Classification of angular quasi-phase matching loci in periodically poled uniaxial crystals

We performed an exhaustive determination and classification of all the possible angular quasi-phase matching (AQPM) directions of three-wave nonlinear optical parametric interactions in periodically poled uniaxial crystals. We report 74 classes of AQPM loci depending on the wavelength dispersion of the principal refractive indices, the period of inversion of the sign of the second-order electric susceptibility, and on the eight possible combinations of polarization of the three interacting waves. Their complete classification is summarized in a schematic table providing the topological understanding of AQPM. The cases of second harmonic and difference-frequency generations in 5%MgO:PPLN are detailed.