Structuring Light: From Knots to Geometrical Phases

Abstract

Undoubtedly, light is one of the physical phenomena that has amazed humanity for millennia. In the past decades, rapid advances in technology have allowed us to study the hidden features of the electromagnetic field. Structured light – light beams whose intensity, phase profile, polarization, or frequency distribution has been tailored on demand – became a tool to explore the intersection between Maxwell’s equations and abstract mathematical concepts. The use of topology has become ubiquitous in photonics, such as the existence of caustics and optical systems that mimic the behavior of solid-state systems, among others. Here, physicists have taken advantage of quantities that stay unchanged under deformations, known as topological invariants, to obtain information regarding the nature of the system of interest. In this work, I propose the use of structured light as a platform to explore the topological effects in different fields of optics. As our first attempt, we numerically explore the relationship between the dislocations carried by a structured field and the landscapes carved on a dispersive-absorptive substrate in the paraxial and nonparaxial regime. Inspired by the three-dimensional fields obtained by means of a high-numerical-aperture lens, we introduce a simple methodology to tie the tip of the electric field and generate knotted polarization states. In parallel, we propose the use of framed knots to encode and share information. In contrast to the non-trivial polarization states, these knots are obtained by tracking the spatial evolution of the singular points in the field along propagation. Finally, we study the nature of the time-independent acquired Pancharatnam-Berry phase as a function of the strength of a measurement. The results of these developments could have implications for current and future research to unveil new physics phenomena inspired by topology. The authors foresee advances in structuring non-paraxial light, exotic light-matter interactions, and optical metrology, among others.