Broadband Green's Function and Applications to Fast Electromagnetic Analysis of High-Speed Interconnects

Thesis (Ph.D.)--University of Washington, 2015

Strategies for Inverse Profiling of Two Dimensional Dielectric Scatterers Using Electromagnetic Illumination

Electromagnetic tomography has been applied to problems in nondestructive evolution, ground-penetrating radar, synthetic aperture radar, target identification, electrical well logging, medical imaging etc. The problem of electromagnetic tomography involves the estimation of cross sectional distribution dielectric permittivity, conductivity etc based on measurement of the scattered fields. The inverse scattering problem of electromagnetic imaging is highly non linear and ill posed, and is liable to get trapped in local minima. The iterative solution techniques employed for computing the inverse scattering problem of electromagnetic imaging are highly computation intensive. Thus the solution to electromagnetic imaging problem is beset with convergence and computational issues. The attempt of this thesis is to develop methods suitable for improving the convergence and reduce the total computations for tomographic imaging of two dimensional dielectric cylinders illuminated by TM polarized waves, where the scattering problem is defmed using scalar equations. A multi resolution frequency hopping approach was proposed as opposed to the conventional frequency hopping approach employed to image large inhomogeneous scatterers. The strategy was tested on both synthetic and experimental data and gave results that were better localized and also accelerated the iterative procedure employed for the imaging. A Degree of Symmetry formulation was introduced to locate the scatterer in the investigation domain when the scatterer cross section was circular. The investigation domain could thus be reduced which reduced the degrees of freedom of the inverse scattering process. Thus the entire measured scattered data was available for the optimization of fewer numbers of pixels. This resulted in better and more robust reconstructions of the scatterer cross sectional profile. The Degree of Symmetry formulation could also be applied to the practical problem of limited angle tomography, as in the case of a buried pipeline, where the ill posedness is much larger. The formulation was also tested using experimental data generated from an experimental setup that was designed. The experimental results confirmed the practical applicability of the formulation.

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

New insights on surface-enhanced Raman scattering based on controlled aggregation and spectroscopic studies, DFT calculations and symmetry analysis for 3,6-bi-2-pyridyl-1,2,4,5-tetrazine adsorbed onto citrate-stabilized gold nanoparticles

Asystematic study on the surface-enhanced Raman scattering (SERS) for 3,6-bi-2-pyridyl-1,2,4,5-tetrazine (bptz) adsorbed onto citrate-modified gold nanoparticles (cit-AuNps) was carried out based on electronic and vibrational spectroscopy and density functional methods. The citrate/bptz exchange was carefully controlled by the stepwise addition of bptz to the cit-AuNps, inducing flocculation and leading to the rise of a characteristic plasmon coupling band in the visible region. Such stepwise procedure led to a uniform decrease of the citrate SERS signals and to the rise of characteristic peaks of bptz, consistent with surface binding via the N heterocyclic atoms. In contrast, single addition of a large amount of bptz promoted complete aggregation of the nanoparticles, leading to a strong enhancement of the SERS signals. In this case, from the distinct Raman profiles involved, the formation of a new SERS environment became apparent, conjugating the influence of the local hot spots and charge-transfer (CT) effects. The most strongly enhanced vibrations belong to a(1) and b(2) representations, and were interpreted in terms of the electromagnetic and the CT mechanisms: the latter involving significant contribution of vibronic coupling in the system. Copyright (C) 2010 John Wiley & Sons, Ltd.

Electrochemical Control of the Time-Dependent Intensity Fluctuations in Surface-Enhanced Raman Scattering (SERS)

Time-dependent fluctuations in surface-enhanced Raman scattering (SERS) intensities were recorded from a roughened silver electrode immersed in diluted solutions of rhodamine 6G (R6G) and congo red (CR). These fluctuations were attributed to a small number of SERS-active molecules probing regions of extremely high electromagnetic field (hot spots) at the nanostructured surface. The time-dependent distribution of SERS intensities followed a tailed statistics at certain applied potentials, which has been linked to single-molecule dynamics. The shape of the distribution was reversibly tuned by the applied voltage. Mixtures of both dyes, R6G and CR, at low concentrations were also investigated. Since R6G is a cationic dye and CR is an anionic dye, the statistics of the SERS intensity distribution of either dye in a mixture were independently controlled by adjusting the applied potential. The potential-controlled distribution of SERS intensities was interpreted by considering the modulation of the surface coverage of the adsorbed dye by the interfacial electric field. This interpretation was supported by a two-dimensional Monte Carlo simulation that took into account the time evolution of the surface configuration of the adsorbed species and their probability to populate a hypothetical hot spot. The potential-controlled SERS dynamics reported here is a first step toward the spectroelectrochemical investigation of redox processes at the single-molecule level by SERS.

Technique for improving the reception of scattering signal behind an obstacle

This thesis presents a solution to the problem of receiving a signal in the shadow and fringe areas. Theoretical and experimental investigation of the field behind an obstacle in a line of sight transmission path for UHF / microwave signals has resulted in a new approach to the analysis of electromagnetic fields in the shadow of an obstacle. Analysis using this approach showed the field to consist of varying amplitude and phase distribution. Additional analysis predicted an increase in received signal could be achieved if correlation between the field and antenna structure could be obtained. This was accomplished with a new antenna design. The thesis presents experimental and photographic evidence to support the theory. A novel technique involving the matching of the antenna structure to the field distribution, resulted in an increase of received signal in the diffracted field of up to 4 dB.

alpha alpha scattering in halo effective field theory

We study the two-alpha-particle (alpha alpha) system in an Effective Field Theory (EFT) for halo-like systems. We propose a power Counting that incorporates the subtle interplay of strong and electromagnetic forces leading to a narrow resonance at an energy of about 0.1 MeV. We investigate the EFT expansion in detail, and compare its results with existing low-energy aa phase shifts and previously determined effective-range parameters. Good description of the data is obtained with a surprising amount of fine-tuning. This scenario can be viewed as an expansion around the limit where, when electromagnetic interactions are turned off, the (8)Be ground state is at threshold and exhibits conformal invariance. We also discuss possible extensions to systems with more than two alpha particles. (c) 2008 Elsevier B.V. All rights reserved.

