Efficient parametric generation in a nonlinear photonic crystal pumped by a dual beam

We investigate parametric down-conversion in a hexagonally poled nonlinear photonic crystal, pumped by a dual pump with a transverse modulation that matches the periodicity of the χ (2) nonlinear grating. A peculiar feature of this resonant configuration is that the two pumps simultaneously generate photon pairs over an entire branch of modes, via quasi-phase matching with both fundamental vectors of the reciprocal lattice of the nonlinearity. The parametric gain of these modes depends thus coherently on the sum of the two pump amplitudes and can be controlled by varying their relative intensities and phases. We find that a significant enhancement of the source conversion efficiency, comparable to that of one-dimensionally poled crystals, can be achieved by a dual symmetric pump. We also show how the four-mode coupling arising among shared modes at resonance can be tailored by changing the dual pump parameters.