# Browsing by Author "Smith, David R."

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Item Open Access Advanced Metamaterials for Beamforming and Physical Layer Processing(2023) Pande, DivyaThe design and characterization of electromagnetic metamaterial structures and their constituent subwavelength metamaterial elements are presented. The proposed structures can be employed in beamforming and physical layer processing applications. The common approach for designing such structures involves extracting the effective medium properties of the elements, a methodology inspired by early metamaterial research. The modeling and simulation method is made computationally feasible by assuming a periodic arrangement of the elements. In the case of aperiodic structures, the periodic assumption is no longer valid, and the electromagnetic behavior cannot be predicted accurately. To get a more accurate picture, the electromagnetic properties of individual elements must be evaluated to design a metamaterial structure. In this dissertation, I outline robust steps to realize electromagnetic metamaterial structures by characterizing metamaterial elements without any periodicity assumptions. The subwavelength elements are modeled as electric and magnetic dipoles, and I use dipole-based optimization techniques to design the structures. The dipolar elements are described by their electric and magnetic polarizabilities. Polarizability extraction methods to characterize the different metamaterial elements using numerical simulations are discussed in detail.

In recent years, the coupled dipole model (CDM) has been fully developed to predict the electromagnetic behavior of metamaterial given the element polarizabilities. However, the inverse problem to arrive at the desired medium given some desired behavior is a non-linear problem and can be computationally expensive to solve. Traditionally, holographic methods are used to linearize the problem in the perturbative limits limit to make it computationally tractable. The recently introduced symphotic method solves the non-linear electromagnetic inverse problem efficiently by iteratively solving two linear systems without making any assumptions. This allows one to encode multiple operations in a volume which is not possible with standard computer-generated holography design methods. Here, the two inverse design tools- holography and symphotic are investigated under the dipole framework and validated both numerically and experimentally using different metamaterial structures and corresponding elements.

Item Open Access Compressive holography.(2012) Lim, Se HoonCompressive holography estimates images from incomplete data by using sparsity priors. Compressive holography combines digital holography and compressive sensing. Digital holography consists of computational image estimation from data captured by an electronic focal plane array. Compressive sensing enables accurate data reconstruction by prior knowledge on desired signal. Computational and optical co-design optimally supports compressive holography in the joint computational and optical domain. This dissertation explores two examples of compressive holography : estimation of 3D tomographic images from 2D data and estimation of images from under sampled apertures. Compressive holography achieves single shot holographic tomography using decompressive inference. In general, 3D image reconstruction suffers from underdetermined measurements with a 2D detector. Specifically, single shot holographic tomography shows the uniqueness problem in the axial direction because the inversion is ill-posed. Compressive sensing alleviates the ill-posed problem by enforcing some sparsity constraints. Holographic tomography is applied for video-rate microscopic imaging and diffuse object imaging. In diffuse object imaging, sparsity priors are not valid in coherent image basis due to speckle. So incoherent image estimation is designed to hold the sparsity in incoherent image basis by support of multiple speckle realizations. High pixel count holography achieves high resolution and wide field-of-view imaging. Coherent aperture synthesis can be one method to increase the aperture size of a detector. Scanning-based synthetic aperture confronts a multivariable global optimization problem due to time-space measurement errors. A hierarchical estimation strategy divides the global problem into multiple local problems with support of computational and optical co-design. Compressive sparse aperture holography can be another method. Compressive sparse sampling collects most of significant field information with a small fill factor because object scattered fields are locally redundant. Incoherent image estimation is adopted for the expanded modulation transfer function and compressive reconstruction.Item Open Access Designing and building microwave metamaterials(2009) Liu, RuopengItem Open Access Infrared Metamaterials for Diffractive Optics(2013) Tsai, Yu-JuIntense developments in optical metamaterials have led to a renaissance in several optics fields. Metamaterials, artificially structured media, provide several additional degrees of freedom that cannot be accessed with conventional materials. For example, metamaterials offer a convenient and precise way to explore a wide range of refractive indices, including negative values.

In this dissertation, I introduce the idea of metamaterial based diffractive optics. Merging diffractive optics with metamaterials has several benefits, including access to almost continuous phase profiles and a wide range of available controlled anisotropy. I demonstrate this concept with several examples. I begin with an example of metamaterial based blazed diffraction grating using gradient index metamaterials for

*f*É = 10.6*f*Êm. A series of non-resonant metamaterial elements were designed and fabricated to mimic a saw-tooth refractive index profile with a linear index variation of . The linear gradient profile is repeated periodically to form the equivalent of a blazed grating, with the gradient occurring across a spatial distance of 61*f*Êm. The index gradient is confirmed by comparing the measured magnitudes of the -1, 0 and +1 diffracted orders to those obtained from full wave simulations.In addition to a metamaterial grating, a metamaterial based computer-generated phase hologram was designed by implementing the Gerchberg-Saxton (GS) iterative algorithm to form a 2D phase panel. A three layer metamaterial hologram was fabricated, with the size of 750

