Element Selectivity in Second-Harmonic Generation of ${\mathrm{GaFeO}}_3$ by a Soft-X-Ray Free-Electron Laser

Nonlinear optical frequency conversion has been challenged to move down to the extreme ultraviolet and x-ray region. However, the extremely low signals have allowed researchers to only perform transmission experiments of the gas phase or ultrathin films. Here, we report second harmonic generation (SHG) of the reflected beam of a soft x-ray free-electron laser from a solid, which is enhanced by the resonant effect. The observation revealed that the double resonance condition can be met by absorption edges for transition metal oxides in the soft x-ray range, and this suggests that the resonant SHG technique can be applicable to a wide range of materials. We discuss the possibility of element-selective SHG spectroscopy measurements in the soft x-ray range.

Figure 1

Second harmonic generation in the ${\mathrm{GaFeO}}_3$ crystal using Fe $3p$ resonance. (a) Energy diagram of SHG. The notations, $g$, $n$’, and $n$ represent the ground state, intermediate state, and excited state, respectively. (b) Projection view along the $c$ axis of the crystal structure of ${\mathrm{GaFeO}}_3$.

Figure 2

Measurement of SHG using SXFEL and resonant enhancement of $I_{2\omega }$. (a) Schematic diagram of the SXFEL beam line at SACLA and the SHG measurement system. (b) Fe $3p$ absorption spectrum of the ${\mathrm{GaFeO}}_3$ crystal. (c) Intensity plot of the $\omega$ component of the reflected SXFEL pulses $I_{\omega }$ with respect to the correspondent incident intensity $I_0$ at the photon energy $\hslash \omega =27.5\mathrm{eV}$. (d) Plot of $I_{2\omega }$ at the photon energy of $2\hslash \omega =55\mathrm{eV}$. (e) Plot of $I_{2\omega }$ at the photon energy of $2\hslash \omega =53\mathrm{eV}$. The dashed lines shown in (c) and (d) were fitted by a power law.

Figure 3

Quadratic dependence of the $I_{2\omega }$ signals. $I_{2\omega }$ is plotted on the left axis for the photon energy of $2\hslash \omega =55\mathrm{eV}$ (red circle), $2\hslash \omega =57\mathrm{eV}$ (blue circle), and $2\hslash \omega =59\mathrm{eV}$ (green circle) in the logarithmic scale. $I_{\omega }$ (orange circle) is plotted on the right axis for $\hslash \omega =27.5\mathrm{eV}$. The dashed lines were fitted using a power law.

Figure 4

The square of the second-order susceptibility tensor, $|{\chi }_{zzz}^{\mathrm{SHG}}{|}^2$, with respect to the photon energy of second harmonics near Fe $3p$ edge. The red and blue lines correspond to the transition process of the double resonance shown in the inset (i), the current case of ${\mathrm{GaFeO}}_3$, and (ii) the ideal case, respectively. (a) Calculated $|{\chi }_{zzz}^{\mathrm{SHG}}{|}^2$ values (left) for (i) with the measured ones (right) (green circles) for $I_0=10\mu \mathrm{J}$, that are normalized by $I_{2\omega }$ at 53 eV. (b) A comparison between the $|{\chi }_{zzz}^{\mathrm{SHG}}{|}^2$ values for the (i) and (ii) cases.