Non-paraxial vectorial moment theory of light beam propagation

The cross sections of arbitrary-shaped non-paraxial light beams are characterized by the zero, first and second order moments of the energy flux spatial distribution. On the basis of the Maxwell equations and a plane wave spectrum representation of electromagnetic fields, the laws governing the change of these moments upon free beam propagation are found. In particular, the change of the second-moment-based width is found to be hyperbolic. The moment-based parameters are calculated and the hyperbolic law applied to some particular non-paraxial beam-like electromagnetic field models to show some new features that arise from this non-paraxial vectorial theory.