Interaction of Very Intense Radiation Fields with Atomic Systems

In this paper a theory is developed which permits one to treat radiation processes involving a large number of photons in first- or second-order perturbation theory. The theory is applied to the interaction of an atomic electron with a very intense linearly polarized laser beam. It is found under certain approximations that induced radiation will occur at all harmonics $n{\omega }_0$ of the fundamental laser frequency ${\omega }_0$. The intensity distribution of this radiation is symmetric about the axis of polarization of the primary beam and is peaked at an angle of about 45° with respect to direction of propagation of the secondary radiation and the polarization of the incident radiation for the first few modes. This angle markedly shifts toward 0° for increasing $n$ (higher harmonics). The transition probabilities are high enough to make the effect readily observable.