Abstract
The theoretical description of the change in optical properties of nonlinear crystal along the surface caused by the propagation of localized excitations is proposed. The nonlinear response sharp changes between focusing and defocusing depending on field amplitude. We derive new types of surface states characterized by composite structure consisting of three parts. The influence of interaction of excitations with crystal surface on structure of the nonlinear surface states and peculiarities of the surface domain formation is analyzed. The new features of localization, which appear when the nonlinear response changes between self-focusing and defocusing, are described.
Similar content being viewed by others
References
Kaplan A.E.: Multistable self-trapping of light and multistable soliton pulse propagation. IEEE J. Quantum Electronics. 21, 1538–1543. https://doi.org/10.1109/JQE.1985.1072828.
Aceves, A.B., Moloney, J.V., Newell, A.C.: Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface. Phys. Rev. A 39, 1809. (1989). https://doi.org/10.1103/PhysRevA.39.1809.
Zakery, A., Elliott, S.R.: Optical nonlinearities in chalcogenide glasses and their applications, vol. 135 of Springer Series in Optical Sciences. Springer-Verlag Berlin Heidelberg (2007)
Aceves, A.B., Moloney, J.V., Newell, A.C.: Theory of light-beam propagation at nonlinear interfaces II Multiple-particle and multiple-interface extensions. Phys. Rev. A. https://doi.org/10.1103/PhysRevA.39.1828.
Abdullaev, FKh., Baizakov, B.B., Umarov, B.A.: Resonance phenomena in interaction of a spatial soliton with the modulated interface of two nonlinear media. Opt. Com. 156, 341–346 (1998). https://doi.org/10.1016/S0030-4018(98)00451-9
Alfassi, B., Rotschild, C., Manela, O., Segev, M., Christodoulides, D.N.: Nonlocal surface-wave solitons. Phys. Rev. Lett. 98, 213901 (2007). https://doi.org/10.1103/PhysRevLett.98.213901
Azzouzi, F., Triki, H., Mezghiche, K., El Akrmi, A.: Solitary wave solutions for high dispersive cubic-quintic nonlinear Schrödinger equation. Chaos, Solitons and Fractals 39, 1304–1307 (2009)
Malomed, B.A., Mihalache, D.: Nonlinear waves in optical and matter-wave media: a topical survey of recent theoretical and experimental results. Rom. J. Phys. 64, 106. (2019). http://www.nipne.ro/rjp/2019_64_5-6/RomJPhys.64.106.pdf
Beletsky, N.N., Hasan, E.A.: Closed dispersion curves for electromagnetic TE waves in a nonlinear film. Phys. Sol. St. 36, 647–652 (1994)
Bian, S., Frejlich, J., Ringhofer, K.H.: Photorefractive saturable Kerr-type nonlinearity in photovoltaic crystals. Phys. Rev. Lett. 78, 4035–4038 (1997). https://doi.org/10.1103/PhysRevLett.78.4035
Boardman, A.D., Shabat, M.M., Wallis, R.F.: TE waves at an interface between linear gyromagnetic and nonlinear dielectric media. J Phy. D Appl. Phy. 24, 1702–1707 (1991). https://doi.org/10.1088/0022-3727/24/10/002
Bogdan, M.M., Gerasimchuk, I.V., Kovalev, A.S.: Dynamics and stability of localized modes in nonlinear media with point defects. Low Temp. Phys. 23, 197–207 (1997). https://doi.org/10.1063/1.593346
Ironside, C.: Semiconductor integrated optics for switching light, pp 74. morgan & claypool publishers, Bristol (2017). https://doi.org/10.1088/978-1-6817-4521-3
Chetkin, S.A., Akhmedzhanov, I.M.: Optical surface wave in a crystal with diffusion photorefractive nonlinearity. Quantum Electron. 41, 980–985 (2011). https://doi.org/10.1070/QE2011v041n11ABEH014660
