Quantum Langevin theory of whispering-gallery-mode microsphere laser

A quantum Langevin theory of whispering-gallery-mode microsphere laser theory is developed. The linear and nonlinear analysis are made for laser operation below and above the threshold. In these analysis, corresponding to the specific property of microsphere, the effect of inversion fluctuation is treated. The coherence functions of laser field are calculated, and the intensity, the amplitude fluctuation and the linewidth of the field are obtained, which are connected with the enhancement factor of whispering-gallery-mode microsphere. It is shown that the strong couple and strong pumping are useful for the amplification of intensity and the decrease of linewidth below the threshold. It is also shown that, for the laser action above threshold, the variances of photon number and the linewidth of internal field are related to the enhancement factor and the square of the enhancement factor, respectively.