Phase-matched sigh harmonics in a high density plasma by intensity-dependent phase

We report the experimental demonstration of phase-matched generation of high harmonics of orders 33 to 45 over 2 mm, in a gas cell filled with 30 torr of neon. Increasing the medium length from 1 to 4 mm is shown to enhance this specific group of harmonics by a factor of 50. To explain these results, we recall how phase-matching conditions are generalized in strong fields. By a phase-matching map formalism, we show how the spatial gradient of the intensity-dependent phase allows one to satisfy those conditions over millimeters.