Nonlinear frequency conversion in 2D x

The analytic solution to the wave equation for small-signal sum-frequency process is derived in 2D x(2) photonic crystals with use of the Green function method. It is predicted that the sum-frequency electrical field at quasi-phase matching (QPM) resonance is proportional to the angle-dependent effective crystal length. This implies that multiple wavelength QPM frequency conversion with controllable intensity output can be realized in a single 2D x(2) photonic crystal. It is revealed that efficient frequency conversion requires both the QPM and the proper structure matching. A novel double-circle construction, different from the conventional Ewald construction, is presented to reflect important QPM processes. It is also shown that the QPM resonance tuning of second-harmonic generation can operate over the whole transparent wavelength range of crystals