Figure 1

The experimentally measured incident pulse profile in Fig. 1a (solid line) can be approximated by the Airy profile (dotted line) corresponding to vacuum coupling parameter of $\chi =0.2$ for a capillary with bore radius $a\sim 90\mu \mathrm{m}$ (the error bars on the experimental data are due to radial averaging). The expected on-axis intensity profile, normalized at $z=0$, for a 1 cm long evacuated capillary (no gas present), assuming the dotted profile in Fig. 1a, is shown in Fig. 1b. The resulting harmonic signal growth for $q=201$ under optimal MMQPM conditions ($p\sim 20\mathrm{mbar}$ Ar, $I_{\max }\sim 1\times {10}^{15}\mathrm{W}{\mathrm{cm}}^{-2}$, solid line) is shown in Fig. 1c normalized to that expected for a single coherence length (dashed line). Also shown (dotted line) is the expected HHG signal growth for idealized two mode beating [from Eq. (3)] under optimized MMQPM conditions and $j=20$ ($L_{\mathrm{QPM}}=200\mu \mathrm{m}$).Reuse & Permissions

Figure 2

Quasi-phase-matched HHG in the water window. The red and blue traces are two separate shots recorded at $p\sim 20\mathrm{mbar}$ Ar with the signal corrected for system transmission, while the black trace is obtained for mismatched conditions with $p\sim 42\mathrm{mbar}$ Ar. Both harmonic signal traces (red and blue) are normalized to the value of the peak of the blue trace (labeled $x$) showing the good short term reproducibility of the data (3-minute interval). The dip in harmonic intensity at $\sim 4.4\mathrm{nm}$ (labeled $y$) is due to uncertainty in the absolute transmission around the C $K$ edge of the $0.2\mu \mathrm{m}$ $\mathrm{Al}/0.3\mu \mathrm{m}$ CH filter used to block optical light. The raw data from the CCD are shown in the inset. A lower limit of the conversion efficiency per harmonic order is calculated by vertical integration of the background subtracted signal in the bright region over the interval “$v_0$” only and correcting for system transmission. Significant signal with clear harmonic structure is present for one side lobe (marked $v_1$ in the inset) either side of the bright central order, $v_0$. Up to six side lobes were observed experimentally and are likely due to off axis QPM.Reuse & Permissions

Figure 3

Multimode quasi-phase-matching at $\sim 30\mathrm{nm}$ wavelength. (a) Under matched conditions an enhancement of $>200$ is observed for 2–3 harmonic orders. Varying $\Delta k$ by a small change in intensity allows the position of the brightest peak to be tuned from the 25th to the 29th harmonic. $I_{\max }=9\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$ (red) and $7\times {10}^{14}$ (blue). Mismatched conditions can be seen in (b) which shows the typical “plateau” structure of almost equal intensities typical of HHG in the absence of phase-matching [1].Reuse & Permissions

Figure 4

Pressure tuning curves (solid lines) calculated for (a) $I_{\max }\sim 1\times {10}^{15}\mathrm{W}{\mathrm{cm}}^{-2}$ ($q=201$, $\chi \sim 0.2$) and (b) $I_{\max }\sim 9\times {10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$ ($q=25$, $\chi \sim 0.3$), showing expected harmonic signal enhancements over the signal expected for a single coherence length. The experimental data (points) is normalized to the peak of the pressure tuning curves. The vertical extent of the data points indicates the experimentally observed shot to shot variation in the intensity of the stated harmonic order.Reuse & Permissions