Non-perturbative results for the spectrum of surface-disordered waveguides

We calculated the spectrum of normal scalar waves in a planar waveguide with absolutely soft randomly rough boundaries beyond the perturbation theories in the roughness heights and slopes, basing on the exact boundary scattering potential. The spectrum is proved to be a nearly real non-analytic function of the dispersion $\zeta^2$ of the roughness heights (with square-root singularity) as $\zeta^2 \to 0$. The opposite case of large boundary defects is summarized.Comment: REVTEX 3, OSA style, 9 pages, no figures. Submitted to Optics Letter

Dynamics of vibroprotecting system when using controlled damping fluids with hereditary factor

Oscillating system with a damper containing controlled damping fluid with hereditary electrorheological characteristics was investigated. Numerical calculation of the system in quasistationary approximation was carried out to prove the accuracy of applied assumptions

On the parabolic equation method in internal wave propagation

A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The results of numerical experiments on propagation of an incident plane wave over a circular-type shoal are presented in comparison with the analytical result, based on Born approximation.Comment: Submitted to Coastal Engineering. 16 pages, 5 figures. One figure was excluded from article because of size problem

Theory of Tunneling for Rough Junctions

A formally exact expression for the tunneling current, for its separation into specular and diffuse components, and for its directionality, is given for a thick tunnel junction with rough interfaces in terms of the properties of appropriately defined scattering amplitudes. An approximate evaluation yields the relative magnitudes of the specular and diffuse components, and the angular dependence of the diffuse component, in terms of certain statistical properties of the junction interfaces.Comment: 4 page

A New Scheme for Acoustical Tomography of the Ocean

Award #: N00014-95-F-0046 http://www.etl.noaa.gov LONG-TERM GOAL The long-term purpose is to develop a new scheme of the acoustical tomography of the ocean of mesoto global scales which is based on measurements of horizontal-refraction angle (HRA) related to different acoustic modes rather than travel time along different rays. OBJECTIVES To develop robust inversion scheme for retrieving 3-D ocean inner structure based on measurements of HRA. In spite of its small value HRA angle can be easily measured with the help of pair of moderesolving line vertical arrays situated about 10 km apart (ocean interferometer). As a first approximation adiabaticity of mode propagation should be assumed. Then the scheme should be generalized to the case of non-adiabatic propagation with mode interaction taken into account in a "N 2-D" approximation, and appropriate computer simulations should be performed. Scattering of acoustic signals from internal waves should be also considered, and its effect on the accuracy of sound speed field retrieval should be estimated. APPROACH A low frequency tonal sound source (F = 30-100 Hz) is assumed to be towed by a vessel around the area of interest with typical horizontal scale of the order of 1000 km. The transmitted signal is received by acoustic interferometers located inside or outside the area. Thus, the area is exposed from different directions, and HRA is known as a function of source position. Those data are then used for tomography inversion. In the general case, acoustic mode interaction due to water mass inhomogeneity should be taken into account. This is accomplished with the help of iterations. In the first approximation mode interaction is neglected, and HRA are inverted into sound speed profiles assuming adiabatic propagation. The inversion proceeds in two stages: 1) 2-D tomography which retrieves propagation constants of different modes at the nodes of horizontal rectangular grid covering the area. 2) 1-D tomography which retrieves sound speed profile (in terms of expansion with respect to a set of empirical orthogonal functions) at each node of horizontal grid based on already determined values of propagation constants. Then the contribution to horizontal refraction due to mode interaction are calculated with respect to retrieved inhomogeneous medium using propagation code which takes into account mode interactions in

Manifestation of the Roughness-Square-Gradient Scattering in Surface-Corrugated Waveguides

We study a new mechanism of wave/electron scattering in multi-mode surface-corrugated waveguides/wires. This mechanism is due to specific square-gradient terms in an effective Hamiltonian describing the surface scattering, that were neglected in all previous studies. With a careful analysis of the role of roughness slopes in a surface profile, we show that these terms strongly contribute to the expression for the inverse attenuation length (mean free path), provided the correlation length of corrugations is relatively small. The analytical results are illustrated by numerical data.Comment: 13 pages, 3 figure

The PML for rough surface scattering

In this paper we investigate the use of the perfectly matched layer (PML) to truncate a time harmonic rough surface scattering problem in the direction away from the scatterer. We prove existence and uniqueness of the solution of the truncated problem as well as an error estimate depending on the thickness and composition of the layer. This global error estimate predicts a linear rate of convergence (under some conditions on the relative size of the real and imaginary parts of the PML function) rather than the usual exponential rate. We then consider scattering by a half-space and show that the solution of the PML truncated problem converges globally at most quadratically (up to logarithmic factors), providing support for our general theory. However we also prove exponential convergence on compact subsets. We continue by proposing an iterative correction method for the PML truncated problem and, using our estimate for the PML approximation, prove convergence of this method. Finally we provide some numerical results in 2D.(C) 2008 IMACS. Published by Elsevier B.V. All rights reserved

Gradient and Amplitude Scattering in Surface-Corrugated Waveguides

We investigate the interplay between amplitude and square-gradient scattering from the rough surfaces in multi-mode waveguides (conducting quantum wires). The main result is that for any (even small in height) roughness the square-gradient terms in the expression for the wave scattering length (electron mean free path) are dominant, provided the correlation length of the surface disorder is small enough. This important effect is missed in existing studies of the surface scattering.Comment: 4 pages, one figur

The Effect of Random Surface Inhomogeneities on Microresonator Spectral Properties: Theory and Modeling at Millimeter Wave Range

The influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields the method of eigen-mode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering which is the highly responsible for non-dissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object we use dielectric disc resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigen-frequencies and the Q-factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.Comment: 17+ pages, 5 figure

Features in the diffraction of a scalar plane wave from doubly-periodic Dirichlet and Neumann surfaces

The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of the diffracted Bragg beams. From the results of these calculations the diffraction efficiencies of several of the lowest order diffracted beams are calculated as functions of the polar and azimuthal angles of incidence. The angular dependencies of the diffraction efficiencies display features that can be identified as Rayleigh anomalies for both types of surfaces. In the case of a Neumann surface additional features are present that can be attributed to the existence of surface waves on such surfaces. Some of the results obtained through the use of the Rayleigh equation are validated by comparing them with results of a rigorous Green's function numerical calculation.Comment: 16 pages, 5 figure