Theory of relativistic optical harmonic generation

We present a theoretical model of optical harmonic generation excited by laser beams sufficiently intense that relativistic effects are important. This model shows that, under relativistic conditions, third-harmonic generation can be excited with comparable efficiency by either linear or circularly polarized light. This result is to be contrasted with experience from traditional (nonrelativistic) nonlinear optics, where group-theoretical arguments show that third-harmonic emission cannot occur under circularly polarized excitation. These results are in good agreement with the observed polarization dependence of the third-harmonic emission reported recently in an experiment conducted under conditions such that relativistic effects are important. Our theoretical model also predicts that all even and odd harmonics of the fundamental laser frequency are emitted in the near-forward direction with an intensity that increases with that of the incident laser field.