  We describe singularities in the distribution of polarized intensity as a
function of Faraday depth (i.e. the Faraday spectrum) caused by line-of-sight
(LOS) magnetic field reversals. We call these features Faraday caustics because
of their similarity to optical caustics. They appear as sharply peaked and
asymmetric profiles in the Faraday spectrum, that have a tail that extends to
one side. The direction in which the tail extends depends on the way in which
the LOS magnetic field reversal occurs (either changing from oncoming to
retreating or vice versa). We describe how Faraday caustics will form
three-dimensional surfaces that relate to boundaries between regions where the
LOS magnetic field has opposite polarity. We present examples from simulations
of the predicted polarized synchrotron emission from the Milky Way. We derive
either the probability or luminosity distribution of Faraday caustics produced
in a Gaussian magnetic field distribution as a function of their strength, F,
and find that for strong Faraday caustics P(F)\proptoF^{-3} . If fully
resolved, this distribution is also shown to depend on the Taylor microscale,
which relates to the largest scale over which dissipation is important in a
turbulent flow.
