Design of a photonic crystal fiber for phase-matched frequency doubling or tripling

We report on a possible phase matching between two fundamental modes guided in an appropriately designed photonic crystal fiber. The phase index matching condition can be perfectly fulfilled for second or third harmonic generation and for wavelengths over a large spectral range, simply by tuning the lattice pitch. This can be achieved in such a structure thanks to the coexistence of total internal reflection and photonic bandgap guidance, leading to two different dispersive behaviours for the fundamental and the harmonic waves.