Absence of Galilean invariance for pure-quartic solitons

Abstract

Optical temporal solitons, arising from self-phase modulation and negative quadratic ($\beta_2$) dispersion, are Galilean invariant, and therefore their properties do not depend on their group velocity. This is no longer true for pure-quartic soliton pulses arising from quartic ($\beta_4$) dispersion, for which a change in group velocity necessarily leads to nonzero quadratic and cubic ($\beta_3$) dispersion. Analyzing the generalized nonlinear Schrödinger equation for such dispersion relations analytically and numerically, we find that pure-quartic solitons are members of a larger family traveling at other speeds. These solitons, which appear to be stable, have a complex phase structure and have an asymmetric spectrum. Our results extend the understanding of solitons arising from high orders of dispersion.