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Aim of this project is to revolutionize the field of electromagnetic solvers by developing a cutting-edge web application. It leverages the power of multiple programming languages, and frameworks to seamlessly integrate and interact with electromagnetic solvers. Our goal is to provide widespread access to the EM solver through a web-based platform, catering to researchers and engineers. Instead of relying on traditional command-line interfaces, a modern and intuitive graphical user interface (GUI) has been developed. This user-friendly GUI improves the overall experience for users and removes the requirement for specialized knowledge of command line interface. This project acts as a bridge between the user and the EM solver, providing a seamless and intuitive interface to input problem parameters, configure simulations, and visualize results. Users can interact with the solver through a browser, eliminating the need for complex software installations and compatibility issues.

This thesis presents a pioneering study in the remote sensing of sea ice-contaminated with oil, employing sophisticated electromagnetic simulation techniques to enhance detection and analysis capabilities. Central to this research are two critical methodologies: the 2D Finite-Difference Time-Domain (2D-FDTD) method and the Surface Volume Surface-Electric Field Integral Equation (SVS-EFIE) solver, both tailored to address the unique challenges presented by the Arctic environment. Initially, the thesis lays a foundational understanding of the physical, thermodynamic, and electromagnetic properties of sea ice, setting the stage for detailed investigations into how crude oil contamination affects these characteristics. The exploration delves into the interactions between sea ice and crude oil, underpinning the development of remote sensing techniques for environmental monitoring in polar regions. Subsequently, the study introduces a comprehensive approach using the 2D-FDTD method, integrated with Monte Carlo simulations, to model the electromagnetic scattering from multi-layered media, including the rough surfaces characteristic of sea ice. Further advancing the research, the application of the SVS-EFIE solver in full-wave electromagnetic analysis provides a deep dive into the effects of oil contamination on sea ice. Through comparative analyses with commercial solvers, such as FEKO, this thesis validates the effectiveness of the proposed models, showcasing their potential to revolutionize environmental monitoring practices by offering more precise and reliable detection of oil spills in Arctic regions. In summary, this thesis not only enhances the understanding of electromagnetic wave interactions with contaminated sea ice but also advances the field of remote sensing. By developing and validating innovative simulation techniques, specifically the 2D-FDTD method and the SVS-EFIE solver, it contributes significantly to the detection and analysis of environmental hazards

This study presents a promising method for microwave imaging using the mathematical characteristics of the Veselago lens. The Veselago lens is a perfect lens that exhibits unique focusing phenomena. The research aims to achieve several key objectives: 1) to investigate the impact of the Veselago lens in regularizing the ill-posedness of the inverse scattering problem; 2) to formulate a simpler solution to the inverse problem by deriving a regularizing Green's operator that improves matrix conditionality, facilitating inversion; 3) to develop a new mathematical foundation for faster, non-expensive, and non-iterative algorithms; and 4) to enhance the accuracy and spatial resolution of reconstructed images, surpassing the diffraction limit and allowing for sub-wavelength resolution. To accomplish these objectives, a comprehensive study was conducted to understand the implications of incorporating the Veselago lens in the inverse scattering problem associated with microwave imaging. A new Helmholtz equation was derived, and explicit analytic expressions for the corresponding Green's function were obtained. The lens was applied in an imaging scenario with an actual lens, and a novel data equation employing the Veselago lens Green's function was used to solve the inverse problem. Numerical analysis of synthetic data confirmed the efficacy of the new operator, demonstrating superior quality reconstructed images even for small features. The study also introduced novel filtering techniques to address noise in reconstructed images caused by the Veselago lens inverse operator. These techniques utilized truncated Singular Value Decomposition of the operators. Although the physical implementation of a Veselago lens may pose challenges, the research explored the possibility of using a virtual Veselago lens in microwave imaging. A mathematical formulation demonstrated the feasibility of virtualizing the lens utilization, allowing for high-quality imaging without the physical prese

