The term “metamaterials” refers to engineered structures that interact with electromagnetic fields in an unusual but controllable way that cannot be observed with natural materials. Metamaterial design at optical frequencies oftentimes makes of controllable plasmonic interactions. Light can excite collective oscillations of conduction band electrons on a metallic nanostructure. These oscillations result in localized surface plasmon modes which can provide high confinement of fields at metal-dielectric interfaces at nanoscale. Additionally scattering and absorption characteristics of plasmon modes can be controlled by geometrical features of the metallic nanostructures. This ease of controllability has lead to the development of new concepts in light manipulation and enhancement of light-material interactions. Fano resonance and plasmonic induced transparency (PIT) are among the most promising of those. The interference between different plasmon modes induced on nanostructures generates PIT/Fano resonance at optical frequencies. The unusual dispersion characteristics observed within the PIT window can be used for designing optical metamaterials to be used in various applications including bio-chemical sensing, slow light, modulation, perfect absorption, and all-optical switching. This thesis focuses on design of novel plasmonic devices to be used in these applications. The fundamental idea behind these designs is the generation of higher-order plasmon modes, which leads to PIT/Fano resonance-like output characteristics. These are then exploited together with dynamic tunability supported by graphene and field enhancement provided by nonlinear materials to prototype novel plasmonic devices. More specifically, this thesis proposes the following plasmonic device designs. I. Nano-disk Fano resonator: Open disk-like plasmonic nanostructures are preferred for bio-chemical sensing because of their higher capacity to be in contact with greater volumes of analyte. High effective refractive index required by sensing applications is achieved though the dispersion characteristics within PIT window. Higher order modes required for Fano resonance are generated through geometrical symmetry breaking by embedding a shifted and elongated cavity into a circular disk. The resulting dual band PIT can be geometrically tuned by varying the cavity's width and rotation angle. II. Tunable Terahertz Fano resonator: The possibility to dynamically tune graphene's conductivity has made it an attractive choice over conventional noble metals to generate surface plasmon modes at Terahertz frequencies. Subsequently, a polarization-independent and dynamically tunable hybrid gold-graphene structure is designed to achieve PIT/Fano resonance by allowing graphene and metallic plasmon modes to interfere. The effective group index of the resulting resonator is found to be very high (ng=1400, several times higher than all previously reported PIT devices) within the PIT window. Dynamic tunability achieved through a gate voltage applied to graphene suggests applications in switching. III. Tunable Terahertz Fano absorber: Many photonic and optical devices rely on their ability to efficiently absorb an incoming electromagnetic field. The absorption in atomically thin graphene sheet is already very high i.e., “2.3%” per layer. However, considering its atomic thickness graphene sheet remains practically transparent to Terahertz waves. The proposed absorber design makes of an asymmetrically patterned graphene layer that supports higher order plasmon modes at Terahertz frequencies. Several of these patterned layers backed by dielectric substrates are stacked on top of each other followed by reflector screen. The dynamically controllable resonances from each graphene layer and the spacing between them are fine tuned to achieve a large bandwidth of 6.9 Terahertz (from 4.7 to 11.6 Terahertz) for over 90% absorption, which is significantly higher than that of existing metallic/graphene absorbers. IV. Three state all-optical switch: The plasmonic resonances are extremely sensitive to dielectric properties of the surrounding medium. A slight change in the dielectric constant near the metal surface results in a significant change in the plasmonic resonance. This sensitivity is enhanced in the presence of a nonlinear change in the dielectric constant. To make use of this effect, Fano resonator is used in conjunction with a Kerr nonlinear material. The resulting resonator exploits multiple (higher order) surface plasmons to generate a multi-band tri-stable response in its output. This cannot be obtained using existing nonlinear plasmonic devices that make use of single mode Lorentzian resonances. Multi-band three-state optical switching that can be realized using the proposed resonator has potential applications in optical communications and computing.

