Theory of relativistic harmonic generation

Summary form only given. In this paper, we show that the argument about vanishing THG breaks down under relativistic conditions. We consider the motion of a free electron in an intense laser field of wavelength /spl lambda/. For field strengths of the order of mc/sup 2///spl lambda/e, which for /spl lambda/=1 /spl mu/m corresponds to an intensity of the order of 2/spl times/10/sup 17/ W/cm/sup 2/, the electron is accelerated to relativistic velocities in a single optical period, and thus the excursion of the electron from its equilibrium position occurs over a distance of the order of /spl lambda/. Under such conditions, the radiation emitted by the electron cannot be described within the electric dipole approximation, and in fact cannot be well described by a multipole expansion for a finite number of terms. We instead calculate the intensity of the emitted radiation through the use of the Lenard-Wiechert potentials.