The theory of light-induced collisional energy transfer (LICET) in the Eu-Sr system is extended to include all the degenerate M states that occur in the separated-atom basis states. Previous treatments were restricted to only the M=0 substates. Numerical solutions are obtained for the resulting nine-state dynamic coupled system to determine transitions probabilities on a given straight-line path. Intense laser fields of linear and circular polarization are treated. It is found that the full M-state treatment results in dependences on the trajectory orientation angles which are much more complex than in the M=0 treatment. The exact and quasisymmetries involving these orientation angles are described in simple group-theoretic terms. The resulting spectral line shapes (LICET transition cross sections as a function of laser detuning) are seen to have structures that are understood in terms of the coupling matrix elements, as well as appreciable Stark shifts. These shifts, which appear to be an essential outcome of the theory, are not yet seen in measurements of the LICET line shape.
A unified quantum treatment is presented for bidirectional two-mode ring lasers using the approach of Haken and co-workers. Equations of motion for the reduced density matrix of the field have been derived and used to study the fluctuation properties of the radiation field in different kinds of active media. The steady-state photon number distribution for an inhomogeneously broadened gas ring laser is derived. It is shown that for equal losses the relative fluctuations and normalized cross correlation of the photon numbers approach values
31 and $\ensuremath{-}\frac{1}{3}$, respectively, for large excitations. For unequal losses the laser may emit typical single-mode laser radiation in the direction of the favored mode and typical equilibrium blackbody radiation in the direction of the weaker mode. Our results generally agree with the predictions of earlier treatments when the losses are equal. However, for unequal losses we predict different behavior for large excitations. Effects of detuning, spatial, and temporal variation of atomic inversion on the fluctuation properties have been investigated in the coherent-state diagonal representation of the density matrix, and steady-state intensity distributions have been derived for various kinds of active atoms. It is shown that for inhomogeneously broadened solid-state ring lasers spatial inhomogeneities may couple the modes strongly and the statistical properties of such lasers, characterized by a double-peaked intensity distribution and large relative-intensity fluctuations, may be similar to those of a homogeneously broadened ring laser. Curves are presented to illustrate the behavior.