An efficient high-order algorithm for acoustic scattering from penetrable thin structures in three dimensions

This paper presents a high-order accelerated algorithm for the solution of the integral-equation formulation of volumetric scattering problems. The scheme is particularly well suited to the analysis of “thin” structures as they arise in certain applications (e.g., material coatings); in addition, it is also designed to be used in conjunction with existing low-order FFT-based codes to upgrade their order of accuracy through a suitable treatment of material interfaces. The high-order convergence of the new procedure is attained through a combination of changes of parametric variables (to resolve the singularities of the Green function) and “partitions of unity” (to allow for a simple implementation of spectrally accurate quadratures away from singular points). Accelerated evaluations of the interaction between degrees of freedom, on the other hand, are accomplished by incorporating (two-face) equivalent source approximations on Cartesian grids. A detailed account of the main algorithmic components of the scheme are presented, together with a brief review of the corresponding error and performance analyses which are exemplified with a variety of numerical results

Surface-Wave Dispersion Retrieval Method and Synthesis Technique for Bianisotropic Metasurfaces

We propose a surface-wave dispersion retrieval method and synthesis technique that applies to bianisotropic metasurfaces that are embedded in symmetric or asymmetric environments. Specifically, we use general zero-thickness sheet transition conditions to relate the propagation constants of surface-wave modes to the bianisotropic susceptibility components of the metasurface, which can themselves be directly related to its scattering parameters. It is then possible to either obtain the metasurface dispersion diagram from its known susceptibilities or, alternatively, compute the susceptibilities required to achieve a desired surface-wave propagation. The validity of the method is demonstrated by comparing its results to those obtained with exact dispersion relations of well known structures such as the propagation of surface plasmons on thin metallic films. In particular, this work reveals that it is possible to achieve surface-wave propagation only on one side of the metasurface either by superposition of symmetric and asymmetric modes in the case of anisotropic metasurfaces or by completely forbidding the existence of the surface wave on one side of the structure using bianisotropic metasurfaces

Development of 3D electromagnetic modeling tools for airborne vehicles

The main goal of this project is to develop methodologies for scattering by airborne composite vehicles. Although our primary focus continues to be the development of a general purpose code for analyzing the entire structure as a single unit, a number of other tasks are also pursued in parallel with this effort. These tasks are important in testing the overall approach and in developing suitable models for materials coatings, junctions and, more generally, in assessing the effectiveness of the various parts comprising the final code. Here, we briefly discuss our progress on the five different tasks which were pursued during this period. Our progress on each of these tasks is described in the detailed reports (listed at the end of this report) and the memoranda included. The first task described below is, of course, the core of this project and deals with the development of the overall code. Undoubtedly, it is the outcome of the research which was funded by NASA-Ames and the Navy over the past three years. During this year we developed the first finite element code for scattering by structures of arbitrary shape and composition. The code employs a new absorbing boundary condition which allows termination of the finite element mesh only 0.3 lambda from the outer surface of the target. This leads to a remarkable reduction of the mesh size and is a unique feature of the code. Other unique features of this code include capabilities to model resistive sheets, impedance sheets and anisotropic materials. This last capability is the latest feature of the code and is still under development. The code has been extensively validated for a number of composite geometries and some examples are given. The validation of the code is still in progress for anisotropic and larger non-metallic geometries and cavities. The developed finite element code is based on a Galerkin's formulation and employs edge-based tetrahedral elements for discretizing the dielectric sections and the region between the target and the outer mesh termination boundary (ATB). This boundary is placed in conformity with the target's outer surface, thus resulting in additional reduction of the unknown count

Extremely asymmetrical scattering in gratings with varying mean structural parameters

Extremely asymmetrical scattering (EAS) is an unusual type of Bragg scattering in slanted periodic gratings with the scattered wave (the +1 diffracted order) propagating parallel to the grating boundaries. Here, a unique and strong sensitivity of EAS to small stepwise variations of mean structural parameters at the grating boundaries is predicted theoretically (by means of approximate and rigorous analyses) for bulk TE electromagnetic waves and slab optical modes of arbitrary polarization in holographic (for bulk waves) and corrugation (for slab modes) gratings. The predicted effects are explained using one of the main physical reasons for EAS--the diffractional divergence of the scattered wave (similar to divergence of a laser beam). The approximate method of analysis is based on this understanding of the role of the divergence of the scattered wave, while the rigorous analysis uses the enhanced T-matrix algorithm. The effect of small and large stepwise variations of the mean permittivity at the grating boundaries is analysed. Two distinctly different and unusual patterns of EAS are predicted in the cases of wide and narrow (compared to a critical width) gratings. Comparison between the approximate and rigorous theories is carried out.Comment: 16 pages, 5 figure

