Nanooptics and photonics

Nonlinear Localized States in the Structured Media with Interfaces
Igor V. Gerasimchuk1,2, Victor S. Gerasimchuk2, Olha V. Konotopchyk2 and Alina V. Grytsai2 
1 Institute of Magnetism, Natl. Acad. of Sci. of Ukraine and Min. of Edu. and Sci. of Ukraine, Akad. Vernadsky Blvd. 36-b, 03142 Kyiv, Ukraine
E-mail: igor.gera@gmail.com
2 National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Peremohy Ave. 37, 03056 Kyiv, Ukraine

The investigations of the structure and dynamic properties of structured media are of great interest now. Of special interest are multilayered structures of different types promising for technological applications. The simultaneous influence of the layered structure of the medium and the nonlinearity give rise to new physical effects such as spatial localization of nonlinear waves in layered and modulated structures (see, for example, [1]), etc. 
We study analytically the localized states of nonlinear waves propagating along two coupled identical parallel plane thin layers (interfaces) in an anharmonic medium. We find the localized soliton solution in the case of attractive character of both interfaces and anharmonic medium outside them. It is demonstrated that the exact solution is controlled by a single scaling variable which describe the ratio between the interface distance and the soliton state localization length. 
We obtain the exact analytical results for the total number of elementary excitations and the energy of the system which are presented as functions of the distance between the interfaces in the universal scaling forms valid for different values of the interface characteristic . We demonstrate a monotonous behavior of the reduced total number of elementary excitations  bound in the localized state as a function of the scaling variable  characterizing the distance between the interfaces. Also the forces acting between the interfaces are found analytically and the numerical study of the characteristics of the system is performed. The obtained results can be applied for the description of nonlinear localization states in structured media of different physical origin. 

1.	Gerasimchuk I. V., Kovalev A. S. Spatial Localization of Nonlinear Waves in Layered and Modulated Media // JETP Letters.-2007.-85, No.10.-P. 488–492.