Excess spontaneous emission in variable-reflectivity-mirror lasers

The so-called excess spontaneous emission factors, or excess noise factors, for the lowest and highest order transverse modes in geometrically stable and unstable laser cavities having Gaussian variable-reflectivity mirrors are calculated. These factors determine both the Schawlow-Townes linewidths or quantum noise fluctuations in laser oscillators and the initial noise levels from which oscillation buildup starts in regenerative laser cavities. The excess emission factor for the lowest order Gaussian mode is found to be near unity for geometrically stable resonators, rises to a value very close to 2 at the stable-unstable boundary (planar-mirror case), and becomes substantially larger than unity for cavities having geometrically unstable optics. Excess emission factors as large as 10-100 times and larger are obtained in cavities having geometric magnifications of order 1.5-2 and aperture Fresnel numbers of a few times unity, increasing quadratically for higher values of the Fresnel number or the square of the magnification. Higher order modes have even larger excess noise factors