A method is presented that allows the use of multiresolution principles in a time domain electromagnetic modeling technique that is applicable to general structures. Specifically, methods are presented that are compatible with the multiresolution time-domain (MRTD) technique using Haar basis functions that allow the modeling of general structures without limiting the cell size to the features of the modeled structure. Existing Haar techniques require that cells be homogenous in regard to PECs and other localized effects (with the exception that permeability and permittivity can vary throughout the cell). The techniques that are presented here allow the modeling of these structures using a subcell technique that permits the modeling of these effects at individual equivalent grid points. This is accomplished by transforming the application of the effects at individual points in the grid into the wavelet domain. There are several other contributions that are provided in this work. First, the MRTD technique is derived for a general wavelet basis using a relatively compact vector notation that both makes the technique easier to understand and allows the differences and similarities between different MRTD schemes more apparent. Second, techniques such as the uniaxial perfectly matched layer (UPML) for arbitrary wavelet resolution and non-uniform gridding are presented for the first time. Using these techniques, any structure that can be simulated in Yee-FDTD can be modeled with Haar-MRTD. For the first time, results for the use of a time-and-space-adaptive grid in an MRTD simulation are presented.

Recently, there is strong interest in the through-wall sensing capabilities of radar for use in law enforcement, search and rescue, and urban military operations. Due to the high attenuation of walls, through-wall radar typically operates in the low GHz frequency region, where resolution is limited. It is worthwhile to explore other means of propagating radar waves into and back out of a building’s interior for sensing applications. One possibility is through duct-like structures that are commonly found in a building, such as metal pipes used for plumbing or air conditioning ducts. The objective of this dissertation is to investigate techniques to acquire radar images of targets through a pipe. First, using the pipe as an electromagnetic propagation channel is studied. A modal approach previously developed for computing the radar cross-section of a circular duct is modified to compute the transmission through a pipe. This modal approach for transmission is validated against measured data. It is also shown that a pipe is a high-pass propagation channel. The modal analysis is then extended to two-way, through-pipe propagation for backscattering analysis. The backscattering from a target is observed through a pipe in simulation and measurement. Next, methods to form two-dimensional radar images from backscattering data collected through a pipe are explored. Four different methods previously developed for free-space imaging are applied to the problem of imaging through a pipe: beamforming, matched filter processing, MUSIC, and compressed sensing. In all four methods it is necessary to take into account the propagation through the pipe in order to properly generate a focused radar image. Each method is demonstrated using simulation and validated against measurement data. The beamforming and matched filter methods are found to suffer from poor cross-range resolution. To improve resolution, the MUSIC algorithm is applied and shown to give superior resolution at the expense of more complicated data collection. The final method, compressed sensing, is shown to achieve good cross-range resolution with simpler data collection. A comparison of the tradeoffs between the four methods is summarized and discussed. Two additional extensions are studied. First, a method for computing the transmission through an arbitrary pipe network using the generalized scattering matrix approach is proposed and implemented. Second, a new method for computing joint time-frequency distributions based on compressed sensing is applied to analyze the backscattering phenomenology from a pipe. / text

The current options for wireless signal prediction in indoor scenarios generally either lack precision or require immense computational resources. Thus, a new method is proposed that attempts to consolidate the desired accuracy with an easy to implement and time efficient scheme. This work identifies and takes advantage of dominant physical qualities of indoor environments to solve indoor channel problems using a hybrid of numerical and analytical approaches. Specifically, the guiding effect of hallway structures is investigated as they allow electromagnetic fields to propagate with relatively low attenuation. Combining waveguide mode analysis and rigorous numerical techniques, the proposed prediction model computes the hallway fields in a large building floorplan both quickly and with good accuracy in comparison to full finite-difference simulations. Signal measurement data will also be used to verify the applicability of the model.

