Propagation of quasisolitons in a fiber Bragg grating written in a slow saturable fiber amplifier

We show, by using numerical simulations, that quasisolitons can propagate over a long distance in a fiber Bragg grating that is written in a slow saturable fiber amplifier, such as an erbium-doped fiber amplifier. During the pulse propagation, the front end of the pulse experiences a net gain while the rear end of pulse is attenuated due to the combination of gain saturation and loss. However, the pulse profile almost does not change after propagating over a length of 5 m that is approximately 2500 times larger than the spatial pulse width. The pulse amplitude has an approximately hyperbolic secant profile. We develop a reduced model by using a multiscale analysis to study solitary-wave propagation when nonlinearity and gain are small. When gain saturation also becomes small we find analytically a new family of solitary-wave hyperbolic-secant solutions that approximately solve the reduced model. The solitary waves propagate slightly faster than Bragg solitons that propagate in fiber Bragg gratings without gain and loss.