Nonlinear wave-mixing processes in the extreme ultraviolet

We present data from two-color high-order harmonic generation in a hollow waveguide, that suggest the presence of a nonlinear-optical frequency conversion process driven by extreme ultraviolet light. By combining the fundamental and second harmonic of an $800\mathrm{nm}$ laser in a hollow-core fiber, with varying relative polarizations, and by observing the pressure and power scaling of the various harmonic orders, we show that the data are consistent with a picture where we drive the process of high-harmonic generation, which in turn drives four-wave frequency mixing processes in the extreme EUV. This work promises a method for extending nonlinear optics into the extreme ultraviolet region of the spectrum using an approach that has not previously been considered, and has compelling implications for generating tunable light at short wavelengths.

Figure 1

(Color online) (a) Harmonic output when excited by $90\mu \mathrm{J}$ of fundamental $\left({\omega }_1\right)$; (b), (c) when excited by a combination of $90\mu \mathrm{J}$ of fundamental and a weak 5 and $15\mu \mathrm{J}$ second-harmonic field $\left({\omega }_2\right)$, respectively.

Figure 2

(Color) Harmonic output as function of ${\omega }_2$ power (a), and ${\omega }_1$ power (b), for the case of $P\left({\omega }_1\right)⪢P\left({\omega }_2\right)$. In (a), odd orders (27, 25, 23 in red) deplete while even orders (14–20 in blue) grow. Some odd orders grow (13–21 in green). In (b), adjacent odd and even harmonic pairs are coupled and exhibit the same ${\omega }_1$ power dependence.

Figure 3

(Color) Harmonic output as function of ${\omega }_1$ power for the case of $P\left({\omega }_2\right)⪢P\left({\omega }_1\right)$, $[P\left({\omega }_2\right)=40\mathrm{mW}]$. The original even orders (10, 14, 18 in black) deplete or do not grow, while new odd and even orders grow. The new odd orders (11, 13, 15, 17 in blue) have an $I^3\left({\omega }_1\right)$ power dependence, while the even orders (12, 16 in red) have an $I^6\left({\omega }_1\right)$ power dependence.