This dissertation describes research conducted on the development and improvement of microwave tomography algorithms for imaging the bulk-electrical parameters of unknown objects. The full derivation of a new inversion algorithm based on the state-of-the-art contrast source inversion (CSI) algorithm coupled to a finite-element method (FEM) discretization of the Helmholtz differential operator formulation for the scattered electromagnetic field is presented. The algorithm is applied to two-dimensional (2D) scalar and vectorial configurations, as well as three-dimensional (3D) full-vectorial problems. The unknown electrical properties of the object are distributed on the elements of arbitrary meshes with varying densities. The use of FEM to represent the Helmholtz operator allows for the flexibility of having an inhomogeneous background medium, as well as the ability to accurately model any boundary shape or type: both conducting and absorbing. The CSI algorithm is used in conjunction with multiplicative regularization (MR), as it is typical in most implementations of CSI. Due to the use of arbitrary meshes in the present implementation, new techniques are introduced to perform the necessary spatial gradient and divergence operators of MR. The approach is different from other MR-CSI implementations where the unknown variables are located on a uniform grid of rectangular cells and represented using pulse basis functions; with rectangular cells finite-difference operators can be used, but this becomes unwieldy in FEM-CSI. Furthermore, an improvement for MR is proposed that accounts for the imbalance between the real and imaginary parts of the electrical properties of the unknown objects. The proposed method is not restricted to any particular formulation of the contrast source inversion. The functionality of the new inversion algorithm with the different enhancements is tested using a wide range of synthetic datasets, as well as experimental data collected by the University of Manitoba electromagnetic imaging group and research centers in Spain and France.

<p>If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers and oscillators. By applying this set of tools and knowledge to microwave metamaterials, I experimentally confirm several novel nonlinear phenomena. Most notably, I construct a backward wave nonlinear medium from varactor-loaded split ring resonators loaded in a rectangular waveguide, capable of generating second-harmonic opposite to conventional nonlinear materials with a conversion efficiency as high as 1.5\%. In addition, I confirm nonlinear magnetoelectric coupling in two dual gap varactor-loaded split ring resonator metamaterials through measurement of the amplitude and phase of the second-harmonic generated in the forward and backward directions from a thin slab. I then use the presence of simultaneous nonlinearities in such metamaterials to observe nonlinear interference, manifest as unidirectional difference frequency generation with contrasts of 6 and 12 dB in the forward and backward directions, respectively. Finally, I apply these principles and intuition to several plasmonic platforms with the goal of achieving similar enhancements and configurations at optical frequencies. Using the example of fluorescence enhancement in optical patch antennas, I develop a semi-classical numerical model for the calculation of field-induced enhancements to both excitation and spontaneous emission rates of an embedded fluorophore, showing qualitative agreement with experimental results, with enhancement factors of more than 30,000. Throughout these series of works, I emphasize the indispensability of effective design and retrieval tools in understanding and optimizing both metamaterials and plasmonic systems. Ultimately, when weighed against the disadvantages in fabrication and optical losses, the results presented here provide a context for the application of nonlinear metamaterials within three distinct areas where a competitive advantage over conventional materials might be obtained: fundamental science demonstrations, linear and nonlinear anisotropy engineering, and extremely compact resonant all-optical devices.</p> / Dissertation