Historically, the design of antenna systems has evolved separately from Shannon theory. Shannon theory adopts a probabilistic approach in the design of communication systems, while antenna design approaches have relied on deterministic Maxwell theory only. This thesis introduces a new approach to the design of broadband antennas/arrays based on information theoretic metrics. The thesis is composed of two parts, where in the first part we will study antennas in the context of the the single-input single-output (SISO) wireless systems. In the second part, the extension is made to study multiple-input multiple-output (MIMO) wireless systems, as well as provide some guidelines for practical implementation. In the SISO setting, to obtain the information-theoretic performance limit, and using ideas from Chu and Bode/Fano theories, I characterize the maximum achievable rate over the SISO wireless communication channels under a restriction on the antenna size at the receiver. I first describe an equivalent Chu's antenna circuit under the physical realizability conditions of its reflection coefficient. The physical realizability conditions are then used to determine the shape of the information-theoretically optimal broadband matching network. I also examine the achievable rate in presence of interference showing that the size constraint is immaterial in interference-limited scenarios. By incorporating the finite antenna size constraint using Chu's theory and under the assumption of canonical-minimum scattering (CMS), I derive the MC between two radiating volumes of fixed sizes. In the MIMO setting, with a simple mathematical extension to account for MC (similar to NFC), I present a model for connected antenna arrays with a large number of tightly integrated antennas in a compact space within the context of masive MIMO communication. The system is refereed to as tightly-coupled massive MIMO. The development shows that tight MC widens the operational bandwidth of antenna arra

Exact solution of the Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) is presented for the problem of radiation in the vicinity of homogeneous dielectric sphere. The solution is obtained via Galerkin Method of Moments (MoM) utilizing rotational and irrotational complete sets of orthogonal vector spherical har- monics as basis and test functions according to the Helmholtz decomposition. In this work, two types of formulations derived from single-source integral equation rep- resentation namely, SVS-EFIE-J and SVS-EFIE-M have been analyzed and solved with the MoM discretization. Excitation in the form of radial and tangential electric dipole situated above the spherical scatterer and the electric field throughout the sphere evaluated via ana- lytic MoM solution of the SVS-EFIE is compared against the exact classical Mie series solution. The two are shown to agree to 12 digits of accuracy upon suffi- cient number of basis/test functions taken in the MoM solution and the Mie series expansion. The exact solution confirms and validates the rigorous nature of the SVS-EFIE formulation. It also reveals the spectral properties of its individual op- erators, their products and their linear combination, as well as the spectrum of the MoM impedance matrix. It is shown that upon choosing basis and test functions in Sobolev space H1/2(S) for SVS-EFIE-J and L2(S) for SVS-EFIE-M, while perform- div ing the testing in the spaces H−1/2(S) and L2(S), respectively, S being the surface of the sphere, the MoM impedance matrix features bounded condition number simi- lar with analogous exact MoM solution of the surface EFIE on perfectly electrically conducting (PEC) sphere and the solution involving MoM of the surface EFIE on perfectly magnetic conductor (PMC). The selection of the proper functional spaces makes proposed SVS-EFIE formulation free of oversampling breakdown. Moreover, both the spectrum of the continuous integral operators of this new magnetic current based

Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving dramatic improvements in performance over their classical counterparts. The potential efficiency of quantum computers is particularly important for numerical simulations, where the capabilities of classical computing systems are often insufficient for the analysis of real-world problems. In this work, we study problems involving the solution of matrix equations, for which there currently exists no efficient, general quantum procedure. We develop a generalization of the Harrow/Hassidim/Lloyd algorithm by providing an alternative unitary for eigenphase estimation. This unitary, which we have adopted from research in the area of quantum walks, has the advantage of being well defined for any arbitrary matrix equation, thereby allowing the solution procedure to be directly implemented on quantum hardware for any well-conditioned system. The procedure is most useful for sparse matrix equations, as it allows for the inverse of a matrix to be applied with O(N_nz log (N)) complexity, where N is the number of unknowns, and N_nz is the total number of nonzero elements in the system matrix. This efficiency is independent of the matrix structure, and hence the quantum procedure can outperform classical methods for many common system types. We show this using the example of sparse approximate inverse (SPAI) preconditioning, which involves the application of matrix inverses for matrices with N_nz = O(N). While these matrices are indeed sparse, it is often found that their inverses are quite dense, and classical methods can require as much as O(N^3) time to apply an inverse preconditioner.