Exciton-exciton interaction in transition-metal dichalcogenide monolayers

We study theoretically the Coulomb interaction between excitons in transition metal dichalcogenide (TMD) monolayers. We calculate direct and exchange interaction for both ground and excited states of excitons. The screening of the Coulomb interaction, specific to monolayer structures, leads to the unique behavior of the exciton-exciton scattering for excited states, characterized by the non-monotonic dependence of the interaction as function of the transferred momentum. We find that the nontrivial screening enables the description of TMD exciton interaction strength by approximate formula which includes exciton binding parameters. The influence of screening and dielectric environment on the exciton-exciton interaction was studied, showing qualitatively different behavior for ground state and excited states of excitons. Furthermore, we consider exciton-electron interaction, which for the excited states is governed by the dominant attractive contribution of the exchange component, which increases with the excitation number. The results provide a quantitative description of the exciton-exciton and exciton-electron scattering in transition metal dichalcogenides, and are of interest for the design of perspective nonlinear optical devices based on TMD monolayers.Comment: 10 pages, 6 figure

Rigorous analysis of extremely asymmetrical scattering of electromagnetic waves in slanted periodic gratings

Extremely asymmetrical scattering (EAS) is a new type of Bragg scattering in thick, slanted, periodic gratings. It is realised when the scattered wave propagates parallel to the front boundary of the grating. Its most important feature is the strong resonant increase in the scattered wave amplitude compared to the amplitude of the incident wave: the smaller the grating amplitude, the larger the amplitude of the scattered wave. In this paper, rigorous numerical analysis of EAS is carried out by means of the enhanced T-matrix algorithm. This includes investigation of harmonic generation inside and outside the grating, unusually strong edge effects, fast oscillations of the incident wave amplitude in the grating, etc. Comparison with the previously developed approximate theory is carried out. In particular, it is demonstrated that the applicability conditions for the two-wave approximation in the case of EAS are noticeably more restrictive than those for the conventional Bragg scattering. At the same time, it is shown that the approximate theory is usually highly accurate in terms of description of EAS in the most interesting cases of scattering with strong resonant increase of the scattered wave amplitude. Physical explanation of the predicted effects is presented.Comment: 14 pages, 7 figures; v2: corrections to metadata and bibliographical info in preprin

Radio Scintillation due to Discontinuities in the Interstellar Plasma Density

We develop the theory of interstellar scintillation as caused by an irregular plasma having a power-law spatial density spectrum with a spectral exponent of 4 corresponding to a medium with abrupt changes in its density. An ``outer scale'' is included in the model representing the typical scale over which the density of the medium remains uniform. Such a spectrum could be used to model plasma shock fronts in supernova remnants or other plasma discontinuities. We investigate and develop equations for the decorrelation bandwidth of diffractive scintillations and the refractive scintillation index and compare our results with pulsar measurements. We consider both a medium concentrated in a thin layer and an extended irregular medium. We conclude that the discontinuity model gives satisfactory agreement for many diffractive measurements, in particular the VLBI meaurements of the structure function exponent between 5/3 and 2. However, it gives less satisfactory agreement for the refractive scintillation index than does the Kolmogorov turbulence spectrum. The comparison suggests that the medium consists of a pervasive background distribution of turbulence embedded with randomly placed discrete plasma structures such as shocks or HII regions. This can be modeled by a composite spectrum following the Kolmogorov form at high wavenumbers and steepening at lower wavenumbers corresponding to the typical (inverse) size of the discrete structures. Such a model can also explain the extreme scattering events. However, lines of sight through the enhanced scattering prevalent at low galactic latitudes are accurately described by the Kolmogorov spectrum in an extended medium and do not appear to have a similar low-wavenumber steepening.Comment: Accpeted for ApJ vol 531, March 200