It is demonstrated that two optical frequencies can be mixed in a medium with a quadratic non-linearity. The radiation at the difference frequency can be tuned in a wide spectral range and can be generated at moderate pumping powers.
The nonlinear interaction of two intense optical waves with three energy levels of an atomic system is analyzed theoretically. The frequencies of the applied fields are assumed to be on or near two of the resonances involving the three levels. Particular attention is given to the generation of power at the difference frequency of the two applied fields where their frequency separation lies in the far-infrared range of the spectrum. In the limit of large input fields where atomic transitions are driven to saturation, the generated difference-frequency power is no longer proportional to the product of the two input powers. It is shown that, in this limit, the total rate of emission of photons at the difference frequency may, in principle, approach a value given by TrN, where N is the total number of atoms, T is the average time of coherent interaction of atoms and the radiation field, and r is a factor which in favorable cases approaches unity at low temperatures. Also, a number of additional effects are encountered due to coherent double-quantum transitions among various levels which may be ignored only for weak input powers. These effects are highly dependent on the modes of relaxations of atomic levels and the details of the line shape. The results are applied to several cases, in which the resonance condition yields large efficiency in nonlinear frequency mixing.
The nonlinear response of sodium vapor with a laser tuned near the 4D two-photon resonance is investigated over a large range of sodium concentrations and pump intensities with emphasis on the influence of coherent cancellation effects on the induced polarizations and the primary mechanism for the generation of the new frequencies. Over a wide range of circumstances, the response of the medium is dominated by parametric four-wave mixing as compared to amplified spontaneous emission or stimulated electronic hyper-Raman scattering. Secondary four-wave-mixing fields are generated by stimulated Raman scattering of one parametric four-wave-mixing field and a coupling of these fields with the driving laser field. A sharp onset of saturation of the parametric four-wave-mixing signals with sodium number density and a transition from a quadratic to a linear power dependence is observed. Both effects are explained in terms of the two-photon cancellation effect.