  High harmonic generation (HHG) is an extreme nonlinear frequency
up-conversion process during which extremely short duration optical pulses at
very short wavelengths are emitted. A major concern of HHG is the small
conversion efficiency at the single emitter level. Thus ensuring that the
emission at different locations are emitted in phase is crucial. At high pump
intensities it is impossible to phase match the radiation without reverting to
ordered modulations of either the medium or the pump field itself, a technique
known as Quasi-Phase-Matching (QPM). To date, demonstrated QPM techniques of
HHG were usually complicated and/or lacked tunability. Here we demonstrate
experimentally a relatively simple, highly and easily tunable QPM technique by
using a structured pump beam made of the interference of different spatial
optical modes. With this technique we demonstrate on-the-fly, tunable
quasi-phase-matching of harmonic orders 25 to 39 with up to 30 fold enhancement
of the emission.
