Spectral line broadening due to resonance absorption and induced emission is investigated for general spectral distributions of the radiation field using the frequency-dependent relaxation operator method. An analytic self-consistent solution is found for the case of equal spectral profiles of field and radiative cross sections. The often-assumed Gaussian distribution of the field in saturated amplifiers is shown to yield symmetrical doublet structure for the radiative cross sections if the induced rates are larger than or comparable to the Gaussian width. A similar calculation was therefore performed for double Gaussian field spectra that reproduces such doublet structure for the cross sections in the case of narrowly spaced Gaussians. Self-consistent solutions of gain and line-broadening equations are accordingly expected to favor the sidebands, and at very high powers and gains amplified-spontaneous-emission lines should generally split into two lines of equal intensity separated by an averaged Rabi frequency. Since the cross-section profiles vary along the amplifier, the overall gain may be diminished, although the local cross sections have enhanced maxima at high powers.

• Received 24 April 1989

DOI:https://doi.org/10.1103/PhysRevA.40.3706