Chun-yang, L., Ying, J., De, S., Yi-ning, M., Ji-kai, Y., Wei-jun, C.: Guided modes in thin layer waveguide induced by photorefractive surface waves. Chinese J Lum. 39, 1572–1578 (2018). https://doi.org/10.3788/fgxb20183911.1572
Corovai, A.V., Khadzhi, P.I.: Optical properties of a semiconductor upon two-photon excitation of biexcitons by a powerful pump pulse and one-photon probing in the M band. Quant. Electron. 31, 937–939 (2001). https://doi.org/10.1070/QE2001v031n10ABEH002080
Christodoulides, D.N., Carvalho, M.I.: Bright, dark, and grey spatial soliton states in photorefractive media. J. Opt. Soc. Am. https://doi.org/10.1364/JOSAB.12.001628
Mihalache, D., Nazmitdinov, R.G., Fedyanin V.K.: Nonlinear optical waves in layered structures. Phys. Elementary Particles Atomic Nucleus 20, 198–253. (1989). http://www1.jinr.ru/Archive/Pepan/1989-v20/v-20-1/5.htm
Dikshtein, I.E., Nikitov, S.A., Nikitov, D.S.: Self-localized nonlinear surface magnetic polaritons in a ferromagnetic medium. Phys. of Solid State 40, 1710–1714 (1998). https://doi.org/10.1134/1.1130640
Enns, R.H., Rangnekar, S.S., Kaplan, A.E.: Bistable-soliton pulse propagation: stability aspects Phys. Rev. A 36, 1270 (1987). https://doi.org/10.1103/PhysRevA.36.1270
Fedorov, L.V., Ljahomskaja, K.D.: Nonlinear surface waves with allowance for the saturation effect. Tech. Phys. Lett. 23, 915–916 (1997). https://doi.org/10.1134/1.1261931
Goodarzi, A., Ghanaatshoar, M., Mozafari, M.: All-optical fiber optic coherent amplifier. Sci. Rep. 8, 15340 (2018). https://doi.org/10.1038/s41598-018-33426-7
Schurmann, H.W., Serov, V.S.: Theory of TE-polarized waves in a lossless cubic-quintic nonlinear planar waveguide. Phys. Review A. 93(6), 063802(8) (2016)
Herrmann, J.: Propagation of ultrashort light pulses in fibers with saturable nonlinearity in the normal-dispersion region. J. Opt. Soc. Am. B 8, 1507–1511 (1991). https://doi.org/10.1364/JOSAB.8.001507
Christian, J.M., McDonald, G.S., Chamorro-Posada, P.: Bistable Helmholtz bright solitons in saturable materials. J. Optical Soc. Am. https://doi.org/10.1364/JOSAB.26.002323
Jarque, E.C., Malyshev, V.A.: Nonlinear reflection from a dense saturable absorber: from stability to chaos. Opt. Commun. 142, 66–70 (1997). https://doi.org/10.1016/S0030-4018(97)00275-7
Jia, Y., Liao, Y., Wu, L., Shan, Y., Dai, X., Cai, H., Xiang, Y., Fan, D.: Nonlinear optical response, all optical switching, and all optical information conversion in NbSe2 nanosheets based on spatial self-phase modulation. Nanoscale 7, 4515 (2019). https://doi.org/10.1039/c8nr08966c
Kartashov, Y.V., Malomed, B.A., Torner, L.: Solitons in nonlinear lattices. Rev. of Mod. Phys. 83, 247 (2011). https://doi.org/10.1103/RevModPhys.83.247
Khadzhi, P.I., Corovai, A.V.: Features of the interaction of ultrashort laser pulses with a thin semiconductor film caused by the generation of excitons and biexcitons. Quant. Electron. 32, 711–716 (2002). https://doi.org/10.1070/QE2002v032n08ABEH002277
Khadzhi, P.I., Fedorov, L.V.: Nonlinear surface waves for the simplest model of nonlinear medium. Phys. Tech. Lett. 61, 110–113 (1991)
Kishikawa, H., Goto, N.: Designing of optical switches controlled by light intensity in cascaded optical couplers. Optical Eng. 46, 044602 (2007). https://doi.org/10.1117/1.2719721
