Beta factor in a random laser.

We develop a definition for the beta factor, the fraction of spontaneous emission that seeds the laser process, for a random laser. With the wavelength-dependence of the gain (and potentially scattering) being the only possible criterion in the competition between gain and loss, our concept of beta is based on the spectral properties of the spontaneous emission and laser light. We find beta approximately equal to 0.1. We discuss the apparent similarities and differences between the beta for a cavity and a random laser.