Theory of resonant second harmonic generation and frequency summation under adiabatic conditions

A theory is developed of resonant second harmonic generation in a medium consisting of threelevel atoms (molecules). Reduced equations for wave propagation are solved without expanding a nonlinear polarization as a series in powers of the field intensities, so that the theory is applicable also to strong resonances. The case of a strong two-photon resonance is investigated and it is shown how the results differ from those obtained using the conventional theory which applies to the nonresonance cases. It is shown that the proposed theory can be generalized to the processes of generation of sum and difference frequencies.