Kivshar, Yu.S., Agrawal, G.P.: Optical solitons: from fibers to photonic crystals, p. 540. Academic Press, San Diego (2003)
Kivshar, Yu.S., Kosevich, A.M., Chubykalo, O.A.: Resonant and non-resonant soliton scattering by impurities. Phys. Lett. A 125, 35–40 (1987). https://doi.org/10.1016/0375-9601(87)90514-7
Kivshar, Yu.S., Kosevich, A.M., Chubykalo, O.A.: Radiative effects in the theory of beam propagation at nonlinear interfaces. Phys. Rev. A 41, 1677–1688 (1990). https://doi.org/10.1103/PhysRevA.41.1677
Korovai, O.V.: Nonlinear s-polarized quasi-surface waves in the symmetric structure with a metamaterial core. Phys. Solid State 57, 1456–1462 (2015). https://doi.org/10.1134/S1063783415070197
Korovai, O.V., Khadzhi, P.I.: Nonlinear asymmetric waves induced in a symmetrical three-layer structure by the generation of excitons and biexcitons in semiconductors. Phys. of the Solid State 50, 1116–1120 (2008). https://doi.org/10.1134/S1063783408060279
Kosevich, A.M.: The crystal lattice, p. 356. Solitons, Dislocations, Superlattices, Wiley, New York, Phonons (2005)
Kosevich, A.M., Kovalev, A.S.: Introduction to nonlinear physical mechanics, p. 304. Naukova Dumka, Kiev (1989)
Kursseva, V., Tikhov, S., Valovik, D.: Electromagnetic wave propagation in a layer with power nonlinearity. J Nonlinear Optical Phy Mater. 28, 1950009 (2019). https://doi.org/10.1142/S0218863519500097
Langbein, U., Lederer, F., Ponath, H.E.: Generalized dispersion relations for nonlinear plate-guided waves. Opt. Commun. 53, 417–420 (1985). https://doi.org/10.1016/0030-4018(85)90030-6
Leung, K.M.: Propagation of nonlinear surface polaritons. Phys. Rev. A 31, 1189–1192 (1985). https://doi.org/10.1103/PhysRevA.31.1189
Liu, W., Yang, C., Liu, M., Yu, W., Zhang, Y., Lei, M., Wei, Z.: Bidirectional all-optical switches based on highly nonlinear optical fibers. Europhy. Lett. 118, 34004–1–4 (2017). https://doi.org/10.1209/0295-5075/118/34004
Luo, Z., Liu, F., Xu, Y., Liu, H., Zhang, T., Xu, J., Tian, J.: Dark surface waves in self-focusing media with diffusion and photovoltaic nonlinearities. Optics Express 21, 15075–15080 (2013). https://doi.org/10.1364/OE.21.015075
Lyakhomskaya, K.D., Khadzhi, P.I.: Self-reflection effect in the simplest non-linear medium. Tech. Phys. 70, 86–90 (2000)
Čada, M., Qasymeh, M., Pištora, J.: Optical wave propagation in Kerr Media. In: Wave propagation theories and applications, pp 175–192. IntechOpen, London. https://doi.org/10.5772/51293
Menzel, R.: Photonics: linear and nonlinear interactions of laser light and matter, pp 1024. Springer Science & Business Media, Berlin (2007)
Mihalache, D., Bertolotti, M., Sibilia, C.: Nonlinear wave propagation in planar structures. Prog. Opt. 27, 229–313 (1989)
Mihalache, D., Stegeman, G.I., Seaton, C.T., Wright, E.M., Zanoni, R., Boardman, A.D., Twardowski, T.: Exact dispersion relations for transverse magnetic polarized guided waves at a nonlinear interface. Opt. Lett. 12, 187–189 (1987). https://doi.org/10.1364/OL.12.000187
Munazza, Z.A.: Nonlinear surface waves in photonic hypercrystals. Phys. Lett A 381(32), 2643–2647 (2017). https://doi.org/10.1016/j.physleta.2017.05.060
Ahmediev, N.N. Korneev, V.I., Kuzmenko, U.V.: Excitation of nonlinear surface waves Gaussian light beams. J. Exper. Theor. Phys. 88, 107–115 (1985). http://www.jetp.ac.ru/cgi-bin/e/index/e/61/1/p62?a=list