Elastic scattering and the proton form factor

We use the QCD pomeron model proposed by Landshoff and Nachtmann to compute the differential and the total cross-sections for pp scattering in order to discuss a QCD-based approach to the proton form factor. This model is quite dependent on the experimental electromagnetic form factor, and it is not totally clear why this form factor gives good results even at moderate transferred momentum. We exchange the electromagnetic form factor by the asymptotic QCD proton form factor determined by Brodsky and Lepage (BL) plus a prescription for its low energy behavior dictated by the existence of a dynamically generated gluon mass. We fit the data with this QCD inspired form factor and a value for the dynamical gluon mass consistent with the ones determined in the literature. Our results also provide a determination of the proton wave function at the origin, which appears in the BL form factor.

Polarization in fermion scattering

The behaviour of the helicity of an initially left-handed beam of massive fermions first interacting with a Coulomb field and then with a charged scalar particle via a photon exchange is analysed. It is found that in both cases the massive fermions have their helicity flipped, while massless fermions seeem to be unaffected by the electromagnetic field as far as their helicity is concerned.

Electromagnetic gauge field interpolation between the instant form and the front form of the Hamiltonian dynamics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Differential cross sections for elastic and inelastic positronium-hydrogen-atom scattering

A time reversal symmetric regularized electron exchange model was used to elastic scattering, target elastic Ps excitations and target inelastic excitation of hydrogen in a five state coupled model. A singlet Ps-H-S-wave resonance at 4.01 eV of width 0.15 eV and a P-wave resonance at 5.08 eV of width 0.004 eV were obtained using this model. The effect on the convergence of the coupled-channel scheme due to the inclusion of the excited Ps and H states was also analyzed.

Co-deposition of gold nanoparticles and metalloporphyrin using the langmuir-blodgett (LB) technique for Surface-Enhanced Raman Scattering (SERS)

The synergistic effect produced by metallic nanoparticles when incorporated into different systems empowers a research field that is growing rapidly. In addition, organometallic materials are at the center of intensive research with diverse applications such as light-emitting devices, transistors, solar cells, and sensors. The Langmuir-Blodgett (LB) technique has proven to be suitable to address challenges inherent to organic devices, since the film properties can be tuned at the molecular level. Here we report a strategy to incorporate gold nanoparticles (AuNPs) into the LB film by co-deposition in order to achieve surface-enhanced Raman scattering (SERS) of the zinc(II)-protoporphyrin (IX) dimethyl ester (ZnPPIX-DME). Prior to the LB co-deposition, the properties of the Langmuir monolayer of ZnPPIX-DME at the air-water interface, containing AuNPs in the subphase, are studied through the surface-pressure versus mean molecular area (π-A) isotherms. The ZnPPIX-DME+AuNPs π-A isotherm presented a significant shift to higher molecular area, suggesting an interaction between both ZnPPIX-DME molecules and AuNPs. Those interactions are a key factor allowing the co-deposition of both AuNPs and ZnPPIX-DME molecules onto a solid substrate, thus forming the LB film. SERS of ZnPPIX-DME was successfully attained, ensuring the spatial distribution of the AuNPs. Higher enhancement factors were found at AuNP aggregates, as a result of the intense local electromagnetic field found in the metal nanoparticle aggregates. The main vibrational bands observed in the SERS spectra suggest a physical adsorption of the ZnPPIX-DME onto the surface of AuNPs. The latter is not only in agreement with the interactions pointed out by the π-A isotherms but also suggests that this interaction is kept upon LB film co-deposition.

Electromagnetic energy within coated spheres containing dispersive metamaterials

An exact expression is derived for the time-averaged electromagnetic energy within a magneto-dielectric coated sphere, which is irradiated by a plane and time-harmonic electromagnetic wave. Both the spherical shell and core are considered to be dispersive and lossy, with a realistic dispersion relation of an isotropic split-ring resonator metamaterial. We obtain analytical expressions for the stored electromagnetic energies inside the core and the shell separately and calculate their contributions to the total average energy density. The stored electromagnetic energy is calculated for two situations involving a metamaterial coated sphere: a dielectric shell and dispersive metamaterial core, and vice versa. An explicit relation between the stored energy and the optical absorption efficiency is also obtained. We show that the stored electromagnetic energy is an observable sensitive to field interferences responsible for the Fano effect. This result, together with the fact that the Fano effect is more likely to occur in metamaterials with negative refraction, suggest that our findings may be explored in applications.

Quantum motion in superposition of Aharonov-Bohm with some additional electromagnetic fields

The structure of additional electromagnetic fields to the Aharonov-Bohm field, for which the Schrodinger, Klein-Gordon, and Dirac equations can be solved exactly are described and the corresponding exact solutions are found. It is demonstrated that aside from the known cases (a constant and uniform magnetic field that is parallel to the Aharonov-Bohm solenoid, a static spherically symmetrical electric field, and the field of a magnetic monopole), there are broad classes of additional fields. Among these new additional fields we have physically interesting electric fields acting during a finite time or localized in a restricted region of space. There are additional time-dependent uniform and isotropic electric fields that allow exact solutions of the Schrodinger equation. In the relativistic case there are additional electric fields propagating along the Aharonov-Bohm solenoid with arbitrary electric pulse shape. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4714352]