We analyse experimentally and theoretically the generation of single-photons through four-wave mixing process in optical fibers in a low power regime. The coupled-equations for the electrical field complex amplitudes are derived and solved. The proposed model is compared with experimental data. We show the importance of the nonlinear contribution to the phase-matching condition and the influence of the polarization effects on the generation of the single-photons. The 8/9 factor for the nonlinear coefficient is confirmed by direct measurement of the number of photons on the idler wave.