The inverse problem of detecting the shape and location of a rigid scatterer fully embedded in a halfplane based solely on surficial measurements of the scatterer's response to illumination by plane waves, is solved numerically in the frequency domain, using integral equations within the general framework of PDE-constrained optimization. Two different, but closely related, physical problems are considered: first, scatterers embedded in the soil where SH waves are used for detection, and secondly, scatterers embedded in an acoustic fluid, where pressure waves are used for detection. The elastic case of SH waves gives rise to a traction-free surface and an associated Neumann condition, whereas the acoustic case gives rise to a pressure-free surface and a Dirichlet condition, respectively. The measurement stations are sparsely located on the free surface and depending on the physical problem, either displacements are measured (SH case), or fluid velocities (or pressure gradients) are recorded (acoustic case). Localizing and detecting the shape of the scatterer entails matching the observed response to the response resulting from the scatterer's assumed location and shape. There arises a misfit minimization problem that is tackled using a PDE-constrained optimization approach, which, in turn, results in state, adjoint, and control problems, necessary for the satisfaction of the first- order optimality conditions. Boundary integral equations are used throughout, whereas operations over moving interfaces that arise naturally during the iterative search process, are treated using the apparatus of total differentiation.To alleviate inherent difficulties with solution multiplicity, amplitude-based misfits and continuation schemes are used. Numerical results, attesting to the efficacy of the methodology in detecting shapes and localizing scatterers, are discussed. / text

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Simulation tools capable of analyzing electromagnetic (EM) field/wave interactions on complex penetrable scatterers have applications in various areas of engineering ranging from the design of integrated antennas to the subsurface imaging. EM simulation tools operating in the time domain can be formulated to directly solve the Maxwell equations or the integral equations obtained by enforcing fundamental field relations or boundary conditions. Time domain integral equation (TDIE) solvers offer several benefits over differential equation solvers: They require smaller number discretization elements/sampling points (both in space and time). Despite the advantages, TDIE solvers suffer from increased computational cost, stability issues of the time-marching algorithms, and limited applicability to complex scatterers. This thesis is focused on addressing the last two issues associated with time domain volume integral equation (TD-VIE) solvers, as the issue of increased computational cost has been addressed by recently developed acceleration methods. More specifically, four new closely-related, but different marching on-in-time (MOT) algorithms are formulated and implemented to solve the time domain electric and magnetic field volume integral equations (TD-EFVIE and TD-MFVIE). The first algorithm solves the TD-EFVIE to analyze EM wave interactions on high-contrast dielectric scatterers. The stability of this MOT scheme is ensured by using two-sided approximate prolate spherical wave (APSW) functions to discretize the time dependence of the unknown current density as well as an extrapolation scheme to restore the causality of matrix system resulting from this discretization. The second MOT scheme solves the TDMFVIE to analyze EM wave interactions on dielectric scatterers. The TD-MFVIE is cast in the form of an ordinary differential equation (ODE) and the unknown magnetic field is expanded using spatial basis functions. The time-dependent coefficients of this expansion are found by integrating the resulting ODE system using a linear multistep method. The third method is formulated and implemented to analyze EM wave interactions on scatterers with Kerr nonlinearity. The former scheme integrates in time a coupled of system of the TD-EFVIE and the nonlinear constitutive relation, which is cast in the form of an ODE system, for the expansion coefficients of the electric field and flux using a linear multistep method. The last method described in this thesis is developed to analyze EM wave interactions on ferrite scatterers.

A variety of open and closed multi-layered nanoparticle structures have been considered analytically and numerically for their use as scatterers and radiators. These include metamaterial-inspired structures based on dielectrics and metals excited by either plane waves or electric Hertzian dipoles at optical frequencies. Both passive and active (gain impregnated dielectric) materials have been considered. Enhanced and mitigated scattering and radiating effects have been modeled. Nano-antenna and nano-amplifier configurations for optical applications have been emphasized. A review of these modeling efforts will be presented.

