Numerical modeling of fiber lasers with long and ultra-long ring cavity.

We highlight two important aspects related to a mathematical modeling of pulsed fiber lasers with long and ultra-long ring cavity -impact of an initial noise and a cavity length on generation of single optical pulses. Using as an example a simple scalar model of a ring fiber laser that describes the radiation build-up from noise and the following intra-cavity pulse dynamics during a round trip we study dependence of generated pulse characteristics on the resonator length in the range from 30 m up to 2 km.