Localized Core Four-Wave Mixing Buildup in the X-ray Spectrum of Chemical Species

Abstract

Using the Kohn–Sham density functional theory, we numerically study the four-wave mixing response of a carbon atom model system exposed to a train of femtosecond two color ω–3ω random phase coherent X-ray pulses near the K-edge. The phase-sensitivity cancellation of the 5ω anti-Stokes component previously described in two- and three-level systems in the infrared and optical regions is extended into the X-ray. Resonances with the absorption lines in the XANES and EXAFS regions produce 5ω peak intensities that increase near the phase-sensitivity cancellation frequencies. Based on this effect, we predict that highly selective intense X-ray 5ω photon energies can be achieved in real systems. The high localization of the ω–3ω four-wave mixing nonlinear technique that we address entails a new valuable tool in X-ray spectroscopies of chemical species as it can readily be extended to different photon energies in other atomic absorption edges, with broad applications.

Resonantly-Enhanced Difference-Frequency Generation in the Core X-ray Absorption of Molecules

“…1−10 Several nonlinear interactions in the X-ray range are accordingly being investigated. 11 In a previous work, 12 we showed how the phase-sensitivity cancellation of the anti-Stokes component previously described in two-and three-level systems in the infrared and optical regions can be extended to the X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) 6 of chemical species by highly localized four-wave-mixing (FWM) nonlinear processes. Femtosecond transient FWM grating spectroscopy with ultrafast X-rays has recently been demonstrated, 13,14 showing experimentally how the large penetration depth of X-rays allows probing the bulk properties of materials, addressing core excited states, and creating excitation gratings with unprecedented nanoscale spatial resolution.…”

Resonantly-Enhanced Difference-Frequency Generation in the Core X-ray Absorption of Molecules

“…[1][2][3][4][5][6][7][8][9][10] Several nonlinear interactions in the X-ray range are accordingly being investigated. 11 In a previous work 12 we showed how the phasesensitivity cancellation of the anti-Stokes component previously described in two-and threelevel systems in the infrared and optical regions can be extended to the X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) 6 of chemical species by highly localized four-wave mixing (FWM) nonlinear processes. Femtosecond transient FWM grating spectroscopy with ultrafast X-rays has recently been demonstrated, 13,14 showing experimentally how the large penetration depth of X-rays allows probing the bulk properties of materials, addressing core excited states, and creating excitation gratings with unprecedented nanoscale spatial resolution.…”

“…range are accordingly being investigated. 11 In a previous work 12 we showed how the phasesensitivity cancellation of the anti-Stokes component previously described in two-and threelevel systems in the infrared and optical regions can be extended to the X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) 6 of chemical species by highly localized four-wave mixing (FWM) nonlinear processes.…”

Resonantly Enhanced Difference-Frequency Generation in the Core X-ray Absorption of Molecules

“…Several nonlinear interactions in the X-ray range are accordingly being investigated . In a previous work, we showed how the phase-sensitivity cancellation of the anti-Stokes component previously described in two- and three-level systems in the infrared and optical regions can be extended to the X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) of chemical species by highly localized four-wave-mixing (FWM) nonlinear processes. Femtosecond transient FWM grating spectroscopy with ultrafast X-rays has recently been demonstrated, , showing experimentally how the large penetration depth of X-rays allows probing the bulk properties of materials, addressing core excited states, and creating excitation gratings with unprecedented nanoscale spatial resolution.…”