Tailoring Čerenkov second-harmonic generation in bulk nonlinear photonic crystal

We investigate theoretically the Čerenkov-type second-harmonic generation in two-dimensional bulk nonlinear photonic crystal with longitudinal modulation of the χ(2) nonlinearity. We show that in this scheme the Čerenkov radiation can be achieved simultaneously at multiple directions with comparable intensities. The angles of emission are controllable by the spatial modulation of the nonlinearity. We propose a design of the periodically poled domain pattern, which maximizes the efficiency of the second-harmonic emission.