This dissertation describes research conducted on the development and improvement of microwave tomography algorithms for imaging the bulk-electrical parameters of unknown objects. The full derivation of a new inversion algorithm based on the state-of-the-art contrast source inversion (CSI) algorithm coupled to a finite-element method (FEM) discretization of the Helmholtz differential operator formulation for the scattered electromagnetic field is presented. The algorithm is applied to two-dimensional (2D) scalar and vectorial configurations, as well as three-dimensional (3D) full-vectorial problems. The unknown electrical properties of the object are distributed on the elements of arbitrary meshes with varying densities. The use of FEM to represent the Helmholtz operator allows for the flexibility of having an inhomogeneous background medium, as well as the ability to accurately model any boundary shape or type: both conducting and absorbing. The CSI algorithm is used in conjunction with multiplicative regularization (MR), as it is typical in most implementations of CSI. Due to the use of arbitrary meshes in the present implementation, new techniques are introduced to perform the necessary spatial gradient and divergence operators of MR. The approach is different from other MR-CSI implementations where the unknown variables are located on a uniform grid of rectangular cells and represented using pulse basis functions; with rectangular cells finite-difference operators can be used, but this becomes unwieldy in FEM-CSI. Furthermore, an improvement for MR is proposed that accounts for the imbalance between the real and imaginary parts of the electrical properties of the unknown objects. The proposed method is not restricted to any particular formulation of the contrast source inversion. The functionality of the new inversion algorithm with the different enhancements is tested using a wide range of synthetic datasets, as well as experimental data collected by the University of Manitoba electromagnetic imaging group and research centers in Spain and France.

<p>In this dissertation, the spectral element method is developed to simulate electromagnetic field in nano-structure consisting of dielectric, metal or semiconductor. The spectral element method is a special kind of high order finite element method, which has spectral accuracy. When the order of the basis function increases, the accuracy increases exponentially. The goal of this dissertation is to implement the spectral element method to calculate the electromagnetic properties of various semiconductor nano-structures, including photonic crystal, photonic crystal slab, finite size photonic crystal block, nano dielectric sphere. The linear electromagnetic characteristics, such as band structure and scattering properties, can be calculated by this method with high accuracy. In addition, I have explored the application of the spectral element method in nonlinear and quantum optics. The effort will focus on second harmonic generation and quantum dot nonlinear dynamics. </p><p>The electromagnetic field can be simulated in both frequency domain and time domain. Each method has different application for research and engineering. In this dissertation, the first half of the dissertation discusses the frequency domain solver, and the second half of the dissertation discusses the time domain solver.</p><p>For frequency domain simulation, the basic equation is the second order vector Helmholtz equation of the electric field. This method is implemented to calculate the band structure of photonic crystals consisting of dielectric material as well as metallic materials. Because the photonic crystal is periodic, only one unit cell need to be simulated in the computational domain, and a periodic boundary condition is applied. The spectral accuracy is inspected. Adding the radiation boundary condition at top and bottom of the computational region, the scattering properties of photonic crystal slab can be calculated. For multiple layers photonic crystal slab, the block-Thomas algorithm is used to increase the efficiency of the calculation. When the simulated photonic crystals are finite size, unlike an infinitely periodic system, the periodic boundary condition does not apply. In order to increase the efficiency of the simulation, the domain decomposition method is implemented. </p><p>The second harmonic generation, which is a kind of nonlinear optical effect, is simulated by the spectral element method. The vector Helmholtz equations of multiple frequencies are solved in parallel and the consistence solution with nonlinear effect is obtained by iterative solver. The sensitivity of the second harmonic generation to the thickness of each layer can be calculated by taking the analytical differential of the equation to the thickness of each element. </p><p>The quantum dot dynamics in semiconductor are described by the Maxwell-Bloch equations. The frequency domain Maxwell-Bloch equations are deduced. The spectral element method is used to solve these equations to inspect the steady state quantum dot dynamic behaviors under the continuous wave electromagnetic excitation.</p><p>For time domain simulation, the first order curl equations in Maxwell equations are the basic equations. A spectral element method based on brick element is implemented to simulate a nano-structure consisting of woodpile photonic crystal. The resonance of a micro-cavity consisting of a point defect in the woodpile photonic crystal block is simulated. In addition, the time domain Maxwell-Bloch equations are implemented in the solver. The spontaneous emission process of quantum dot in the micro-cavity is inspected. </p><p>Another effort is to implement the Maxwell-Bloch equations in a previously implemented domain decomposition spectral element/finite element time domain solver. The solver can handle unstructured mesh, which can simulate complicated structure. The time dependent dynamics of a quantum dot in the middle of a nano-sphere are investigated by this implementation. The population inversion under continuous and pulse excitation is investigated. </p><p>In conclusion, the spectral element method is implemented for frequency domain and time domain solvers. High efficient and accurate solutions for multiple layers nano-structures are obtained. The solvers can be applied to design nano-structures, such as photonic crystal slab resonators, and nano-scale semiconductor lasers.</p> / Dissertation