N. N. Akhmediev, A. Ankevich, Solitons, Nonlinear Pulses and Beams, Chapman and Hall, London, (1997).
Naim Ben Ali: Narrow stop band microwave filters by using hybrid generalized quasi-periodic photonic crystals. Chinese J. of Phys. 55, 2384–2392 (2017). https://doi.org/10.1016/j.cjph.2017.10.008
Nurligareev, DKh., Usievich, B.A., Sychugov, V.A., Ivleva, L.I.: Characteristics of surface photorefractive waves in a nonlinear SBN-75 crystal coated with a metal film. Quantum Electron. 43, 14–20 (2013). https://doi.org/10.1070/QE2013v043n01ABEH014913
Ovchinnikov, A.A.: Localized long-lived vibrational states in molecular crystals. JETP 30, 147–150 (1970)
Khadzhi, P.I., Shibarshina, G.D., Rotaru, A. Kh.: Optical bistability in a system of coherent excitons and biexcitons in semiconductors, Chisinau, Shtiintsa 121 (1988)
Petrov, M., Stepanov, S., Khomenko, A.: in Photorefractive crystals in coherent optics. Springer-Verlag, Berlin (1991)
Carretero-González, R., Cuevas-Maraver, J., Frantzeskakis, D., Karachalios, N., Kevrekidis, P. Palmero-Acebedo F.: Localized excitations in nonlinear complex systems. Springer Science & Business Media, p. 432 (2013)
Raschetova, D.V., Tikhov, S.V., Valovik, D.V.: Electromagnetic guided waves in a lossless cubic-quintic nonlinear waveguide. Lobachevskii J Math. 39, 1108–1116 (2018). https://doi.org/10.1134/S1995080218080085
Reyna, A.S., Jorge, K.C., de Araujo, C.B.: Two-dimensional solitons in a quintic-septimal medium. Phy. Rev. A 90, 063835 (2014)
Gatz, S., Herrmann, J.: Soliton propagation in materials with saturable nonlinearity. J. Opt. Soc. Am. B 8, 2296–2302 (1991). https://www.osapublishing.org/josab/abstract.cfm?URI=josab-8-11-2296
Savotchenko, S.E.: The energy fluxes of surface waves propagating along the interface between nonlinear media with different characteristics, Pramana. J. Phys. https://doi.org/10.1007/s12043-019-1840-1
Sakaguchi, H., Malomed, B.A.: Matter-wave soliton interferometer based on a nonlinear splitter. New J. Phys. 18, 025020–025033 (2016). https://doi.org/10.1088/1367-2630/18/2/025020
Savotchenko, S.E.: Effect of the temperature on the redistribution of an energy flux carried by surface waves along the interface between crystals with different mechanisms of formation of a nonlinear response. J Exp. Theor. Phy. Lett. 109, 744–748 (2019). https://doi.org/10.1134/S0021364019110146
Savotchenko, S.E.: Surface waves in a medium with Kerr nonlinearity switching. Phy. Lett. A. 384, 126451 (2020). https://doi.org/10.1016/j.physleta.2020.126451
Savotchenko, S.E.: Peculiarities of localization in the presence of surface interaction in the crystal characterized by the jump change of Kerr nonlinearity. Euro. Phy. J B 93, 182 (2020). https://doi.org/10.1140/epjb/e2020-10316-x
Schuzgen, A., Peyghambarian, N., Hughes, S.: Doppler shifted self reflection from a semiconductor. Phys. Stat. Sol. (b) 206, 125–130 (1999). https://doi.org/10.1002/(SICI)1521-3951(199803)206:1%3C125::AID-PSSB125%3E3.0.CO;2-8
Shandarov, S.M., Shandarov, E.S.: Photorefractive slit waves. Tech. Phys. Lett. 23(8), 586–588 (1997). https://doi.org/10.1134/1.1261760
Suchkov, S.V., Sukhorukov, A.A., Huang, J., Dmitriev, S.V., Lee, C., Kivshar, Yu.S.: Nonlinear switching and solitons in PT-symmetric photonic systems. Laser Photonics Rev. 10, 177–213 (2016). https://doi.org/10.1002/lpor.201500227
Sukhorukov, A.A., Kivshar, Yu.S.: Nonlinear guided waves and spatial solitons in a periodic layered medium. J. Opt. Soc. Am. B 19, 772–781 (2002). https://doi.org/10.1364/JOSAB.19.000772
Surface waves: new trends and developments, Ed. by F. Ebrahimi, IntechOpen, London, p. 154 (2018). https://doi.org/10.5772/intechopen.68840
