  In nonrelativistic quantum mechanics the spontaneous generation of
singularities in smooth and finite wave functions, is a well understood
phenomenon also occurring for free particles. We use the familiar analogy
between the two-dimensional Schroedinger equation and the optical paraxial wave
equation to define a new class of square-integrable paraxial optical fields
which develop a spatial singularity in the focal point of a weakly-focusing
thin lens. These fields are characterized by a single real parameter whose
value determines the nature of the singularity. This novel field enhancement
mechanism may stimulate fruitful researches for diverse technological and
scientific applications.
