  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 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-phasematching 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.
