Stimulated emission and population inversion in diatomic bound-continuum transitions

Abstract

Exact expressions are derived for the rate of stimulated emission and the conditions for population inversion in a diatomic bound-continuum transition. The resultant formulae resemble those of a simple, homogeneously broadened, discrete transition with the Lorentzian lineshape replaced by a continuum lineshape, g ^C(hv = E_v ′ - ε″), which is approximately equal to the square of the overlap between the initial, emitting, vibrational level v′ and the final, energy-normalized continuum state ε″, i.e. g ^C ≈ v′|ε″>². Using the ‘reflection method’, which is most applicable to a strongly repulsive final state, equations are obtained which allow simple, but accurate, estimation of the pertinent parameters which influence lasing action. Some general conclusions are extracted, and specific results are presented for the stimulated vacuum ultra-violet emission in high pressure Xe.