Theoretical investigation of three-dimensional quasi-phase-matching photonic structures

We present a full theoretical analysis of quasi-phase-matching (QPM) in three-dimensional (3D) periodic structures and point up optimum nonlinear structures, which promote the best nonlinear conversion efficiencies and are close to real structures. The QPM properties of 14 Bravais lattices are investigated as a function of motifs (orthorhombic and spherical) and of modulation types (+/- and +/0). This full 3D QPM theory allows us to produce all results of one-and two-dimensional QPM structures by choosing appropriate lattice periodicity and motif. The optimization of nonlinear conversion efficiencies in 3D QPM is obtained by analyzing four particular structures (simple cubic, body-centered cubic, face-centered cubic, and diamond cubic lattices) with different filling factors and motifs. In particular, 3D structures, which are very close to those realized in practice, are proposed and simulated, creating a guide for fabrication of real optimum QPM structures.