One-dimensional model of a single-mode laser with correlation between additive and multiplicative noises

Recently, Zhu [Phys. Rev. A 47 (1993) 2405] and Jia ei al. [Phys. Rev. A 51 (1995) 3196] investigated the statistical properties of a single-mode laser with correlation between additive and multiplicative noises by using a one-dimensional model with a one-dimensional Langevin equation of the single-mode laser derived by Fox et al. [Phys. Rev. A 35 (1987) 1838], We point out that this one-dimensional model, whose Langevin equation was obtained under the assumption that the noises are uncorrelated, is not always stochastically equivalent to the single-mode cubic laser model when additive and multiplicative noises are correlated, As a modification, a general model which is stochastically equivalent to the cubic model of a single-mode laser driven by correlated noises is derived. Based on this, a different one-dimensional model is given in the case where the former one used by Zhu and Jia et al, is not suitable.