  Exact four-photon resonance of collinear planar laser pulses is known to be
prohibited by the classical dispersion law of electromagnetic waves in plasma.
We show here that the renormalization produced by an arbitrarily small
relativistic electron nonlinearity removes this prohibition. The laser
frequency shifts in collinear resonant four-photon scattering increase with
laser intensities. For laser pulses of frequencies much greater than the
electron plasma frequency, the shifts can also be much greater than the plasma
frequency and even nearly double the input laser frequency at still small
relativistic electron nonlinearities. This may enable broad range tunable
lasers of very high frequencies and powers. Since the four-photon scattering
does not rely on the Langmuir wave, which is very sensitive to plasma
homogeneity, such lasers would also be able to operate at much larger plasma
inhomogeneities than lasers based on stimulated Raman scattering in plasma.
