ABSTRACT
In Chaps. 8 and 9, we considered a laser medium consisting of homo geneously broadened, stationary atoms. When the lasing atoms move as in a gas, they see an electric field with shifted frequency due to the Doppler effect, as shown in Fig. 10-1. One might argue that it is merely necessary to average the complex polarization or the susceptibility Xn over the frequency range corresponding to the velocity distribution, that is, calculate a new ^ n , for which
Here the frequency co = coo + Kv, where coo is the frequency at atomic line
(1)
center, v is the component of velocity along the laser (z) axis, and the frequen cy distribution is determined by a Maxwell-Boltzmann velocity distribution
W(y) = ( w)-1 exp [ - (v/w)2]. (2)
Here u is the most probable speed of the atom, and K is the wave number. The simple recipe (1) is, in fact, valid for an inhomogeneously broadened mediumt consisting of stationary atoms such as ruby at low temperatures. However, in the standing-wave laser, the atoms not only see Doppler-shifted frequencies, but also move through the standing-wave electric field, effectively seeing an amplitude-modulated field. Equivalently, each atom sees two frequencies, for the standing-wave field is the sum of oppositely directed running waves, one of which appears to be Doppler upshifted, one down shifted. Hence it is necessary to consider both the frequency shift and the time dependence of the atomic z coordinate when calculating the polarization of a gaseous medium.
