The physics of the nonlinear optics of plasmas at relativistic intensities for short-pulse lasers

The nonlinear optics of plasmas at relativistic intensities are analyzed using only the physically intuitive processes of longitudinal bunching of laser energy, transverse focusing of laser energy, and photon acceleration, together with the assumption of conservation of photons, i.e., the classical action. All that is required are the well-known formula for the phase and group velocity of light in plasma, and the effects of the ponderomotive force on the dielectric function. This formalism is useful when the dielectric function of the plasma is almost constant in the frame of the light wave. This is the case for Raman forward scattering (RFS), envelope self-modulation (SM), relativistic self-focusing (SF), and relativistic self-phase modulation (SPM). In the past, the growth rates for RFS and SPM have been derived in terms of wave-wave interactions. Here we rederive all of the aforementioned processes in terms of longitudinal bunching, transverse focusing, and photon acceleration. As a result, the physical mechanisms behind each are made clear and the relationship between RFS and envelope SM is made explicitly clear. This allows a single differential equation to be obtained which couples RFS and SM, so that the relative importance between each process can now be predicted for given experimental conditions.