Resonant x-ray second-harmonic generation in atomic gases

We explore the x-ray second-harmonic generation process induced by resonant two-photon absorption in systems with inversion symmetry. We show that this process becomes allowed in the x-ray region due to nondipole contributions. It is found that, although a plane-wave pump field generates only a longitudinal second-harmonic field, a Gaussian pump beam creates also a radially polarized transverse second-harmonic field which is stronger than the longitudinal one. Contrary to the longitudinal component, the transverse second-harmonic field with zero intensity on the axis of the pump beam can run in free space. Our theory is applied to Ar and Ne atomic vapors and predicts an energy conversion efficiency of x-ray second-harmonic generation of 3.2 x 10(-11) and 1.3 x 10(-12), respectively.