Theory of the frequency comb output from a femtosecond fiber laser

The output of a femtosecond fiber laser will form a frequency comb that can be phase-locked through feedback to the cavity length and pump power. A perturbative theory is developed to describe this frequency comb output, in particular for a solitonic fiber laser. The effects of resonant dispersion, saturation of the self-amplitude modulation, cavity loss, third-order dispersion, Raman scattering, self-phase modulation, and self-steepening on the spacing and offset of the fiber-laser frequency comb are given. The mechanisms by which the pump power, cavity length and cavity loss control the frequency comb spacing and offset are identified. Transfer functions are derived for the comb response to change in cavity length, pump power or cavity loss. This theory can potentially be applied to other frequency comb sources as well.