  A scheme for the detection of photons generated by vacuum mixing processes is
proposed. The strategy consists in the utilization of a high numerical aperture
parabolic mirror which tightly focuses two co-propagating laser beams with
different frequencies. This produces a very high intensity region in the
vicinity of the focus, where the photon-photon nonlinear interaction can then
induce new electromagnetic radiation by wave mixing processes. These processes
are investigated theoretically. The field at the focus is obtained from the
Stratton-Chu vector diffraction theory, which can accomodate any configuration
of an incoming laser beam. The number of photons generated is evaluated for an
incident radially polarized beam. It is demonstrated that using this field
configuration, vacuum mixing processes could be detected with envisaged laser
technologies.