*f*Êm ~ 750*f*Êm. Each pixel is comprised of metamaterial elements. This simple demonstration shows the potential for practical applications of metamaterial based diffractive optics.The demand for compact and integrated optoelectronic systems increases the urgency for optical components that can simultaneously perform various functions. This dissertation also presents an optical element capable of multiplexing two diffraction patterns for two orthogonal linear polarizations, based on the use of non-resonant metamaterial cross elements. The metamaterial cross elements provide unique building blocks for engineering arbitrary birefringence. As a proof-of-concept demonstration, I present the design and experimental characterization of a polarization multiplexed blazed diffraction grating and a polarization multiplexed computer-generated hologram, for the telecommunication wavelength of

*f*É = 1.55*f*Êm. A quantitative study of the polarization multiplexed grating reveals that this approach yields a very large polarization contrast ratio. The results show that metamaterials can form the basis for a versatile and compact platform useful in the design of multi-functional photonic devices.The examples I have mentioned only provide a glimpse of the opportunities for metamaterials. I envision more compact optical devices, with greater functionality, being realized with metamaterials.

Item Open Access Metamaterial Waveguide Holography and Optical Bistability(2019) Huang, ZhiqinOver the last twenty years, progress on metamaterials (MMs), defined as three-dimensional artificial composites, has sprouted unprecedented phenomena through the manipulation of electromagnetic, acoustic and other waves, making the connection \textit{from structure to function}. By virtue of their spatial and spectral control of wave-matter interactions, MMs have emerged as a powerful building block for practical applications, including imaging, sensing, energy harvesting, beam shaping and steering, and many more. In recent years, the metasurface, as an alternative to volumetric metamaterials, with its reduced 2D profile, has gained increased attention for applications where weight, power and cost are of importance. In this dissertation, I will mainly explore two optical applications where the flexibility in design of a metasurface provides unique capabilities. In one application, waveguide holography, a multifunctional metasurface is used to couple light from a waveguide to free space, forming multicolor or multipolarization holograms. In the second application, a metasurface is used to enhance optical bistability.

First, in this dissertation I will present an investigation of a multicolor computer-generated hologram (CGH) in an all-dielectric metamaterial waveguide system. Light beams from three different color laser sources (red, green and blue) are coupled into the waveguide via a single period grating without any beam-splitters or prisms. A multicolor holographic image can be decoupled in the far field through a binary CGH without any lenses. This technology enables lens-free, ultra-miniature augmented and virtual reality displays. Then, I will continue to illustrate polarization-selective waveguide holography at optical frequencies based on a similar metamaterial multilayer system. I will show that two orthogonally polarized, spatially separated or overlapped holographic images can be incorporated into a single binary CGH, and use these two images to produce composite, stereo vision, 3D effect images observable using linear or circularly polarized lens glasses. Both polarizations are also used to construct radially and azimuthally polarized beams. The fundamental mode and the second mode of TM and TE modes in the waveguide are used to guide the two polarization states. We envision that incorporating polarization selection into waveguide holograms may be used to realize chip-scale displays and beams for optical trapping.

Furthermore, I will introduce another example of the principle \textit{from structure to function}, optical bistablity, in a film-coupled metasurface system, which is a promising platform for low-energy and all-optical switches. The large field enhancements that can be achieved in the dielectric spacer region between a nanopatch optical antenna and a metallic substrate can substantially enhance optical nonlinear processes. Utilizing a dielectric material that exhibits an optical Kerr effect as the spacer layer, we propose a new simulation method to vividly show the optical bistability processes. We expect this new method to be highly accurate compared with other numerical approaches, such as those based on graphical post-processing techniques, since it self-consistently solves for both the spatial field distribution and the intensity-dependent refractive index distribution of the spacer layer. This method offers an alternative approach to finite-difference time-domain (FDTD) modelling. One of the bistability metasurface designs exhibits exceptionally low switching intensities, corresponding to switching energies on the order of tens of attojoules. We propose our method as an effective tool for designing all-optical switches and modulators.

Item Open Access Metamaterial-Enabled Transformation Optics(2013) Landy, NathanTransformation Optics is a design methodology that uses the form invariance of Maxwell's equations to distort electromagnetic fields. This distortion is imposed on a region of space by mimicking a curvilinear coordinate system with prescribed magnetoelectric material parameters. By simply specifying the correct coordinate transformation, researchers have created such exotic devices as invisibility cloaks, ``perfect'' lenses, and illusion devices.

Unfortunately, these devices typically require correspondingly exotic material parameters that do not occur in Nature. Researchers have therefore turned to complex artificial media known as metamaterials to approximate the desired responses. However, the metamaterial design process is complex, and there are limitations on the responses that they achieve.

