  We construct a family of exact solutions to Maxwell's equations in which the
points of zero intensity form knotted lines topologically equivalent to a given
but arbitrary algebraic link. These lines of zero intensity, more commonly
referred to as optical vortices, and their topology are preserved as time
evolves and the fields have finite energy. To derive explicit expressions for
these new electromagnetic fields that satisfy the nullness property, we make
use of the Bateman variables for the Hopf field as well as complex polynomials
in two variables whose zero sets give rise to algebraic links. The class of
algebraic links includes not only all torus knots and links thereof, but also
more intricate cable knots. While the unknot has been considered before, the
solutions presented here show that more general knotted structures can also
arise as optical vortices in exact solutions to Maxwell's equations.
