Sculpting the dark: Singularity engineering with metasurfaces

Abstract

Optical singularities refer to the phenomenon of light's zeros. They constitute a broad class of field behavior in which zeros of various observable electromagnetic parameters appear. This thesis examines the properties of optical singularities, their applications in metrology and microscopy, and the design principles required for their creation. We introduce a straightforward classification system for singularities based on their co-dimension, providing a framework to manage the diverse array of terms referring to the same singular behavior. We further illustrate that superoscillations, a counterintuitive wave phenomenon resulting from near-complete destructive interference, owe their oscillatory behavior to the proximity of singularities. Even when a superoscillatory function lacks complex zeros on the real line, its spatial behavior can be elucidated via complex zeros located nearby in the imaginary direction. Optical singularities can be shaped by wavefront shaping devices such as metasurfaces, a burgeoning class of optical devices composed of subwavelength nanostructures precisely arranged on a flat surface. We demonstrate the use of efficient computational algorithms, such as automatic differentiation, to inverse-design optical devices capable of generating high-fidelity singular light. These design algorithms maximize a parameter known as the phase gradient as a proxy to enforce singular behavior. We experimentally realize rare, non-generic optical singularities using nanofabricated dielectric metasurfaces and examine how these singularities can be utilized in microscopy, remote sensing, and atomic trapping applications. Finally, we identify future directions and areas of growth that these unique singular characteristics may enable.