The quantum-statistical properties of the optical field of a two-mode laser with two coupled transitions have been studied by means of a generalization of the Scully and Lamb theory. The photon number distribution and the mode intensity distribution are obtained in the steady state for a system of homogeneously broadened atoms in resonance with the laser field. It is shown that the mode-coupling constant $\ensuremath{\xi}$ is unity and that near threshold the results of earlier treatments are recovered. Furthermore, it is shown that certain limit measures for the relative intensity fluctuations predicted by the semiclassical Fokker-Planck treatments based on the third-order theory are valid even in the limit of arbitrarily high gain levels.
The theory of small-signal laser amplification is developed for homogeneously broadened systems in which the three main decay rates, for the collective atomic dipole moment, the population inversion, and the field in the laser cavity, have arbitrary relative magnitudes. The calculations extend previous work on class-
A and -
B lasers, where the dipole decay rate greatly exceeds the other two rates, to class-
C lasers, where the dipole decay rate is comparable to the others. The free-running laser is assumed to excite a single longitudinal mode of the cavity, whose frequency generally differs from that of the coupled atomic transition. The linear gains of the laser are derived for input signals whose frequencies are close to that of the lasing mode or to one of its adjacent nonlasing longitudinal modes. Divergences in the gain that occur for these two arrangements are associated with the previously studied single-mode and multimode instabilities of the free-running laser, respectively.