Figure 1

Noncollinear harmonic generation from the superposition of an intense fundamental ${\omega }_1$ (800 nm, $I_1=1.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$) and weaker ${\omega }_2$ (400 nm, $I_2=1.5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$) fields in randomly aligned ${\mathrm{N}}_2$ gas. (a) Schematic representation: The ${\omega }_1$ beam is in the horizontal plane and the ${\omega }_2$ beam points upwards at an angle $\varphi \approx 14\mathrm{mrad}$ such that they form a plane parallel to the entrance slit of the XUV spectrometer. (b) XUV emission as seen on the spectrometer detector. Each field’s contribution is labeled as ($n_1,n_2$) at frequency $\Omega =n_1{\omega }_1+n_2{\omega }_2$.Reuse & Permissions

Figure 2

Frequency-domain perspective on two-color noncollinear HHG. (a) Sum and difference frequency emission $\Omega =n_1{\omega }_1+n_2{\omega }_2$: only the odd net totals $n=n_1+n_2$ are dipole-allowed transitions; see text. Illustrated is the production of $\Omega =8{\omega }_1$ with $n_2=\pm 1$. (b) Momentum conservation yields phase-matched XUV radiation in the direction of ${\overrightarrow{k}}_{\Omega }(n_1,n_2)=n_1{\overrightarrow{k}}_1+n_2{\overrightarrow{k}}_2$.Reuse & Permissions

Figure 3

(a) Experiment: Power scaling of the noncollinear harmonic emission as a function of the weak-field (400 nm) peak intensity ($I_2$) for different numbers ($n_2$ from 0 to 6) of weak ${\omega }_2$ field photons absorbed. The intensity of the fundamental ${\omega }_1$ field is kept constant ($I_1=1.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$). The measured curves are labeled by $n_2$ and, respectively, multiplied vertically by a factor ($1,1/2,1/8,1/10,1/40,1/60,1/150$) for clarity. Slopes of $n_2$ from 0 to 6 are also displayed (dashed line). (b) Theory: Calculated power scaling. Noncollinear XUV spectra are obtained by solving for two-color HHG in the laser focus on a 2D grid (plane formed by ${\overrightarrow{k}}_1+{\overrightarrow{k}}_2$, see text) and adding coherently the radiation in the far field. Each curve is scaled vertically by the same factors as in Fig. 3a and theoretical slopes of $n_2$ from 0 to 4 are displayed (dashed line).Reuse & Permissions