Quasi-phase-matched second-harmonic generation in nonlinear crystals with harmonic modulation of nonlinearity

We propose a new type of nonlinear photonic crystal with the lattice representing a harmonic function of the propagation coordinate. This type of spatial modulation of the quadratic nonlinearity is implemented to enhance the second-harmonic generation (SHG) efficiency. The process resembles that realized in periodic nonlinear photonic crystals with rectangular nonlinearity modulation under quasi-phase-matching. Residual periodic oscillations of the second-harmonic intensity were found. Comparison of the unipolar and bipolar modulations showed that they are equivalent with regard to the oscillations. The SHG efficiency in the harmonic lattices is 1.6 times lower compared with the efficiency corresponding to the quasi-phase-matching in periodic nonlinear photonic crystals with rectangular lattices.