Table-top extreme ultraviolet second harmonic generation

Abstract

The lack of available table-top extreme ultraviolet (XUV) sources with high enough fluxes and coherence properties has limited the availability of nonlinear XUV and x-ray spectroscopies to free-electron lasers (FELs). Here, we demonstrate second harmonic generation (SHG) on a table-top XUV source by observing SHG near the Ti M_2,3 edge with a high-harmonic seeded soft x-ray laser. Furthermore, this experiment represents the first SHG experiment in the XUV. First-principles electronic structure calculations suggest the surface specificity and separate the observed signal into its resonant and nonresonant contributions. The realization of XUV-SHG on a table-top source opens up more accessible opportunities for the study of element-specific dynamics in multicomponent systems where surface, interfacial, and bulk-phase asymmetries play a driving role.

Fig. 1. Experimental setup and energy diagram for SXRL-SHG at the Ti M_2,3 edge.

(A) From left, the setup includes the incoming 37.8-eV HHG-SXRL pulse (red beam, far-field beam profile in inset) that is focused by an ellipsoidal mirror onto the Ti foil surface, where SHG is generated (blue beam) and propagates collinearly with the fundamental. The divergent field is refocused with a toroidal mirror onto a grating that disperses the SHG and fundamental beams simultaneously onto a CCD camera. (B) Schematic diagram of the origin of the SHG emission. Inversion symmetry is broken on the front Ti surface, allowing for SHG. The fundamental and SHG beams exit from the rear foil surface. (C) Ti orbital-resolved density of states (DOS) (40). The SHG emission results from on-resonant excitation of 3p core states (−32.6 eV) to an empty intermediate state of 3d character (+5.2 eV) and subsequently to a virtual state (+43 eV).

Fig. 2. Representative spectrum of fundamental and second harmonic peaks where the second harmonic response scales quadratically with that of the fundamental.

(A) Representative spectrum of the fundamental and SHG signals (black). The linewidth is not resolved in this spectrum because of the spectrometer being optimized for high sensitivity exhibiting poor spectral resolution. The true linewidth of the SXRL was separately measured (∆E ≈ 2.6 meV) with a high-resolution spectrometer (red line). The linewidth of the SHG signal is assumed to be of the same order of magnitude as that of the fundamental. (B) The nonlinear energy dependence of the SHG signal with respect to the fundamental. A linear equation (red line) is fit to experimental data plotted as |E(ω)|² versus E(2ω) (black dots with 1 SD error bars, determined by the SD in photon counts on the CCD resulting from averaging shots at the same fundamental pulse energy together).

Fig. 3. The linear absorption spectrum from a broadband HHG source of the Ti foil.

The experimentally measured onset of the Ti M_2,3 edge can clearly be seen (gray) and is confirmed by a calculated absorption spectrum (red). The incident energy used in the SHG experiment of 37.8 eV (black dashed line) lies well within the resonantly enhanced region of the absorption spectrum. a.u., arbitrary units.