Elimination of beam walk-off in second-harmonic generation

Efficient second harmonic generation requires phase matching. Precise phase matching is achieved at a fixed incidence angle with respect to the optical axis of the birefringent crystal, for a given frequency. Phase mismatch depends linearly on the incidence angle in the vicinity of the phase matching point. In the spatial domain, the linear phase mismatch corresponds to the walk-off of the interacting beams. We show that the periodic modulation of the refractive index of the nonlinear material (both in the transverse and longitudinal directions, on a wavelength scale) can modify the angular dispersion of interacting waves. This can alter phase-matching characteristics and can affect the beam walk-off. In an ideal case, this can result in phase matching over a finite angular range, eliminating or significantly reducing walk-off effects. This can ultimately enhance the efficiency of second-harmonic generation, particularly when working with narrow beams.