Localized states in symmetric three-layered structure consisting of linear layer between focusing media separated by interfaces with nonlinear response

2019 ◽  
Vol 33 (11) ◽  
pp. 1850127
Author(s):  
S. E. Savotchenko
Keyword(s):  
Nonlinear Response ◽  
Mathematical Formulation ◽  
Localized States ◽  
Stationary States ◽  
Nonlinear Media ◽  
One Dimensional ◽  
Symmetric Structure ◽  
Linear Layer ◽  
Dimensional Boundary ◽  
Interface Parameters

We analyze the localization in three-layered symmetric structure consisting of linear layer between focusing nonlinear media separated by nonlinear interfaces. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. We find nonlinear localized states of two types of symmetry. We derive the energies of obtained stationary states in explicit form. We obtain the localization energies as exact solutions of dispersion equations choosing the amplitude of the interface oscillations as a free parameter. We analyze the conditions of their existence depending on the combination of signs of interface parameters.

scholarly journals Локализация возбуждений в слоистой структуре с границами раздела, характеризующимися нелинейным откликом

2019 ◽  
Vol 61 (3) ◽  
pp. 571
Author(s):  
С.Е. Савотченко
Keyword(s):  
Surface Waves ◽  
Nonlinear Response ◽  
Layer Structure ◽  
Localized States ◽  
Frequency Range ◽  
One Dimensional ◽  
Localized State ◽  
Symmetric Structure ◽  
The Media ◽  
Field Localization

AbstractThe features of localization of excitations in a three-layer structure in which linear media are separated by boundaries with their own nonlinear response have been examined. It is shown that in the three-layer structure under consideration, localized states of two types can exist that differ in the distribution of the field in the inner layer, as well as in the frequency range of existence. Dispersion relations have been obtained that determine the energy dependence on system parameters in each case. The damping factors of surface waves are obtained in an explicit form. The conditions of the field localization are specified, depending on the characteristics of the layers and their interfaces. The energies of localized states have been found that do not exist in a symmetric structure without a wave interacting with the interfaces of the layers. Moreover, the presence of a nonlinear response of the boundaries is mandatory. It is shown that the interaction of a wave with the interfaces of the layers can lead to the absence of a localized state in a one-dimensional symmetric potential well with infinitely high walls and a nonlinear response. The influence of the media parameters and their interfaces on the flux carried by surface waves has been analyzed.

Peculiarities of linear wave interaction with nonlinear media interface

2018 ◽  
Vol 32 (30) ◽  
pp. 1850371 ◽  
Author(s):  
S. E. Savotchenko
Keyword(s):  
Guided Waves ◽  
Mathematical Formulation ◽  
Wave Interaction ◽  
Linear Wave ◽  
Stationary Waves ◽  
One Dimensional ◽  
Nonlinear Properties ◽  
Dimensional Boundary ◽  
Nonlinear Interface ◽  
Plane Defect

We analyze guided waves in the linear media separated nonlinear interface. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. The Kerr type nonlinearity in the equation is taken into account only inside the waveguide. We show that the existence of nonlinear stationary waves of three types is possible in defined frequency ranges. We derive the frequency of obtained stationary states in explicit form and find the conditions of its existence. We show that it is possible to obtain the total wave transition through a plane defect. We determine the condition for realizing of such a resonance. We obtain the reflection and transition coefficients in the vicinity of the resonance. We establish that complete wave propagation with nonzero defect parameters can occur only when the nonlinear properties of the defect are taken into account.

scholarly journals Локализация возбуждений вблизи тонкого дефектного слоя с нелинейными свойствами, разделяющего линейный и нелинейный кристаллы

2019 ◽  
Vol 89 (9) ◽  
pp. 1307
Author(s):  
С.Е. Савотченко
Keyword(s):  
Mathematical Formulation ◽  
Defect Layer ◽  
Field Amplitude ◽  
Localized States ◽  
Stationary States ◽  
Linear Medium ◽  
Nonlinear Properties ◽  
Self Focusing ◽  
Proposed Model ◽  
Linear And Nonlinear

It is shown that the localized and quasi-local stationary states exist near a thin defect layer with nonlinear properties separating a linear medium from a non-linear medium of Kerr type. Localized states are characterized by a monotonically decreasing field amplitude on both sides of the interface. Quasi-local states are described by a field in the form of a standing wave in a linear medium and monotonously decreasing in a nonlinear medium. The contacts with nonlinear self-focusing and defocusing media are analyzed. The mathematical formulation of the proposed model is a system of linear and nonlinear Schrödinger equations with a potential that is nonlinear with respect to the field and which simulates a thin defect layer with nonlinear properties. Dispersion relations determining the energy of local and quasi-local states are obtained. The expressions for energies were obtained explicitly in limiting cases and the conditions for their existence were indicated.

scholarly journals Stable One-Dimensional Periodic Wave in Kerr-Type and Quadratic Nonlinear Media

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Roxana Savastru ◽  
Simona Dontu ◽  
Dan Savastru ◽  
Marina Tautan ◽  
Vasile Babin
Keyword(s):  
Nonlinear Response ◽  
Power Level ◽  
Periodic Wave ◽  
Threshold Power ◽  
Periodic Waves ◽  
Nonlinear Media ◽  
One Dimensional ◽  
Kerr Media ◽  
The Laplace Transform ◽  
Soliton Stability

We present the propagation of optical beams and the properties of one-dimensional (1D) spatial solitons (“bright” and “dark”) in saturated Kerr-type and quadratic nonlinear media. Special attention is paid to the recent advances of the theory of soliton stability. We show that the stabilization of bright periodic waves occurs above a certain threshold power level and the dark periodic waves can be destabilized by the saturation of the nonlinear response, while the dark quadratic waves turn out to be metastable in the broad range of material parameters. The propagation of (1+1) a dimension-optical field on saturated Kerr media using nonlinear Schrödinger equations is described. A model for the envelope one-dimensional evolution equation is built up using the Laplace transform.

Nonlinear Response of a Clean One-Dimensional Wire

2004 ◽  
Vol 92 (3) ◽  
Author(s):  
R. de Picciotto ◽  
L. N. Pfeiffer ◽  
K. W. Baldwin ◽  
K. W. West
Keyword(s):  
Nonlinear Response ◽  
One Dimensional
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