  Caustics are optical phenomena which occur when a family of rays creates an
envelope of divergent intensity. Here we show that caustic surfaces also appear
when a real or complex field is mapped to its order parameter manifold. We
study these structures in the context of spin-1/2 fields, where the order
parameter manifold is the Bloch sphere. These generic structures are a
manifestation of catastrophe theory and are stable with respect to
perturbations. The corresponding field configurations are also stable and
represent a new type of topological defect. Equations governing the conditions
for their existence and unfolding are derived.