Efficient computation in deterministic and uncertain electromagnetic propagation environments, tackled by parabolic equation methods, is the subject of interest of this dissertation. Our work is comprised of two parts. In the first part we determine efficient absorbing boundary conditions for propagation over deterministic terrain and in the second part we study techniques for efficient quantification of random parameters/outputs in volume and surface based electromagnetic problems. Domain truncation by transparent boundary conditions for open problems where parabolic equation is utilized to govern wave propagation are in general computationally costly. For the deterministic problem, we utilize two approximations to a convolution-in-space type discrete boundary condition to reduce the cost, while maintaining accuracy in far range solutions. Perfectly matched layer adapted to the Crank-Nicolson finite difference scheme is also verified for a 2-D model problem, where implemented results and stability analyses for different approaches are compared. For the random problem, efficient moment calculation of electromagnetic propagation/scattering in various propagation environments is demonstrated, where the dimensionality of the random space varies from N = 2 to N = 100. Sparse grid collocation methods are used to obtain expected values and distributions, as a non-intrusive sampling method. Due to the low convergence rate in the sparse grid methods for moderate dimensionality and above, two different adaptive strategies are utilized in the sparse grid construction. These strategies are implemented in three different problems. Two problems are concerned with uncertainty in propagation domain intrinsic parameters, whereas the other problem has uncertainty in the boundary shape of the terrain, which is realized as the perfectly conducting (PEC) Earth surface.

The synthesis and physical characterization of a series of poly(p-phenylene vinylene-co-2,5-thienylene vinylene) (PPV-co-PTV) were reported. The synthetic route used was a variation on the Wessling route to poly(p-phenylene vinylene) which involved a precursor polymer. The copolymeric nature of the materials produced were investigated by IR analyses of the trans-vinylene absorption of these systems. The results of the attempts to produce other polyarylene vinylene (PAV) copolymers were also reported. The conductivity and orientational properties of PPV-co-PTV in comparison with those of the blends of poly(p-phenylene vinylene) (PPV) and poly(2,5-thienylene vinylene) (PTV) were investigated. The interrelation of the PTV contents, sequence distributions, conductivities, draw ratios, morphology and order parameters for the copolymers and blends were discussed. The effects due to the random copolymeric nature of PPV-co-PTV were emphasized.

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Microwave imaging has been used to observe optically obscured targets for over 40 years. Recently, there has been a push towards developing a microwave imaging technology for use in medical diagnostics. Microwave imaging technology has several advantages over current imaging modalities, including use of nonionizing radiation, and compact inexpensive electronics. However, no microwave diagnostic technology exists yet for clinical use. This is due to complications in estimating the complex near-field scattering of the microwave radiation. Recently, advancements in a direct inversion algorithm known as microwave holography have adapted it to operate on near-field measurements. This method, with simulations, has demonstrated the ability to estimate the relative permittivity of the imaged structures. The purpose of this work is to develop quantitative microwave holography for use in tissue imaging. In addition to the previous version of quantitative microwave holography using the Born approximation, a new version of the method using Rytov's approximation is derived, expanding the versatility of the algorithm. Filtering strategies are also developed to enhance the image-reconstruction quality. However, nonphysical permittivity values are still generated. One possible solution is a constrained optimization strategy, which is derived and implemented. Finally, experimental studies demonstrate the ability of quantitative microwave holography to produce reconstructions of several tissue phantoms. / Thesis / Master of Applied Science (MASc)

