Enhancement of harmonic generation by an intense driving laser with high-order waveguide modes in a high-pressure gas-filled hollow waveguide.

High-order harmonics have been widely used as reliable tabletop coherent radiation sources recently, but their applications have often been limited by the available pulse energy. Here, we report that by using an overdriven intense laser in a long waveguide with high-pressure gas, phase matching can be achieved in three distinct "regimes". In the third regime, favorable phase matching is achieved at near-axis positions to enhance harmonic yields. Our results are supported by a full theoretical analysis, and we demonstrate that coupling of the driving laser with the high-order waveguide modes (instead of the fundamental mode used in most prior experiments) is responsible for achieving phase matching. Furthermore, we establish that this phase matching (and harmonic enhancement) is robust, and a scaling relation is derived for the necessary waveguide and gas parameters, allowing our predictions to be tested immediately in any laboratory today.