  According to the theory of quantum electrodynamics, photon-photon scattering
can take place via exchange of virtual electron-positron pairs. Effectively,
the interaction can be formulated in terms of non-linear corrections to
Maxwell's equations, and hence may be treated by classical non-linear
electrodynamics. Due to the strong electromagnetic fields needed to reach any
noticeable effect, photon-photon scattering has not yet been observed
experimentally, but recent improvements in laser technology have increased the
possibility of direct detection. A verification of the phenomena would be of
great scientific value as a confirmation of quantum electrodynamics. In this
thesis the possibility of direct detection of elastic photon-photon scattering
through four-wave coupling is investigated, both for current and future
systems. It is shown how three colliding laser pulses satisfying certain
matching conditions, can generate scattered radiation in a fourth resonant
direction. The interaction is modeled, and the number of scattered photons is
estimated for optimized configurations of incoming pulses, both for the Vulcan
laser at the Rutherford Appleton Laboratory as well as for the planned XFEL at
DESY. An experiment using the Vulcan laser is predicted to produce 22 scattered
photons per shot, an amount which is definitely detectable. The usefulness of
the XFEL highly depends on future developments in laser technology, but a
realistic estimation gives a result of 30000 scattered photons per second.
