Soft X-Ray Second Harmonic Generation as an Interfacial Probe

Nonlinear optical processes at soft x-ray wavelengths have remained largely unexplored due to the lack of available light sources with the requisite intensity and coherence. Here we report the observation of soft x-ray second harmonic generation near the carbon $K$ edge ($\sim 284\mathrm{eV}$) in graphite thin films generated by high intensity, coherent soft x-ray pulses at the FERMI free electron laser. Our experimental results and accompanying first-principles theoretical analysis highlight the effect of resonant enhancement above the carbon $K$ edge and show the technique to be interfacially sensitive in a centrosymmetric sample with second harmonic intensity arising primarily from the first atomic layer at the open surface. 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.

Figure 1

Experimental design. (a) X-ray pulses are passed through a 2 mm iris, then focused by an ellipsoidal mirror (not shown) onto the graphite sample (spot size $\sim 350\mu {\mathrm{m}}^2$) at normal incidence. The transmitted beam and the collinear second harmonic signal (double the fundamental photon energy) are passed through a 600 nm aluminum filter and into a spectrometer, spatially separating the second harmonic signal from the fundamental. A schematic energy level diagram of the SHG process is shown in the inset. (b) The CCD image and projection of the transmitted FEL beam and the SHG signal for a single FEL pulse. (c) Linear, total electron yield x-ray absorption spectrum of a 500 nm graphite sample. X-ray SHG measurements were made at the three discrete photon energies (${\omega }_1$) shown in the dashed lines. The nonresonant (below the C $K$ edge) and resonant (above the C $K$ edge) regions are shaded in orange and green, respectively.

Figure 2

Pulse energy dependence of soft x-ray SHG. The second harmonic response at 260.49 (a), 284.18 (b), and 307.86 eV (c) of graphite thin films (100 nm, red diamond; 300 nm, blue circle; 500 nm, orange square; 720 nm, green triangle). The dashed lines represent quadratic fits to all the points at a given photon energy constrained to show no detectable second harmonic signal generated below a threshold pulse energy. The vertical and horizontal error bars represent the standard error of the SH response and the standard deviation of the pulse energies in each bin, respectively. (d) The slope of the linearized pulse energy dependence curve for each photon energy. The relative $|X_{\mathrm{eff}}^{(2)}{|}^2$ response is proportional to the slope of the linearized pulse energy dependence curve (SH response vs $[\mathrm{input}\mathrm{power}{]}^2$). Error bars represent the standard deviation from the linear regression analysis. The nonresonant and resonant regions are shaded in orange and green, respectively.

Figure 3

Second harmonic susceptibility from first-principles theory. (a) Imaginary part (green solid) of the linear dielectric function corresponding to the calculated linear spectrum at the C $K$-edge NEXAFS region calculated with a density-functional-theory-based supercell approach for an eight-layer slab of graphite compared with the experimental linear spectrum (gray, dashed). The ${\pi }^{*}$ and ${\sigma }^{*}$ transitions are labeled in red and blue, respectively. The experimental peak between the marked ${\pi }^{*}$ and ${\sigma }^{*}$ regions corresponds to oxidized graphite. Note that a more realistic comparison between theory and experiment can be obtained by sampling a finite temperature molecular dynamics simulation as inhomogeneity in thermalized samples is a significant contributor to spectral broadening. (b) Calculated C $1s$ core level contribution to the magnitude $|X_{zzz}^{(2)}|$ of the $zzz$ component of the second-order nonlinear susceptibility tensor $X^{(2)}(2\omega ,\omega ,\omega )$ relevant to SHG near the C $K$ edge of a graphite surface. C $1s$ core levels from the top four surface layers of an eight-layer slab of graphite [shown in (d)] are considered in the simulation. The $z$ axis is perpendicular to the surface of the slab. (c) Convergence of the calculated $|X_{zzz}^{(2)}|$ as a function of the number of surface layers whose C $1s$ core states are included in the simulation. The inset shows the percentage contribution to $|X_{zzz}^{(2)}|$ from each of the top four individual layers obtained by integrating $|X_{zzz}^{(2)}|$ over a 260–340 eV energy window plotted as a function of the layer index. Contribution to the overall response is seen to decay exponentially moving into the bulk of the slab with the top layer accounting for $\sim 63\%$ of the signal. (d) Periodic supercell of the eight-layer graphite slab employed in the simulations.