Shape identification in inverse medium scattering problems with a single far-field pattern

Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset \mathbb R^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be H\"older continuous near the corners. If $D\subset \mathbb R^2$ is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions $N \geq 3$, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of non-scattering wavenumbers in domains with corners. As a byproduct, we show that the smoothness conditions in previous corner scattering results are only required near the corners

Çeşitli sıradışı özelliklere sahip üç boyutlu metamalzemelerin hesaplamalı benzetimleri ve gerçeklenmeleri.

In this study, computational analysis and realization of three-dimensional metamaterial structures that induce negative and zero permittivity and/or permeability values in their host environment, as well as plasmonic nanoparticles that are used to design metamaterials at optical frequencies are presented. All these electromagnetic problems are challenging since effective material properties become negative/zero, while numerical solvers are commonly developed for ordinary positive parameters. In real life, three-dimensional metamaterial structures, involving split-ring resonators (SRR), thin wires, and similar subwavelength elements, are designed to exhibit single negativity (imaginary refractive index) and double negativity (negative refractive index) behaviors. However, metamaterial elements have small details with respect to wavelength and they operate when they resonate. Then, their numerical models lead to large matrix equations that are also ill-conditioned, making their solutions extremely difficult, if not impossible. If performed accurately, homogenization simplifies the analysis of metamaterials, while new challenges arise due to extreme parameters. For example, a combination of zero-index (ZI) and near-zero-index (NZI) materials with ordinary media (metals, free space, etc.) results in a high-contrast problem, and numerical instabilities occur particularly due to huge values of wavelength. Similar difficulties arise when considering the plasmonic effects of metals at optical frequencies since they must be modeled as penetrable bodies with negative real permittivity, leading to imaginary index values. Different surface-integral-equation (SIE) formulations and broadband multilevel fast multipole algorithm (MLFMA) implementations are extensively tested for accurate and efficient numerical solutions of ZI, NZI, imaginary-index, and negative-index materials. In addition to their computational simulations, metamaterial designs are fabricated with a low-cost inkjet-printing setup, which is based on using conventional printers that are modified and loaded with silver-based inks. Measurements demonstrate the feasibility of fabricating very low-cost three-dimensional metamaterials using simple inkjet printing.Thesis (M.S.) -- Graduate School of Natural and Applied Sciences. Electrical and Electronics Engineering

Effective Dielectric Tensor for Electromagnetic Wave Propagation in Random Media

We derive exact strong-contrast expansions for the effective dielectric tensor \epeff of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the $n$-point correlation functions of the medium. Our focus is the long-wavelength regime, i.e., when the wavelength is much larger than the scale of inhomogeneities in the medium. Lower-order truncations of these expansions lead to approximations for the effective dielectric constant that depend upon whether the medium is below or above the percolation threshold. In particular, we apply two- and three-point approximations for \epeff to a variety of different three-dimensional model microstructures, including dispersions of hard spheres, hard oriented spheroids and fully penetrable spheres as well as Debye random media, the random checkerboard, and power-law-correlated materials. We demonstrate the importance of employing $n$-point correlation functions of order higher than two for high dielectric-phase-contrast ratio. We show that disorder in the microstructure results in an imaginary component of the effective dielectric tensor that is directly related to the {\it coarseness} of the composite, i.e., local volume-fraction fluctuations for infinitely large windows. The source of this imaginary component is the attenuation of the coherent homogenized wave due to scattering. We also remark on whether there is such attenuation in the case of a two-phase medium with a quasiperiodic structure.Comment: 40 pages, 13 figure