Quantum theory of third-harmonic generation in a gaseous system - Part I

We present a theoretical treatment for third-harmonic generation in gaseous systems by describing the atomic system as well as the radiation field quantum mechanically. The atomic system is represented by two energy levels. The effects of detuning in the two-photon interactions and the atomic motion on the third-harmonic generation are taken into account. The photon statistics of the third-harmonic field are obtained. The average photon number, second-order coherence, and output variance of the third-harmonic field are discussed. The above results show a nonlinear dependence on the detuning in the two-photon interactions and the Doppler parameter.