Radiotekhnika
Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS


Тел.: +7 (495) 625-9241

 

Peculiarities of the excitation localization near the nonlinear layer between linear media separatedby the plane defects with nonlinear properties

Keywords:

S.E. Savotchenko  Dr.Sc. (Phys.-Math.), Professor, Belgorod State Technological University named after V.G. Shukhov
E-mail: savotchenkose@mail.ru


Local states in a three-layer structure are considered. It is a thin plate of finite thickness characterized by an anharmonic (nonlinear) interaction of elementary excitations enclosed between two half-spaces in which the interaction of elementary excitations is harmonic (linear). The nonlinearity of the inner layer is the Kerr type. The cases of self-focusing and defocusing in a nonlinear layer are consi-dered. The interfaces of the layers are represented as plane defects with nonlinear properties described by a nonlinear short-range potential. The excitations are described by a linear Schrodinger equation with a nonlinear potential. The problem is reduced to the so-lution of the nonlinear Schrödinger equation with nonlinear boundary conditions of a special kind. It is shown that along the interfaces of the layers there the several types of localized states characterized by monotonically decreasing field amplitude on either side of the inner nonlinear layer are exist. The existence of nonlinear localized excitations of three types is possible in wide energy range. It is shown that there are two different types of localized states with energies below the boundaries of the continuous-spectrum zone near the self-focusing nonlinear plate corresponding to NLSE with positive nonlinearity. The excitations of such a type are described by distinguishing types of nonlinear periodic NLSE solutions corresponding to the elliptic functions cn and dn. There is one localized state described by the elliptical sine near the defocusing nonlinear plate corresponding to NLSE with negative nonlinearity. Its energy lies in the interval between the boundary of the zone of the continuous spectrum of the stationary states of the plate and the smallest boundary of the zone of the continuous spectrum of linear semi-infinite crystals. The expressions for the energies of the localized states are obtained in explicit analytical form. The conditions for their existence determined by the relations between the parameters of media and defects are derived. The amplitudes of the oscillations of the interface boundaries are calculated. These values are determined by the parameters of the parameter of the nonlinearity of the inner plate and its thickness and the intensity of the interaction of the field with the interface of the layers.

References:
  1. Ahmediev N.N. Novyj klass nelinejnyh poverhnostnyh voln // ZHEHTF. 1982. T. 83. № 2. S. 545-553.
  2. Boardman A.D., Shabat M.M., Wallis R.F. TE waves at an interface between linear gyromagnetic and nonlinear dielectric media // Journal of Physics D: Applied Physics. 1991. V. 24. № 10. P. 1702-1707.
  3. Ashour H.S., Assa’d A.I. S-Polarized Surface waves in Ferrite bounded by Nonlinear Nonmagnetic Negative Permittivity Metamaterial // Journal of Al Azhar University-Gaza (Natural Sciences). 2011. V. 13. P. 93-108.
  4. Mihalake D., Nazmitdinov R.G., Fedyanin V.K. Nelinejnye opticheskie volny v sloistyh strukturah // Fizika ehlemen-tarnyh chastic i atomnogo yadra. 1989. T. 20. № 1. S. 198-253.
  5. Korovaj O.V., Hadzhi P.I. Nelinejnye poverhnostnye volny v simmetrichnoj trekhslojnoj strukture, obuslovlennye generaciej ehksitonov i biehksitonov v poluprovodnikah // FTT. 2003. T. 45. № 2. S. 364-368.
  6. Kivshar Yu.S., Kosevich A.M., Chubykalo O.A. Resonant and non-resonant soliton scattering by impurities // Phys. Lett. A. 1987. V. 125. Р. 35-40.
  7. Gerasimchuk I.V., Kovalev A.S. Lokalizaciya nelinejnyh voln v sloistyh sredah // FNT. 2000. T. 26. № 8. S. 799-809.
  8. Gerasimchuk I.V., Kovalev A.S. Prostranstvennaya lokalizaciya nelinejnyh voln v sloistyh i modulirovannyh sredah // Pis'ma v ZHEHTF 2007. T. 85. Vyp. 10. S. 594-598.
  9. Gerasimchuk I.V., Gerasimchuk V.S., Sommer J.U. Adsorption of polymer chains at two impenetrable interfaces // Pis’ma v ZhETF. 2011. V. 93. Р. 447-481.
  10. Krasil'nikov V.V., Savotchenko S.E. Osobennosti rasseyaniya chastic tochechnym defektom s vnutrennej strukturoj // Izvestiya tul'skogo gosudarstvennogo universiteta. Estestvennye nauki. 2015. № 4. S. 178-183.
  11. Savotchenko S.E. Osobennosti vzaimodejstviya volny s tochechnym defektom v srede s prostranstvennoj dispersiej // Izvestiya Voronezhskogo gosudarstvennogo pedagogicheskogo universiteta. 2016. № 1(270). S. 196-199.
  12. Savotchenko S.E. Osobennosti lokalizacii nelinejnyh vozbuzhdenij vblizi defekta s vnutrennej strukturoj // Vestnik Voronezhskogo gosudarstvennogo universiteta. Ser. Fizika. Matematika. 2016. № 4. S. 51-59
  13. Savotchenko S.E. Lokalizovannye sostoyaniya v defokusiruyushchej nelinejnoj srede s defektom s vnutrennej strukturoj // Nauchnye vedomosti BelGU. Ser. Matematika. Fizika. 2017. № 20(269). Vyp. 48. S. 79-85.
  14. Gerasimchuk I.V. Lokalizovannye sostoyaniya i ih ustojchivost' v angarmonicheskoj srede s nelinejnym defektom // ZHEHTF. 2015. T. 121. № 4. S. 596-605.

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio