Fig. 1: HHG with two orthogonally polarized optical fields.

a Experimental setup. Two orthogonally polarized pulses with photon energies ħω1 and ħω2 and field strengths E1 and E2 are focused onto the sample (bulk GaSe with a thickness of 30 μm). The generated HHs (observed at the energies mħω1 + nħω2) are decomposed along the two mutually orthogonal directions of the electric fields E1(t) and E2(t), and their intensities, \(I_1^{{\mathrm{HH}}}\) and \(I_2^{{\mathrm{HH}}}\), are measured as a function of the crystal rotation angle φ (rotation axis: pulse propagation direction). b The \(I_2^{{\mathrm{HH}}}\) component in the HH spectra separately obtained by excitation with E1(t) (red data), E2(t) (blue data), and E1(t) + E2(t) (purple data) for φ = 15°. To distinguish the different mixed harmonic orders, we use ordered pairs, (m,n). Photoluminescence (PL) appears around 2 eV31. c Harmonic intensities as a function of E1 for the harmonic orders (m,n) = (4,1), (2,2), (3,0), (2,1), (1,2) (solid circles), while E2 = 0.5 MV/cm. The black broken lines are proportional to E2m and serve as guides for the eye. The data sets are offset for clarity. Inset: E2 dependences of the (4,1)-, (2,2)-, (1,2)- and (2,1)-order harmonics’ intensities, while E1 = 5 MV/cm; the black broken lines are proportional to E2n.