SUM-FREQUENCY GENERATION IN A 2-DIMENSIONAL PHOTONIC LATTICE

We have formulated the Green's-function method for describing nonlinea r optical processes in an arbitrary tao-dimensional photonic lattice w ith particular regard to sum-frequency generation. In addition to the derivation of the generalized phase-matching condition, we have shown that the field intensity and the average Poynting's vector of the sum- frequency component are proportional to its (group velocity)(-2) and ( group velocity)(-1), respectively. Therefore, an enhancement is expect ed for both of them at photonic band edges, where the group velocity t ends to zero. This method was applied to a square lattice composed of circular air-rods formed in a LiNbO3 crystal, and the average intensit y of the electric field of the second harmonic and the effective nonli near susceptibility were numerically calculated.