Transition from inhomogeneous to homogeneous broadening at a lasing prethreshold

The emission linewidth in active medium emerges due to homogeneous and inhomogeneous broadening. We demonstrate that in lasers with inhomogeneous broadening there is a critical pump rate, above which the special mode forms. This mode consists of locked-in oscillations of cavity mode and of the active particles with different transition frequencies. Below the critical value of the pump rate, the radiation spectrum of the laser has a Gaussian profile, provided that inhomogeneous broadening is dominant. Above the critical value of pump rate, the special mode mostly determines the laser radiation spectrum. As the result, the spectrum attains Lorentz shape characteristic for homogeneous broadening. We demonstrate that the formation of the special mode precedes lasing and that the critical pump rate plays the role of lasing prethreshold. We obtain expressions for the threshold and generation frequency of single-mode laser where both homogeneous and inhomogeneous broadening are present.