Two-Time Green's Function Theory for Laser

Abstract

By means of the retarded Green's function (response function) we derive the threshold condition, the oscillation frequency and the time-limited band width of lasers. The statistical property of the set of identical two-level atoms are taken into account on the basis of the Dicke-Haken's model. This property gives rise to atom-field correlation terms in the polarization operator. It is found that this terms influence the imaginary part of the oscillation frequency and the effect becomes large as the photon density increases or the occupancy difference tends to zero. In this respect the relation with the super-radiation is discussed. The customary approximation of considering only the interaction which is conservative for the particle number is tested. Under the resonance condition this approximation is correct up to the order of |ω k -ω 0 |/ω 0 , where ω 0 is the transition frequency of the atoms and ω k is the frequency of the free field.