This thesis presents a novel single source-surface integral equation (SSSIE) formulation for 2-D and 3-D electromagnetic fields analysis in complex multilayered media. The new integral equation named SVS-EFIE provides a solution for magneto-quasi-static analysis of 2-D transmission lines above lossy layered substrates. Traditionally, the solution of the modelling current flow in 2-D conductors is obtained through the volume electric field integral equation (V-EFIE) which has unknown current density in the cross-section of conductors. The proposed integral equation is transformed from this classical V-EFIE, and it has single unknown current density on the boundary of the conductors. Further, the pole-residual representation of the 2-D spectrum domain Green's function is introduced to enable evaluation of the required spatial Green's function in closed form in both shielded and open media. SVS-EFIE is also developed for full wave analysis of homogeneous 3-D scattering objects situated in multilayered media. Traditionally, the solution of scattering problems is obtained through the two-source surface integral equations. In this case, the curl operators acting on dyadic Green's functions cannot be eliminated through gradient or divergence theorems. As the result, the derivatives from the curl operator need to be moved into the Sommerfeld integrals and make the convergence of Sommerfeld integrals harder. Unlike the traditional surface integral equations, the new integral equation has only electric field dyadic Green's function due to the single unknown fictitious electric surface current density on the boundary of the scatterer. After moving gradient and divergence operators to the basis and testing functions, the novel layered media integral equation does not have derivatives on the Green's function. Consequently, it can be formulated in Michalski-Zheng's mixed-potential form with the spectrum domain layered medium Green's function in the mixed-potential form obtained f

This thesis focuses on monitoring stored grain through the use of electromagnetic inversion. Electromagnetic inversion is the process of illuminating a target with electromagnetic waves, and from limited field measurements attempting to reconstruct the target. Specifically, we aim to obtain an image of grain/air interface inside metallic-walled bins. Finding the grain/air interface is a starting point for full 3-D imaging of stored grain. The methods currently used to estimate the grain/air interface are computationally expensive, and have not been designed to image non-symmetric grain surfaces. To obtain the grain/air interface we studied and applied linear inversion methods, which are typically good at locating material boundaries (but not the exact permittivity of the materials). We use the linear Orthogonality Sampling Method (OSM), which we show is a specific form of back-propagated imaging. The identification of OSM as a back-propagation technique allows us to formulate the linear imaging problem with an arbitrary Green's function, which is a necessary step as grain bins are made of metallic shapes that do not have analytic Green's functions. To test our proposed technique for finding the grain/air interface, we consider a series of 2-D scalar simulations on both simple rectangular and grain bin-cross section-shaped boundaries. To compute our fields and numerical Green's functions, we use a Discontinuous Galerkin Method (DGM) solver. Initially applying the back-propagation technique in a background material of free space does not lead to reasonable results: images that should show the grain/air interface instead closely resembled the resonant modes of the electromagnetic fields inside the bin. To address this problem, we switch the background medium used in the back-propagation algorithm to closely resemble the permittivity of the grain. In this case, we could obtain reasonable images of the grain/air interface in our simulations. In brief, we show that using

This thesis aims to investigate the use of electromagnetic metasurfaces in microwave imaging (MWI) to provide advantages for the development of imaging systems. In particular, this thesis is focused on two main contributions: (1) the use of absorbing metasurfaces in MWI, and (2) the use of matching metasurfaces in MWI. Firstly, metallic-backed absorbing metasurfaces are proposed to be used as the casing of MWI systems to not only shield the imaging system from external noise but also reduce the reflections from the casing back to the imaging domain. Metasurfaces are thin and light weight, thus making them suitable for portable MWI systems. In addition, metasurfaces at the microwave frequency range can be fabricated using standard printed circuit board (PCB) technology. Using simulated data in Ansys HFSS, we demonstrate the potential of using this type of enclosure for MWI systems. Finally, we fabricate one metallic-backed absorbing metasurface to evaluate its reflectivity. Secondly, matching metasurfaces are investigated for MWI as impedance transformers to more efficiently couple microwave energy into the target. This is important as sufficient interrogation of the target is essential for successful imaging. This will also alleviate the necessity of using coupling liquids in MWI. Similar to the absorbing metasurfaces, matching metasurfaces are also thin, light weight, and easy to manufacture at the microwave frequency range, thus making them suitable for MWI. Using simulated data in Ansys HFSS and an appropriate calibration technique, we demonstrate the possibility of using matching metasurfaces in MWI. Also, one matching metasurface is fabricated and measured to verify its matching performance. For both cases, the disadvantages of using metasurfaces for MWI are discussed. For the metasurfaces that we used in this research, the main disadvantage is their angular dependency, which affects their performance for complex scattering scenarios. The main future work shoul

