X-ray two-photon absorption competing against single and sequential multiphoton processes

State-Population Narrowing Effect in Two-Photon Absorption for Intense Hard X-ray Pulses

“…We assumed that the excitation of the N 3 state is possible only through the intermediate N 2 state, i.e., only a sequential two-photon absorption process is possible. Direct, simultaneous two-photon absorption is neglected here, because it is expected that the cross-sections for this process are three orders of magnitude lower than the sequential TPA mechanism [9]. Assuming a sequential model for the two-photon absorption mechanism, the following rate equations are considered:…”

“…The ability to access nonlinear light-matter interactions at X-ray wavelengths became possible only recently thanks to the development of X-ray Free Electron Lasers (XFELs) [5,6]. In contrast to the optical laser wavelengths, the photon-atom interaction at hard X-ray wavelengths involves bound core-electrons, and leads to the excitation of intermediate electronic states with sub-femtosecond lifetimes [7][8][9][10]. Consequently, at femtosecond-durations, the intense pulses made available by XFELs presently allow us to access a thus-far-uninvestigated area of physics, and to probe the physical mechanisms that drive the nonlinear interaction of X-rays with matter [11][12][13].…”

Optics for coherent X-ray applications

“…The first KB system serves to expand the beam size, while the second one generates a small focus with a large NA. We successfully generated ultra-intense X-ray pulses of 10 20 W cm À2 with a size of 30 nm  55 nm for 9.9 keV XFEL pulses from SACLA , which were applied to observe two-photon absorption for the germanium K-absorption edge of 11.1 keV (Tamasaku et al, 2014). We note that this system is widely applicable for generating small spots for beamlines with a limited length.…”

X-Ray Probe Targets Interfaces

“…This technique and the associated theoretical framework demonstrate the ability to selectively probe interfaces, including those that are buried, with elemental specificity, providing a new tool for a range of scientific problems. DOI: 10.1103/PhysRevLett.120.023901 Nonlinear optics has recently been extended from visible and near UV wavelengths to new regimes with the development of x-ray free electron lasers (XFELs) capable of delivering x-ray pulses with high brightness, ultrashort pulse duration, and high coherence [1][2][3][4][5][6][7]. One fundamental nonlinear probe is second harmonic generation (SHG), a secondorder process which combines two photons of the same energy to generate a single photon with twice the energy [8].…”

“…Prior to the development of free electron lasers (FELs), only parametric downconversion had been observed [17]. While the advent of XFELs has recently enabled second-and third-order nonlinear spectroscopies at hard x-ray energies, including SHG [2], SFG [1], two-photon absorption [4], and inelastic Compton scattering [18], current hard x-ray FELs lack the longitudinal and temporal coherence necessary for efficiently satisfying the phase-matching conditions required for nonlinear spectroscopies, thus, making the exploitation of some of these techniques difficult [19,20]. Furthermore, the shorter hard x-ray wavelengths (λ < 0.2 nm) induce second harmonic and sum frequency generation even within centrosymmetric media, as the observed response depends on material inhomogeneity on the length scale of the x-ray wavelength, similar to how SHG is seen in a plasma, and effectively making this method a bulk probe [21].…”