Le speckle laser est un effet d'interférence longtemps considéré comme néfaste lors de l'utilisation de sources de lumière cohérente. Cependant, pour certaines applications, cet effet peut être bénéfique et utilisé comme source d'information. C’est le cas du domaine biomédical.Ainsi, le speckle laser est utilisé depuis des décennies pour la surveillance du flux sanguin microvasculaire. Il commence à être considéré aussi pour l'extraction de paramètres de la macrocirculation sanguine. Ce travail vise donc tout d’abord à démontrer que le speckle laser permet d'évaluer les paramètres hémodynamiques de la macrocirculation avec fiabilité et à partir d’une technique identique à celle employée dans l’étude de la microcirculation. Ceci conduira à une intégration rapide du dispositif dans les instruments existants. Par ailleurs, l'un des problèmes les plus importants du speckle laser,empêchant l’obtention d’une analyse totalement quantitative, est l'effet des diffuseurs statiques. Ce type de diffuseurs influence fortement le contraste de speckle, conduisant à une mauvaise interprétation des données. Le second objectif de ce travail est donc d'étudier l'effet des diffuseurs statiques sur la corrélation et le contraste du speckle laser. Nos résultats montrent tout d’abord que le speckle laser est un phénomène intéressant pour extraire les paramètres hémodynamiques de la macrocirculation. Par ailleurs, nos études révèlent que le calcul de la corrélation du speckle laser permet d'estimer le rapport entre diffuseurs statiques / dynamiques avec une bonne fiabilité. En outre, le contraste temporel permet de déterminer les diffuseurs dynamiques possédant des vitesses différentes. / The laser speckle is an interference effect that has been considered as a main drawback in the use of coherent light sources. However, for a specific set of applications, this effect can become a source of information. Among these applications there are the biomedical ones. The laser speckle has been used for decades to monitor microvascular blood flow but only now starts to be considered as a method that can also be used for macrocirculation parameters extraction. This work first aims at demonstrating that laser speckle can be used for macrocirculation assessment with good reliability, using the same technique as the one employed in microcirculation assessment. The use of the same methods could lead to a rapid inclusion of this new evaluation in the existing devices. Furthermore, one of the most important laser speckle issues, that prevents a fully quantitative analysis, is the effect of static scatterers. This type of scatterers strongly influences the speckle contrast, leading to a wrong interpretation of the data. The second objective of this work is to study the effect of statics catterers on the laser speckle correlation and contrast. Our results show that the laser speckle is an interesting phenomenon to extract hemodynamic parameters in the macrocirculation. This work also demonstrates that the laser speckle correlation is able to estimate the ratio between static/dynamic scatterers with good reliability. Moreover, the temporal speckle contrast achieved a very good performance in discerning dynamic scatterers with different velocities.

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In this thesis, coda waves recorded by local seismographic networks will be analyzed to estimate the three-dimensional spatial distribution of scatterers (SDS). This will be done by using the single scattering approximation. This approach leads to a huge system of equations that can not be solved by traditional methods. For the first time, we will use the Simultaneous Iterative Reconstructive Technique (SIRT) to solve this kind of system in seismological applications. SIRT is slow but provides a means to carry out the inversion with greater accuracy. There is also a very fast non-iterative method that allows to carry out the inversion 102 times faster, with a higher resolution and reasonable accuracy: the Filtered Back-Projection (FBP). If one wishes to use this technique it is necessary to adapt it to the geometry of our problem. This will be done for the first time in this thesis. The theory necessary to carry out the adaptation will be developed and a simple expression will be derived to carry out the inversion.FBP and SIRT are then used to determine the SDS in southern India. Results are almost independent of the inversion method used and they are frequency dependent. They show a remarkably uniform distribution of the scattering strength in the crust around GBA. However, a shallow (0-24 km) strong scattering structure, which is only visible at low frequencies, seems to coincide with de Closepet granitic batholith which is the boundary between the eastern and western parts of the Dharwar craton.Also, the SDS is estimated for the Galeras volcano, Colombia. Results reveal a highly non-uniform SDS. Strong scatterers show frequency dependence, which is interpreted in terms if the scale of the heterogeneities producing scattering. Two zones of strong scattering are detected: the shallower one is located at a depth from 4 km to 8 km under the summit whereas the deeper one is imaged at a depth of ~37 km from the Earth's surface. Both zones may be correlated with the magmatic plumbing system beneath Galeras volcano. The second strong scattering zone may be probably related to the deeper magma reservoir that feeds the system.

This thesis investigates analysis and simulation of the backscattering enhancement phenomenon from randomly distributed point scatterers. These point scatterers are randomly distributed within a cube or a sphere and then the backscattering enhancement phenomenon from both cubical and spherical distributions are examined throughout the thesis. The general characteristic differences between cubical and spherical distribution about the scattering phenomenon are observed. T-matrix method is used for analytic investigations of the backscattering enhancement and also a certain number of approximate formulas are obtained. As for Monte Carlo simulation method, it is used for simulated investigations of the backscattering enhancement. Some Monte Carlo simulations are prepared by using MATLAB programming language and verified by showing their confidence intervals. Both analytic and simulated investigations of the backscattering enhancement due to single and double scattering are analyzed / however, only simulated investigation of the backscattering enhancement due to multiple scattering are analyzed because of its computational complexity. The thesis traces differences between single scattering and multiple scattering from randomly distributed point scatterers. Effects of both incident field frequency and point scatterer density on the backscattering enhancement are indicated. The thesis seeks answers to questions such as which conditions cause the backscattering enhancement phenomenon from randomly distributed point scatterers, why we need to consider multiple scattering to examine the backscattering phenomenon and how we can discriminate the backscattering enhancement from the specular enhancement.