Study of a mode-locked erbium-doped frequency-shifted-feedback fiber laser incorporating a broad bandpass filter: Numerical results

We present a comprehensive numerical study on the spectral and temporal behaviors of a mode-locked erbium-doped frequency-shifted-feedback fiber laser as a function of the frequency shift and optical bandwidth of the laser cavity. For this we develop a numerical model which is based on the rate equation and nonlinear Schrödinger equation for the fiber-based active cavity. We numerically verify that if the ratio of the filter bandwidth to the frequency-shift value is higher than ~400 times, the spectral broadening of the laser output tends to break up and form a secondary spectral band (SSB) on the wavelength side of the spectrum where the spectral components of the cavity modes are constantly shifted by the intracavity frequency shifter. We also verify that the SSB forms a satellite pulse in the time domain, traveling on either the trailing edge or leading edge of the main pulse, depending on whether the SSB is formed on the shorter or longer wavelength side of the pulse spectrum. We emphasize that these numerical results are also in good agreement with the experimental results discussed in our previous report [25].