Dynamics of passive modelocking with saturable Bragg reflector (SBR) in fiber lasers

In this paper we present theoretical and numerical studies of the modelocked fiber cavity including a description of the pulse formation dynamics and its interaction with the saturable Bragg reflector (SBR). The modelocking description equations have approximated the pulse changes per roundtrip as being small and linearized effects such as self phase modulation (SPM). However, in a fiber laser the SPM can be strong per roundtrip, equivalent to several it of nonlinear phase shift, and the linearized approach often fails to describe the correct and complicated pulse spectral evolution. We consider a Fabry-Perot fiber cavity consisting of gain, loss, group velocity dispersion (GVD), SPM, and and the SBR action.