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Maxwell's equations allow for some remarkable solutions consisting of pulsedbeams of light which have linked and knotted field lines. The preservation ofthe topological structure of the field lines in these solutions has previouslybeen ascribed to the fact that the electric and magnetic helicity, a measure ofthe degree of linking and knotting between field lines, are conserved. Here weshow that the elegant evolution of the field is due to the stricter conditionthat the electric and magnetic fields be everywhere orthogonal. The field linesthen satisfy a `frozen field' condition and evolve as if they were unbreakablefilaments embedded in a fluid. The preservation of the orthogonality of theelectric and magnetic field lines is guaranteed for null, shear-free fieldssuch as the ones considered here by a theorem of Robinson. We calculate theflow field of a particular solution and find it to have the form of a Hopffibration moving at the speed of light in a direction opposite to thepropagation of the pulsed light beam, a familiar structure in this type ofsolution. The difference between smooth evolution of individual field lines andconservation of electric and magnetic helicity is illustrated by considering afurther example in which the helicities are conserved, but the field lines arenot everywhere orthogonal. The field line configuration at time t=0 correspondsto a nested family of torus knots but unravels upon evolution.

Linked and knotted beams of light, conservation of helicity and the flow of null electromagnetic fields