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Broad spectral range phase matched second harmonic generation in sub-diffractive two-dimensional photonic crystals

The extremely rich dispersive properties of the photonic crystals lead to highly unusual refractive properties, significant enhancement of the linear-matter interaction due to low group velocities and novel possibilities for realizing phase matching in nonlinear optical applications. By careful choice of parameters (modulation amplitude and period), one can compensate the dispersion of the material, as well as the induced dispersion in planar structures [1, 2]. Here, we combine two ideas: 1) the dispersion of material and of planar waveguide can be compensated, and the phase matching can be reached in principle in photonic crystals for plane waves propagating along a particular direction due to the distortion of dispersion curves belonging to different bands; 2) if the phase matching is achieved in one particular direction, it can be extended in the angular space, due to the distortion (the flattening) of the diffraction curves. We show, in addition, that the phase matching can be obtained also in a broad spectral range given by the similar slopes of the two dispersion curves [3].