Quantum Langevin theory of whispering-gallery-mode microsphere laser

A quantum Langevin theory of whispering-gallery-mode microsphere laser theo ry is developed. The linear and nonlinear analysis are made for laser opera tion below and above the threshold. In these analysis, corresponding to the specific property of microsphere, the effect of inversion fluctuation is t reated. The coherence functions of laser field are calculated, and the inte nsity, the amplitude fluctuation and the linewidth of the field are obtaine d, which are connected with the enhancement factor of whispering-gallery-mo de microsphere. It is shown that the strong couple and strong pumping are u seful for the amplification of intensity and the decrease of linewidth belo w the threshold. It is also shown that, for the laser action above threshol d, the variances of photon number and the linewidth of internal field are r elated to the enhancement factor and the square of the enhancement factor, respectively.