Nonlinear Interaction of Light in a Vacuum

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Abstract
Semiclassical methods are used to study the nonlinear interaction of light in vacuum. The study was motivated by a desire to investigate the possibility of using recently developed light sources (lasers) to demonstrate the existence of these minute nonlinear effects. As is well known, Maxwell's equations can be modified by the addition of certain nonlinear terms so that they correctly describe the interaction of low-energy photons. Using these equations, an expression is derived for the counting rate for photons produced by two photons colliding inelastically in the presence of an external, static electric field. A derivation along these lines is also given for the well-known scattering cross section in the case of two photons colliding elastically to give two photons.