Spontaneous generation of singularities in paraxial optical fields
arXiv:1512.01444 · doi:10.1364/OL.41.001668
Abstract
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.
5 pages, 6 figures. Published as: Opt. Lett. Vol. 41(7) 1668-1671, (2016)