This thesis focuses on the theory, development, and implementation of a time-harmonic hybridizable discontinuous Galerkin method forward solver. This algorithm is capable of representing the physics and geometry of the problem as high-order polynomial expansions. It computes the scattered electric and magnetic fields on unstructured grids with high-order accuracy, and supports boundary conditions and inhomogeneous backgrounds. The high-order capabilities improve convergence which are examined for both synthetic and experimental problems. Furthermore, the algorithm has been accelerated for modern computing architectures allowing it to scale to large problem sizes. The forward solver is integrated into an existing contrast source inversion algorithm used for radiowave and microwave imaging which improves the modeling capabilities and computational demand. Results of the hybridizable discontinuous Galerkin method forward solver are presented, which show improved capabilities and performance over existing solvers.

This thesis presents the theory and development of a framework for the design of electromagnetic metasurfaces. These metasurfaces can be used to systematically transform an incident electromagnetic field into a different transmitted field, providing new levels of control not typically possible with conventional materials. Although a metasurface is made up of subwavelength scattering elements, it can be macroscopically represented as a homogenized model using effective surface susceptibilities. These tensorial surface susceptibilities define the relationship between the tangential electric and magnetic fields on either side of the metasurface through a set of generalized boundary conditions known as the generalized sheet transition conditions. In this work we concern ourselves with macroscopic metasurface design, the goal of which is to find an appropriate set of surface susceptibilities to support a desired field transformation. Up until now, macroscopic design methods have been mostly limited to ideal cases in which analytical expressions of the input and output fields are fully known. While this limitation is acceptable for simpler applications such as refraction, reflection, or polarization manipulation of plane waves, more general transformations, such as producing a desired far-field radiation pattern, pose a challenge. To address the above limitation, we propose framing macroscopic metasurface design as an electromagnetic inverse source problem. We show that the equivalent currents produced by solving an appropriately constructed inverse source problem are directly related to the tangential transmitted fields required to compute the surface susceptibility parameters that characterize the metasurface. The design method is developed for several different types of field specifications, namely complex (amplitude and phase) fields, phaseless (amplitude-only) power patterns, and far-field performance criteria (e.g., main beam direction, beamwidth, null locations, et

In this thesis, I performed a study on the electromagnetic behaviors of an Electromagnetic Bandgap (EBG) structure with a specific set of parameters, and explored the effects of the geometrical parameters on its bandgap, which can be a stepping stone for designing future EBG structures with desired electromagnetic bandgaps. Later, the performance of a microstrip patch antenna when its ground plane is replaced by a lattice of the studied EBG units is investigated. This led to a noticeable bandwidth and gain enhancement, which motivated me to perform a parameter study to seek further bandwidth improvement. No restriction was placed on the range of parameters, and wider band antennas were observed when parameters fell outside the band gap requirements. Furthermore, I developed methods and designs that can be used to reduce the antenna size and weight by applying some structural modifications. I introduced two antennas, which I named “the puck antenna” and “suspended EBG-backed antenna”. The presented simulation results describe the performance of these antennas. The use of an EBG structure as the ground plane of a microstrip patch antenna is shown here to enhance the gain of the antenna. This motivated me to look for further gain enhancement by placing a dielectric cover on top of the antenna, referred to as “superstrate”. In the literature, the gain enhancement effect of the superstrate on different antennas including microstrip patch antennas has been confirmed. But using a superstrate on an EBG-backed microstrip patch antenna can be considered as another novelty of this thesis project, which led to further gain enhancement.