The Higher Precision expressions of the Unified Expansion Theory (HPUET) which can be simultaneously applied to the case of large or small correlation time, are obtained by means of improving the accuracy of calculation. We investigate the colored-gain-noise model for a single-mode laser, and the analytic expressions of the probability, the mean and the variance of the steady-state laser intensity are obtained through the HPUET. Comparison shows that the results of the HPUET are in better agreement with the simulation results than the results of the other theory.
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