Coherence manifestation in a continuous-wave laser

We extend the existing theory of continuous-wave lasers by systematically considering spontaneous emission. In a simple rate-equation approach, the laser eigenvalue, defined as the ratio of coherent photons coupled out of the resonator divided by the number of photons coupled in via spontaneous emission, emerges as the fundamental parameter describing a continuous-wave laser. We derive a general equation for the laser eigenvalue and confirm the point at which coherence manifests itself in the resonator. The theory describes all types of lasers of three-level, four-level, or any intermediate nature.