Symmetrical localized states in three-layered structure consisting of linear layer between defocusing media separated by interfaces with nonlinear response

2021 ◽  
Vol 75 (1) ◽  
Author(s):  
S. E. Savotchenko
2019 ◽  
Vol 33 (11) ◽  
pp. 1850127
Author(s):  
S. E. Savotchenko

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.


2020 ◽  
Vol 62 (3) ◽  
pp. 457
Author(s):  
С.Е. Савотченко

The localized states in a three-layer structure consisting of two nonlinear crystals with positive nonlinearity, between which a linear plate of finite thickness is clamped, and the layer interfaces are characterized by a nonlinear response are arised. The frequencies of such localized states are obtained that exist only at different values of the intensity of interaction of the layer interfaces with excitations. The conditions for the existence of such states are found and estimates of the characteristic scale of field localization are obtained.


2019 ◽  
Vol 61 (3) ◽  
pp. 571
Author(s):  
С.Е. Савотченко

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.


Author(s):  
Tai D. Nguyen ◽  
Ronald Gronsky ◽  
Jeffrey B. Kortright

Nanometer period Ru/C multilayers are one of the prime candidates for normal incident reflecting mirrors at wavelengths < 10 nm. Superior performance, which requires uniform layers and smooth interfaces, and high stability of the layered structure under thermal loadings are some of the demands in practical applications. Previous studies however show that the Ru layers in the 2 nm period Ru/C multilayer agglomerate upon moderate annealing, and the layered structure is no longer retained. This agglomeration and crystallization of the Ru layers upon annealing to form almost spherical crystallites is a result of the reduction of surface or interfacial energy from die amorphous high energy non-equilibrium state of the as-prepared sample dirough diffusive arrangements of the atoms. Proposed models for mechanism of thin film agglomeration include one analogous to Rayleigh instability, and grain boundary grooving in polycrystalline films. These models however are not necessarily appropriate to explain for the agglomeration in the sub-nanometer amorphous Ru layers in Ru/C multilayers. The Ru-C phase diagram shows a wide miscible gap, which indicates the preference of phase separation between these two materials and provides an additional driving force for agglomeration. In this paper, we study the evolution of the microstructures and layered structure via in-situ Transmission Electron Microscopy (TEM), and attempt to determine the order of occurence of agglomeration and crystallization in the Ru layers by observing the diffraction patterns.


1972 ◽  
Vol 33 (C3) ◽  
pp. C3-21-C3-25 ◽  
Author(s):  
F. BASSANI

1981 ◽  
Vol 42 (C4) ◽  
pp. C4-383-C4-386 ◽  
Author(s):  
S. G. Bishop ◽  
B. V. Shanabrook ◽  
U. Strom ◽  
P. C. Taylor

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