Abstract
The statistical noise properties of the laser radiation in a low-Q (bad) cavity are theoretically investigated. The bad-cavity laser system is shown to be exactly equivalent to the stochastic Toda oscillator (STO) in the case of negligible polarization noise. Transforming the STO Langevin equation to the Fokker-Planck equation with a position-dependent diffusion coefficient, analytical expressions of the probability distribution are obtained as particular solutions in a stationary state with the aid of the expansion into a complete orthogonal set. We predict novel statistical features of the laser light, e.g., a power tail of the intensity distribution function, non-Gaussian nature of the field fluctuation, and super-Poissonian photoelectron statistics. General solutions are also given in a closed form in terms of the matrix continued fraction to compare with the particular solutions. The good-cavity case is reanalyzed in our formalism to root out differences between them.
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