Formation of non-Galilean invariant optical solitons in a fiber laser

We theoretically and experimentally study the formation of non-Galilean invariant optical solitons in a passively mode-locked fiber laser with asymmetric dispersion profiles combining second-, third-, and fourth-order dispersion. The laser cavity incorporates a spectral pulse-shaper, which allows the net-cavity dispersion to be programmed arbitrarily. We find that the solitons, which grow from noise, form around the unique frequency where the third-order dispersion locally vanishes, minimizing the effects of the asymmetric dispersion. We demonstrate this by measuring the soliton's central frequency, the repetition rate of the laser, and the spectral positions of the Kelly sidebands. Our results are in very good agreement with theoretical and numerical predictions.