This thesis presents a full-vectorial mode matching method for whispering gallery microcavity analysis. With this technique, optical properties such as resonance wavelength, quality factor and electromagnetic field distribution of an arbitrarily shaped microcavity can be computed with high accuracy. To illustrate this, a mode matching analysis that involves a single propagating whispering gallery mode is performed on a microtoroid in the presence of individual nonplasmonic nanoparticle on its surface. This method is also extended to the analysis of cavity adsorbed by a plasmonic nanoparticle at a wavelength close to plasmon resonance where the resulting field distortion invalidates other approaches. The simulation demonstrates high efficiency and is in close agreement with experimental measurements reported in previous work. Furthermore, we extend our mode matching analysis to the case where multiple whispering gallery modes are involved in the course of light propagation. The new formalism is performed on a cavity-waveguide coupling system to investigate the light delivery from a tapered optical waveguide to a microcavity at high precision. A novel hybrid integration scheme to implement an ultra-high quality factor microcavity on a silicon-on-insulator platform is proposed based on the related modelling results. / Graduate / 0752 / 0544 / duxuanmax@gmail.com

The current options for wireless signal prediction in indoor scenarios generally either lack precision or require immense computational resources. Thus, a new method is proposed that attempts to consolidate the desired accuracy with an easy to implement and time efficient scheme. This work identifies and takes advantage of dominant physical qualities of indoor environments to solve indoor channel problems using a hybrid of numerical and analytical approaches. Specifically, the guiding effect of hallway structures is investigated as they allow electromagnetic fields to propagate with relatively low attenuation. Combining waveguide mode analysis and rigorous numerical techniques, the proposed prediction model computes the hallway fields in a large building floorplan both quickly and with good accuracy in comparison to full finite-difference simulations. Signal measurement data will also be used to verify the applicability of the model.

The discontinuous Galerkin method (DGM) is applied to a number of problems in computational electromagnetics. This is achieved by obtaining numerical solutions to Maxwell's equations using the DGM. The aim of these simulations is to highlight the strengths of the method while showing its resilience in handling problems other schemes may not be able to accurately model. Although no method will ever be the best choice for every problem in electromagnetics, the discontinuous Galerkin method is able to accurately approximate any problem, although the computational costs can make the scheme impractical for some. Like other time domain schemes, the DGM becomes inefficient on large domains where the solution contains small wavelengths. We demonstrate that all of the different types of boundary conditions in electromagnetic wave propagation can be implemented into the DGM. Reflection and transmission boundaries fit easily into the framework, whereas perfect absorption requires a more advanced technique known as the perfectly matched layer. We begin by simulating mirrors with several different geometries, and analyze how the DGM method performs, and how it offers a more complete evaluation of the behavior in this problem than some other methods. Since Maxwell's equations describe the macroscopic features of electromagnetics, our simulations are able to capture the wave features of electromagnetics, such as interference and diffraction. We demonstrate this by accurately modelling Young's double slit experiment, a classic experiment which features well understood interference and diffraction phenomena. We also extend the basic electromagnetic wave propagation simulations to include situations where the waves travel into new media. The formulation of the DGM for Maxwell's equations allows the numerical solutions to accurately resolve the features at the interface of two media as predicted by the Fresnel coefficients. This allows the DGM to model lenses and other sources of refraction. We predict that the DGM will become an increasingly valuable method for computational electromagnetics because of its wide range of applicability as well as the lack of undesirable features in the numerical solutions. Furthermore, the only limiting factor for applying DGM, its computational cost, will become less influential as computing power continues to increase, allowing us to apply the DGM to an increasing set of applications.