Peculiarities of the wave localization in a three-layered structure consisting of linear media with interfaces characterized by general form of nonlinear response

2019 ◽  
Vol 15 ◽  
pp. 191-198 ◽  
Author(s):  
S.E. Savotchenko
Author(s):  
S. E. Savotchenko

The nonlinear surface waves propagating along the ultra-thin-film layers with nonlinear properties separating three nonlinear media layers are considered. The model based on a stationary nonlinear Schrödinger equation with a nonlinear potential modeling the interaction of a wave with the interface in a short-range approximation is proposed. We concentrated on effects induced by the difference of characteristics of the layers and their two interfaces. The surface waves of three types exist in the system considered. The dispersion relations determining the dependence of surface waves energy on interface intensities and medium layer characteristics are obtained and analyzed. The localization energy is calculated in explicit form for many difference cases. The conditions of the wave localization on dependence of the layer and interface characteristics are derived. The surface waves with definite energies in specific cases existing only in the presence of the interface nonlinear response are found. All results are obtained in an explicit analytical form.


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.


AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1543-1557 ◽  
Author(s):  
Deman Tang ◽  
Denis Kholodar ◽  
Earl H. Dowell

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 962-965
Author(s):  
Abdulmuhsen H. Ali

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