Laine, T.A.: Electromagnetic wave propagation in nonlinear kerr media. Royal Institute of Technology (KTH), Department of Physics, Stockholm, p. 47 (2000). http://www.diva-portal.org/smash/get/diva2:8732/FULLTEXT01.pdf
Strudley, T., Bruck, R., Mills, B., Muskens, O.L.: An ultrafast reconfigurable nanophotonic switch using wavefront shaping of light in a nonlinear nanomaterial. Light Sci. Appl. https://doi.org/10.1038/lsa.2014.88
Takayama, O., Bogdanov, A.A., Lavrinenko, A.V.: Photonic surface waves on metamaterial interfaces. J Phy. Condens. Matter 29, 463001 (2017). https://doi.org/10.1088/1361-648X/aa8bdd
Usievich, B.A., Nurligareev, DKh., Sychugov, V.A., Ivleva, L.I., Lykov, P.A., Bogodaev, N.V.: Nonlinear surface waves on the boundary of a photorefractive crystal. Quantum Electron. 40, 437–440 (2010). https://doi.org/10.1070/QE2010v040n05ABEH014223
Usievich, B.A., Nurligareev, DKh., Sychugov, V.A., Ivleva, L.I., Lykov, P.A., Bogodaev, N.V.: Surface photorefractive wave on the boundary of a photorefractive metal-coated crystal. Quantum Electron. 41, 262–266 (2011). https://doi.org/10.1070/QE2013v043n01ABEH014913
Trofimov, V.A., Zakharova, I.G., Shestakov, P.Y.: Nonlinear localization of chirped femtosecond pulse in layered photonic structure, 2017 Progress. In: Electromagnetics Research Symposium - Spring (PIERS), St. Petersburg, 3378-3382 (2017). https://doi.org/10.1109/PIERS.2017.8262342
Valovik, D.V.: Propagation of electromagnetic TE Waves in a nonlinear medium with saturation. J Commun. Tech. Electron. 56, 1311–1316 (2011). https://doi.org/10.1134/S1064226911110179
Valovik, D.V.: On the existence of infinitely many nonperturbative solutions in a transmission eigenvalue problem for nonlinear Helmholtz equation with polynomial nonlinearity. Appl. Math. Model. 53, 296–309 (2018). https://doi.org/10.1016/j.apm.2017.09.019
Wood, V.E., Evans, E.D., Kenan, R.P.: Soluble saturable refractive-index nonlinearity model. Opt. Commun. 69, 156–160 (1988). https://doi.org/10.1016/0030-4018(88)90302-1
Yongan, X., Shengqiang, Tang.: New exact solutions for high dispersive cubic-quintic nonlinear Schrödinger equation. J. Appl. Math. 826746 (2014)
Zhan, Kaiyun, Tian, Hao, Li, Xin, Xianfeng, Xu., Jiao, Zhiyong, Jia, Yulei: Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity. Scien. Rep. 6, 32990–1–9 (2016). https://doi.org/10.1038/srep32990
Zhang, D., Li, Z., Hu, W., Cheng, B.: Broadband optical reflector - an application of light localization in one dimension. Appl. Phys. Lett. 67, 2431 (1995). https://doi.org/10.1063/1.114597
Zhang, T.H., Ren, X.K., Wang, B.H., Lou, C.B., Hu, Z.J., Shao, W.W., Xu, Y.H., Kang, H.Z., Yang, J., Yang, D.P., Feng, L., Xu, J.J.: Surface waves with photorefractive nonlinearity. Phys. Rev. A 76, 013827 (2007). https://doi.org/10.1103/PhysRevA.76.013827
Zhao, Li-Chen., Liu, Chong, Yang, Zhan-Ying.: The rogue waves with quintic nonlinearity and nonlinear dispersion effects in nonlinear optical fibers. Commun. Nonlinear Sci. Num. Simul. 20, 9–13 (2015)
Zhu, B., Zhang, T., Ma, H., Yan, Z., Yang, X., Li, X., Shao, W., Lou, C., Ren, X., Xu, J., Tian, J.: Photorefractive lattice surface waves with diffusion nonlinearity. J Optical Soc. Am. B 27, 1381–1387 (2010). https://doi.org/10.1364/JOSAB.27.001381
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Savotchenko, S.E. Localized states in the crystal characterized by the switching between self-focusing and defocusing Kerr type nonlinearities and the surface interaction. Opt Quant Electron 53, 365 (2021). https://doi.org/10.1007/s11082-021-03016-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-021-03016-5