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Physical Review A

Resonant x-ray second-harmonic generation in atomic gases

Ji‐Cai Liu, Catalin Miron, Hans Ågren, Sergey P. Polyutov, Faris Gel’mukhanov

Published Dec 2, 2019• 3 citations
Publisher

Abstract

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 $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$, respectively.

DOI
10.1103/physreva.100.063403

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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\ifmmode×\else\texttimes\fi10\ensuremath−113.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}3.2\ifmmode×\else\texttimes\fi10\ensuremath−11 and 1.3\ifmmode×\else\texttimes\fi10\ensuremath−121.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}1.3\ifmmode×\else\texttimes\fi10\ensuremath−12, respectively.
Second harmonic generation (SHG) in atomic Li vapor is studied when the 2 2 S 1/2 -3 2 S 1/2 two-photon transition is resonantly excited. This is an SHG in a medium with inversion symmetry, with no externally apptied electric or magnetic field, and with no apparent multipole moments associated with the resonant excitation. The SH polarization is found to be parallel to the intensity gradient of the incident laser beam when a cylindrical lens focusing is applied. The mechanism of this highly forbidden SHG is explained by the radial electric field induced by free expansion of photo-electrons around the laser beam axis.
Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180\ifmmode^\circ\else\textdegree\fi{} out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for nnn-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.
Optical harmonic generation and mixing in the gas phase has been proposed as a technique for the generation of coherent radiation in the vacuum ultraviolet and soft x-ray spectral region. At the high field strengths required by these processes the interaction between atoms and the electromagnetic field shows intensity-dependent resonances. In this paper we modify harmonic generation theory to include the effect of these frequency shifts. Closed-form expressions for generated dipole moment, absorption probability, and coherence length are presented. The most important consequences of frequency shifts on resonantly enhanced processes are that the pump laser must be tuned away from the small-field resonance frequency, that the conversion efficiency may saturate, and that the dispersion of the medium may change sign. As an example, the generation of 198-\AA{} radiation by a five-photon mixing process in Li+{\mathrm{Li}}^{+}Li+ is considered.
A high-resolution study of magnetic-field-induced second-harmonic generation in sodium vapor has been carried out with use of a single-frequency continuous-wave dye laser. Resonant enhancement was obtained by tuning the laser to the frequency of the 3S\ensuremath{\rightarrow}4D two-photon transition of the sodium atom. Experimental and theoretical results are presented showing the variation of the power and polarization properties of the second-harmonic radiation as the laser is tuned across the two-photon resonance, and as the transverse magnetic field is varied.