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

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.

Some exact solutions for light beams

“…Better understanding of this phenomenon will help in the design of interesting new beams, with possible application to tractor beams [42,43,44]. The structure of the field lines in electromagnetic waves is also highly nontrivial and of increasing interest [39,40,41]. Knotted field lines occur in the class of electromagnetic beams described here, and the field lines are in general highly intricate unless the beam has a particularly simple polarization structure (such as the radial/azimuthal polarization of Sec.…”

Theoretical proposal for the experimental realisation of a monochromatic electromagnetic knot

“…In this section we briefly summarise the unusual electromagnetic disturbances described in [22]. We work in vacuum.…”

“…One of us recently described a collection of 'unusual electromagnetic disturbances' [22], which are essentially electromagnetic standing waves [23] that appear to be well localised in 3D, even in complete vacuum. Included among these are various monochromatic electromagnetic knots, closely related to the well-known Rañada-Hopf type electromagnetic knots but simpler in their construction.…”

A note on conserved quantities for electromagnetic waves

“…When magnetic helicity is conserved it thus provides an interesting topological constraint on field dynamics. For electromagnetic waves, conserved magnetic helicity is particularly interesting when it is accompanied by knotted lines of B. Electromagnetic waves with knotted field lines have been found in the case of pulses [55,56,61,62], standing waves [63] and monochromatic beams [64]. In the pulse and beam cases the magnetic helicity of knotted B fields is conserved.…”