Noncollinear phase-matching of high harmonic generation in solids

We propose and experimentally demonstrate a scheme allowing to reach noncollinear phase-matching of high harmonic generation in solids, which may potentially lead to an enhancement of the generation efficiency. The principle is based on high-order frequency mixing of two light waves with identical frequencies but different directions of wavevectors. In this process, $N$-th harmonic frequency is produced by frequency mixing of $N$+1 photons from a wave with high amplitude of electric field and a single photon from a wave with low field amplitude, which are propagating noncollinearly in an optically isotropic media. We experimentally verify the feasibility of this scheme by demonstrating phase-matched generation of third and fifth harmonic frequency in sapphire.