The method of Fourier transforms applied to electromagnetic knots

TL;DR

This paper demonstrates how Fourier transforms can be used to generate electromagnetic knots, solutions of Maxwell's equations with complex topologies, emphasizing accessible calculations suitable for undergraduate education.

Contribution

It introduces a straightforward Fourier transform method for constructing electromagnetic knots and utilizes helicity basis to analyze their properties, making the approach accessible.

Findings

Electromagnetic knots can be explicitly constructed using Fourier transforms.

The method allows calculation of electromagnetic helicity and photon content.

Accessible educational approach for complex topological solutions.

Abstract

The Fourier transform method can be applied to obtain electromagnetic knots, which are solutions of Maxwell equations in vacuum with non-trivial topology of the field lines and especial properties. The program followed in this work allows to present the main ideas and the explicit calculations at undergraduate level, so they are not obscured by a more involved formulation. We make use of helicity basis for calculating the electromagnetic helicity and the photon content of the fields.