Topology optimization of cables, cloaks, and embedded lattices

Materials play a critical role in the behavior and functionality of natural and engineered systems. For example, the use of cast-iron and steel led to dramatically increased bridge spans per material volume with the move from compression-dominant arch bridges to tensile-capable truss, suspension, and cable-stayed bridges; materials underlie many of the major technological advancements in the auto and aerospace industries that have made cars and airplanes increasingly light, strong, and damage tolerant; and the great diversity of biological materials and bio-composites enable complex biological and mechanical functions in nature. Topology optimization is a computational design method that simultaneously enhances efficiency and design freedom of engineered parts, but is often limited to a single, solid, isotropic, linear-elastic material. To understand how the material space can be tailored to enhance design freedom and/or promote desired mechanical behavior, several topology optimization problems are explored in this dissertation in which the space of available materials is either relaxed or restricted. Specifically, in a discrete topology optimization setting defined by 1D (truss) elements, tension-only systems are targeted by restricting the material space to that of a tension-only material and tailoring a formulation to handle the associated nonlinear mechanics. The discrete setting is then enhanced to handle 2D (beam) elements in pursuit of cloaking devices that hide the effect of a hole or defect on the elastostatic response of lattice systems. In this case the material space is relaxed to allow for a continuous range of stiffness and the objective is formulated as a weighted least squares function in which the physically-motivated weights promote global stiffness matching between the cloaked and undisturbed systems. Continuous 2D and 3D structures are also explored in a density-based topology optimization setting in which the material space is relaxed to accommodate an arbitrary number of candidate materials in a general continuum mechanics framework that can handle material anisotropy. The theoretical and physical relevance of such framework is highlighted via a continuous embedding scheme that enables manufacturing in the relaxed (or restricted) design space of lattice-based microstructural-materials. Implications of varying the material design space on the mechanics, mathematics, and computations needed for topology optimization are discussed in detail.Ph.D

Polarization State Manipulation of Electromagnetic Waves with Metamaterials and Its Applications in Nanophotonics

Polarization state is an important characteristic of electromagnetic waves. The arbitrary control of the polarization state of such wave has attracted great interest in the scientific community because of the wide range of modern optical applications that such control can afford. Recent advances in metamaterials provide an alternative method of realizing arbitrary manipulation of polarization state of electromagnetic waves in nanoscale via ultrathin, miniaturized, and easily integrable designs. In this chapter, we give a review of recent developments on polarization state manipulation of electromagnetic waves in metamaterials and discuss their applications in nanophotonics, such as polarization converter, wavefront controller, information coding, and so on

A review of dielectric optical metasurfaces for wavefront control

During the past few years, metasurfaces have been used to demonstrate optical elements and systems with capabilities that surpass those of conventional diffractive optics. Here, we review some of these recent developments, with a focus on dielectric structures for shaping optical wavefronts. We discuss the mechanisms for achieving steep phase gradients with high efficiency, simultaneous polarization and phase control, controlling the chromatic dispersion, and controlling the angular response. Then, we review applications in imaging, conformal optics, tunable devices, and optical systems. We conclude with an outlook on future potentials and challenges that need to be overcome

Doctor of Philosophy

dissertationMicrowave/millimeter-wave imaging systems have become ubiquitous and have found applications in areas like astronomy, bio-medical diagnostics, remote sensing, and security surveillance. These areas have so far relied on conventional imaging devices (empl

Geometric optical metasurface for polarization control

Like amplitude and phase, polarization is one of the fundamental properties of light. Controlling polarization in a desirable manner is fundamental to science and technology. However, practical applications based on polarization manipulation are mainly hindered by the complexity of experimental system, bulky size and poor spatial resolution. In recent years, metasurfaces have drawn considerable attention in the scientific community due to their exotic electromagnetic properties and potential breakthrough for light manipulation. With the development of nanophotonics, the generation of arbitrary spatially-varying polarization from an input beam is achievable. The objective of this thesis is to develop metasurface approaches to control phase and polarization of light in subwavelength scale for novel applications, such as polarization-controlled hologram generation and structured beam generation. The emphasis of the thesis is placed on the polarization control using geometric plasmonic metasurfaces. We start by reviewing recent progress regarding novel planar optical components. After the introduction of mechanism of light-nanostructure interaction and the far-field scattering of metal nanostructure arrays based on Mie theory, we discuss the abrupt phase change emerging from rotated nanostrips and the generalized Snell’s law. To demonstrate the precise phase manipulation, we develop a metasurface approach for polarization-controlled hologram generation. Moreover, we propose and experimentally demonstrate a novel method to realise the superposition of orbital angular momentum states in multiple channels using a single device. Spring from the superposition of two opposite circular polarizations, two different approaches for polarization manipulation at nanoscale are developed and experimentally verified. Based on the first approach, a vector vortex beam with inhomogeneous polarization and phase distributions is demonstrated, which features the spin-rotation coupling and the superposition of two orthogonal circular components, i.e., the converted part with an additional phase pickup and the residual part without a phase change. The second approach is to control the phase of the two orthogonal circular components simultaneously to engineer the polarization profile. Furthermore, we adopt this approach to develop a compact metasurface device which can hide a high-resolution grayscale image in a laser beam. The compactness of metasurface approach in polarization manipulation renders this technology very attractive for diverse applications such as encryption, imaging, optical communications, quantum science, and fundamental physics

Gradient metasurfaces: a review of fundamentals and applications

In the wake of intense research on metamaterials the two-dimensional analogue, known as metasurfaces, has attracted progressively increasing attention in recent years due to the ease of fabrication and smaller insertion losses, while enabling an unprecedented control over spatial distributions of transmitted and reflected optical fields. Metasurfaces represent optically thin planar arrays of resonant subwavelength elements that can be arranged in a strictly or quasi periodic fashion, or even in an aperiodic manner, depending on targeted optical wavefronts to be molded with their help. This paper reviews a broad subclass of metasurfaces, viz. gradient metasurfaces, which are devised to exhibit spatially varying optical responses resulting in spatially varying amplitudes, phases and polarizations of scattered fields. Starting with introducing the concept of gradient metasurfaces, we present classification of different metasurfaces from the viewpoint of their responses, differentiating electrical-dipole, geometric, reflective and Huygens' metasurfaces. The fundamental building blocks essential for the realization of metasurfaces are then discussed in order to elucidate the underlying physics of various physical realizations of both plasmonic and purely dielectric metasurfaces. We then overview the main applications of gradient metasurfaces, including waveplates, flat lenses, spiral phase plates, broadband absorbers, color printing, holograms, polarimeters and surface wave couplers. The review is terminated with a short section on recently developed nonlinear metasurfaces, followed by the outlook presenting our view on possible future developments and perspectives for future applications.Comment: Accepted for publication in Reports on Progress in Physic