. 23, 915 (1997)
K. Zhan, H. Tian, X. Li, X. Xu, Z. Jiao, Y. Jia, Sci. Rep. 6, 32990 (2016)
D.V. Valovik, Appl. Math. Model. 53, 296 (2018)
D.V. Raschetova, S.V. Tikhov, D.V. Valovik, Lobachevskii, J. Math. 39, 1108 (2018)
V. Kursseva, S. Tikhov, D. Valovik, J. Nonlinear Opt. Phys. Mater. 28, 1950009 (2019)
O.V. Korovai, P.I. Khadzhi, Phys. Solid State 50, 1116 (2008)
O.V. Korovai, Phys. Solid State 57, 1456 (2015)
S.E. Savotchenko, Russ. Phys. J. 62, 1 (2019)
S.E. Savotchenko, Surf. Interfaces 15, 191 (2019)
T.A. Laine, inElectromagnetic Wave Propagation in Nonlinear Kerr Media (Royal Institute of Technology (KTH), Department of Physics, Stockholm, Sweden, 2000)
Yu.S. Kivshar, G.P. Agrawal,Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
M. Čada, M. Qasymeh, J. Pištora, inWave Propagation Theories and Applications (IntechOpen, 2013)
Yu.S. Kivshar, A.M. Kosevich, O.A. Chubykalo, Phys. Lett. A 125, 35 (1987)
Yu.S. Kivshar, A.M. Kosevich, O.A. Chubykalo, Phys. Rev. A 41, 1677 (1990)
M.M. Bogdan, I.V. Gerasimchuk, A.S. Kovalev, Low Temp. Phys. 23, 197 (1997)
I.V. Gerasimchuk, A.S. Kovalev, Low Temp. Phys. 26, 586 (2000)
A.A. Sukhorukov, Yu.S. Kivshar, J. Opt. Soc. Am. B 19, 772 (2002)
S.E. Savotchenko, Russ. Phys. J. 47, 556 (2004)
Y.V. Kartashov, B.A. Malomed, L. Torner, Rev. Mod. Phys. 83, 247 (2011)
S.E. Savotchenko, Condens. Matter Interphases 19, 291 (2017)
S.E. Savotchenko, Commun. Nonlinear Sci. Numer. Simul. 63, 171 (2018)
S.E. Savotchenko, Tech. Phys. 62, 1772 (2017)
S.E. Savotchenko, Pramana – J. Phys. 93, 77 (2019)
D.V. Valovik, J. Nonlinear Opt. Phys. Mater. 25, 1650051 (2016)
N.B. Ali, Chin. J. Phys. 55, 2384 (2017)
Surface Waves: New Trends and Developments, edited by F. Ebrahimi (IntechOpen, 2018)
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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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DOI: https://doi.org/10.1140/epjb/e2020-10316-x