Theoretical analysis of the spatial phase-matching loci for second-harmonic generation and multiwave-mixing interactions

We report a theoretical analysis on spatial noncolinear phase matching of multiwave mixing and its application to a second-harmonic-generation (SHG) experiment. From the numeric calculations, the noncolinear phase-matching properties in general situations were determined. The theory gives the applicability for all noncolinear phase matching. Fine coincidences between theoretical calculations and observed spatial loci on noncollinear phase-matching SHG were confirmed. Relations that allow the calculation of the noncollinear phase-matching angle for any case of SHG are established. As an example, the noncolinear phase-matched SHG pattern on a screen is calculated numerically in the case of SHG of 1064 nm from a Nd:YAG laser under the phase-matched condition for two organic nonlinear crystals: 1-(2-thienyl)-3-(4-methyphenyl) propene-1 (TC-28), which is biaxial, and (2-furyl) methacrylic anhydride (FMA), which is uniaxial. Experimental results compared quite favorably with the theoretical analysis. Noncolinear phase matching may be of great practical interest in optical multiwave-mixing processes, such as optical parametric oscillation and optical parametric amplification. This technique also can be used for the measurement of crystal optical constants.