Roadband phase-matched second-harmonic generation for narrow beams in planar two-dimensional photonic crystals

Abstract

We show that photonic crystals made of materials with normal dispersion allow simultaneous broad angular range and broad spectral range phase matching in nonlinear wave mixing processes, in particular second harmonic generation. The configuration proposed ensures subdiffractive propagation regimes for both interacting waves and the slopes of the two dispersion curves (for the fundamental and second harmonic waves) at the phase-matching frequencies are similar (at frequencies slightly shifted from the phase-matched one the phase-mismatch remains very small). The numerical simulations confirm both the broad angular range (by the use of narrow beams, with the width of few wavelengths) and the broad spectral range (by the spectral width of the generated second harmonic beam) for the phase matching, showing a significant increasing of the conversion efficiency with respect to the case of plane waves in homogeneous materials.