  Maxwell's equations allow for some remarkable solutions consisting of pulsed
beams of light which have linked and knotted field lines. The preservation of
the topological structure of the field lines in these solutions has previously
been ascribed to the fact that the electric and magnetic helicity, a measure of
the degree of linking and knotting between field lines, are conserved. Here we
show that the elegant evolution of the field is due to the stricter condition
that the electric and magnetic fields be everywhere orthogonal. The field lines
then satisfy a `frozen field' condition and evolve as if they were unbreakable
filaments embedded in a fluid. The preservation of the orthogonality of the
electric and magnetic field lines is guaranteed for null, shear-free fields
such as the ones considered here by a theorem of Robinson. We calculate the
flow field of a particular solution and find it to have the form of a Hopf
fibration moving at the speed of light in a direction opposite to the
propagation of the pulsed light beam, a familiar structure in this type of
solution. The difference between smooth evolution of individual field lines and
conservation of electric and magnetic helicity is illustrated by considering a
further example in which the helicities are conserved, but the field lines are
not everywhere orthogonal. The field line configuration at time t=0 corresponds
to a nested family of torus knots but unravels upon evolution.
