# Monochromatic knots and other unusual electromagnetic disturbances: light localised in 3D

## TL;DR

This paper introduces a new class of exact, monochromatic electromagnetic solutions with knotted field lines that are localized in 3D space, including the first explicit examples of electromagnetic knots, and discusses their potential laboratory generation and applications.

## Contribution

It presents the first explicit examples of monochromatic electromagnetic knots and explores their generation and potential use in 3D display technologies.

## Key findings

- Existence of exact monochromatic electromagnetic solutions with knotted field lines.
- Potential methods for laboratory generation of these electromagnetic disturbances.
- Possible applications in three-dimensional display technology.

## Abstract

We introduce and examine a collection of unusual electromagnetic disturbances. Each of these is an exact, monochromatic solution of Maxwell's equations in free space with looped electric and magnetic field lines of finite extent and a localised appearance in all three spatial dimensions. Included are the first explicit examples of monochromatic electromagnetic knots. We also consider the generation of our unusual electromagnetic disturbances in the laboratory, at both low and high frequencies, and highlight possible directions for future research, including the use of unusual electromagnetic disturbances as the basis of a new form of three-dimensional display.