Theory of Atomic Scattering in a He-Ne Laser

Abstract

The scattering theory of laser atoms developed by Berman and Lamb is found to have implications for the collision theory of a high-intensity laser. Assuming scattering in the lower laser state (2p A ) to dominate, one can fit the experiments on a 0.63~MHI He-Ne laser by Cordover and Bonczyk.This paper includes the work by Berman and Lamb 1 into the theory of collisions in a laser. 2 We paraphrase their discussion to see its implications: The pumping process injects atoms with the velocity distribution W(v). Their ensemble is described by the density matrix p(p, p') = 6(p~p')W^(p/m) in the plane-wave basis of the laser volume V.With (ft equal to the range of atomic interaction, we assign a volume 7 c »(ft 3 to each collision. The classical description can be retained when the field varies little over V c and in times r = V c 1/3 /v. The theory of Ref. 1 applies inside V c , and between the collisions the atoms are propagated as in Ref. 2. With (ft^10 " 9 m, X^l(T 6 m, and v^ 10 3 m/sec we take V c 1/3 = 10' 8 m, T=KT n sec, whereas field changes require y ab~l -10" 7 sec.An atom in state la) enters V c with the velocity p/m, and with Ref. 1 we assume different scattering in the two laser states. We take the upper state \a) to be unaffected 3 in V c and the state lb) to scatter with the elastic-scattering amplitude/(/>, 0). The dipole moment after scattering is