The quest of null electromagnetics knots from Seifert fibration

Abstract

In this work we find new null electromagnetic fields that are exact solutions of Maxwell equations in vacuum and generalize the hopfion. The hopfion is an exact solution of Maxwell equations in vacuum in which all the field lines (both electric and magnetic) are topologically equivalent to closed and linked circles, forming a mathematical structure called Hopf fibration. Here we present a generalization to include other field lines topology, such as the Seifert fibration in which the field lines form linked torus knots. Included in this generalization are fields that ergodically fill torus surfaces.