In the field of antenna design and analysis, often the need arises to numerically extrapolate the far-zone performance of a radiating structure from its known (or assumed known) near-zone electromagnetic field. Mathematical processes developed to accomplish such a task are known in the literature as near-zone to far-zone transformations (NZ-FZTs) as well as near-field far-field (NF-FF) transformations. These processes make use of sampled near-zone field quantities along some virtual surface, viz., the transformation surface, that surrounds the radiating structure of interest. Depending upon the application, samples of the required near-zone field quantities are supplied via analytical, empirical, or computational means. Over the years, a number of NZ-FZT processes have been developed to meet the demands of many applications. In short, their differences include, but are not limited to, the following: (1) the size and shape of the transformation surface, (2) the required near-zone field quantities and how they are sampled, (3) the computational methodology used, and (4) the imbedding of various application-driven features. Each process has its pros and cons depending upon its specific application as well as the type of radiation structure under consideration. In this dissertation we put forth a new and original NZ-FZT process that allows the transformation surface along which the near-zone is sampled to be spheroidal in shape: namely a prolate or oblate spheroid. Naturally, there are benefits gained in doing so. Our approach uses a formulated eigenfunction expansion of spheroidal wave-harmonics to develop two distinct, yet closely related, NZ-FZT algorithms for each type of spheroidal transformation surface. The process only requires knowledge of the E-field along the transformation surface and does not need the corresponding H-field. Given is a systematic exposition of the formulation, implementation, and verification of the newly developed NZ-FZT process. Accordingly, computer software is developed to implement both NZ-FZT algorithms. In the validation process, analytical and empirical radiation structures serve as computational benchmarks. Numerical models of both benchmark structures are created by integrating the software with a field solver, viz., a finite-difference time-domain (FDTD) code. Results of these computer models are compared with theoretical and empirical data to provide additional validation. / Ph. D.

In many applications, it is necessary to simulate wave scattering from surfaces that have small radii of curvature relative to the incident wavelength. Surface features smaller than an electromagnetic wavelength are known to create diffracted fields over a wide range of scattering angles. In this thesis, the significance of such effects at low grazing angles with the presence of an extended planar surface is considered. The magnetic field integral equation (MFIE) describing the currents on such surfaces is used to solve for the bistatic scattered fields. The integral equations are discretized using the moment method and solved using the Method of Ordered Multiple Interactions (MOMI) iterative procedure. This thesis will concentrate on normal incidence and low grazing angle (LGA) incidence, specifically an incident angle of 80 degrees. The surface used in the analysis is a one-dimensional, perfectly-conducting wedge-on-a-plane with a varying radius of curvature at the wedge tip and Gaussian tails that smoothly extend the wedge to the plane surface. This surface displays continuous first and second derivatives over the entire surface. The radius of curvature at the wedge tip is varied between 0.0125 wavelengths and 8 wavelengths. The form of the bistatic scattered fields will be investigated for three different wedge height to wedge width geometries. The surface scattering mechanisms and their respective location and form in the scattered field will be discussed. The dependence of the scattered field pattern on the radius of curvature at the wedge tip and the beam width of the incident field will be considered. The difficulties associated with using a numerical technique on extended surfaces where a significant source of diffracted energy is present will also be examined. This includes the issue of sampling a surface that contains areas of small radii of curvature and the issue of surface truncation when significant currents due to tip diffraction are produced well outside the illuminated area. Both TE (VV) and TM (HH) polarization will be considered. This thesis also analyzes the scattered fields for a perfect electric conducting (PEC) ridge and well in the presence of an extended planar surface for an incident angle of 70 degrees. The dual-surface magnetic field integral equation (DMFIE) formulation for a one-dimensional extended surface will be used to solve for the unknown currents on the surface of the scatterer. The DMFIE formulation leads to a second kind integral equation that can be solved via the MOMI series with the proper choice of the parameters appearing in the DMFIE formulation. The bistatic scattered fields for several ridge and well geometries are examined for both TE and TM polarization. / Master of Science

Higher-order basis functions are widely used to model currents and fields in numerical simulations of electromagnetics problems because of the greater accuracy and computational efficiency they can provide. Different problem formulations, such as method of moments (MoM) and the finite element method (FEM) require different constraints on basis functions for optimal performance, such as normal or tangential continuity between cells. In this thesis, a method of automatically generating bases that satisfy the desired basis constraints is applied to a MoM formulation for scattering problems using surface integral equations. Numerical results demonstrate the accuracy of this approach, and show good system matrix conditioning when compared to other higher-order bases.