In this dissertation, we explore both the applicability and limitations of metamaterials in Transformation Optics design. We begin in Chapter 2 by investigating the freedoms available to use in the transformation optics design process itself. We show that quasi-conformal mappings may be used to alleviate some of the complexity of material design in both two- and three-dimensional design. We then go on in Chapter 3 to apply this method to the design of a transformation-optics modified optic. We show that even a highly-approximate implementation of such a lens would retain many of the key performance feautures that we would expect from a full material prescription.

However, the approximations made in the design of our lens may not be valid in other areas of transformation optical design. For instance, the high-frequency approximations of our lens design ignore the effects of impedance mismatch, and the approximation is not valid when the material parameters vary on the order of a wavelength. Therefore, in Chapter 4 we use other freedoms available to us to design a full-parameter cloak of invisibility. By tailoring the electromagnetic environment of our cloak, we are able to achieve three distinct material responses with a singe metamaterial unit cell. We show the power of our design by experimentally demonstrating a cloak of ten wavelengths in diameter at microwave frequencies.

In addition to these specific examples, we seek a general method to simulate transformation optics devices containing metamaterial inclusions. In Chapter 5, we examine the discrete-approximation, and we apply it to the design of an electromagnetic cloak. We show that the point-dipole description of metamaterial elements allows us to correct for some aberrations that appear when the limits of homogenization are violated.

Finally, we examine so-called ``complementary metamaterials'' and their utility in transformation optics devices. Complementary metamaterials exchange the void and metallized regions of conventional metamaterial elements, and thereby offer a dual response to the electromagnetic field. This duality is attractive because it provides a straightforward method of creating broadband, highly-anisotropic magnetics. We analyze these elements and show that they may be incorporated into our discrete-dipole model. However, we show that the unique characteristics of complementary elements limit their functionality when used as effective materials.

Item Open Access Metamaterials Analysis, Modeling, and Design in the Point Dipole Approximation(2017) Bowen, PatrickThis dissertation is focused on applying the discrete dipole approximation to modeling metamaterial structures and devices. In particular, it is focused on modeling the linear and nonlinear behavior of one particular kind of metasurface, called a film-coupled metasurface. Film-coupled metasurfaces are periodic structures of metamaterial elements where the elements are placed a deeply subwavelength distance away from a metal film. The optical nanopatch antenna is an example of a particularly interesting film-coupled metasurface, and it is explored in depth in this dissertation. Starting with fundamental coupled mode theory approaches, fully predictive, analytic formula are developed that solve for the polarizabilities of the elements, which in turn are used to compute the reflective properties of the metasurface, including the effects of spatial dispersion using the language of effective medium theory. The theory is able to explain Wood's anomalies of the structure from an effective medium standpoint, again using purely analytic results that show excellent agreement with experiments and full-wave simulations. fThe linear optical theory is extended in later chapters to applications in nonlinear optics including bistability and lasing in four-level systems. The final chapter is devoted to solving for surface modes of the structure with complex eigenfrequencies, which may be useful in future work for explaining recent experiments that show lasing in modes that are spatially coherent across the surface.

Modeling other metamaterial devices using the discrete dipole approximation, including radio frequency metamaterial antennas, is discussed in the appendices.

Item Open Access Plasmonic Nanoparticles: Factors Controlling Refractive Index Sensitivity(2007-05-10T15:23:09Z) Miller, Molly McBainPlasmonic nanoparticles support surface plasmon resonances that are sensitive to the environment. Factors contributing to the refractive index sensitivity are explored systematically through simulation, theory, and experiment. Particles small with respect to the wavelength of light and with size parameters much less than 1 have optical properties accurately predicted by quasi-electrostatic theory while particles with larger size parameters necessitate electrodynamics. A theory is developed that captures the effects of geometry on the refractive index sensitivity with a single factor, plasmon band location, and, although based on electrostatic theory, well predicts the sensitivity of particles whose properties are beyond the electrostatic limit. This theory is validated by high quality simulations for compact particles with shape parameters approaching 1 and, therefore, electrodynamic in nature, as well as higher aspect ratio particles that are electrostatic. Experimentally observed optical spectra for nanorods immobilized on glass and subjected to changes in n of the medium are used to calculate the sensitivity of the particles, found to be well matched by a variation on the homogeneous plasmon band theory. The separate electrostatic and electrodynamic components of plasmon band width, are explored and the overall width is found to affect the observability of the aforementioned sensitivity similarly within each particle class. The extent of the sensing volume around a spherical particle is explored and found to vary with particle size for small particles. Through simulation of oriented dielectric layers, it is shown particles are most sensitive to material located in regions of highest field enhancement. Variations on seed-mediated growth of gold nanorods results in spectra exhibiting a middle peak, intermediate to the generally accepted longitudinal and transverse modes. Simulated optical properties and calculated field enhancement illustrates the correlation between geometry and optical properties and allows for identification of the middle peak.