Theoretical analysis of stability in a passively mode-locked fiber laser with polarization effect

A novel model describing the operation of a passively mode-locked fiber laser with polarization effect is developed. The combinational effect of the linear gain, nonlinear gain arising from saturable absorption, gain filtering and polarization effect has been investigated. In this paper we analyze the Schrodinger equation with the polarization effect linearly, and obtain the growth rate of the modulational instability, as well as get the relationship between the growth rate and the laser´ s gain. With regard to CW situation, if the linear gain is below the threshold, then the growth rate is positive and the CW solution becomes unstable; if it is above the threshold, then the rate is negative, suppressing the modulational instability and making CW to stabilize. Therefore, in this way, the mode locking for the optical fiber laser can be realized.