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

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.