Sum-frequency generation in the bulk of an isotropic gyrotropic medium with two collinear pump beams

We theoretically investigate sum-frequency generation with two interacting coaxial Gaussian beams in the bulk of a noncentrosymmetric liquid due to a local electric-dipole quadratic optical susceptibility of the medium <(chi) over cap>((2)). It is demonstrated that this effect, forbidden in the plane -wave approximation, may occur only in focused pump beams. Quadrature formu las for the electric field and the power of the signal wave are derived. Pa rticular cases when these expressions can be reduced to an analytical form are considered. The case of pump beams tightly focused into the center of a long medium is thoroughly investigated. Transverse distribution of the sig nal-wave intensity and the dependences of this quantity on the mismatch of the wave vectors, the ratio of pump-beam half-widths in the waist plane, an d the polarization states of these beams are studied. Quasi-phase-matching conditions, allowing the efficiency of the considered three-wave mixing pro cess to be substantially improved, are found.