Absence of Galilean invariance for pure-quartic solitons
Justin Widjaja, Erekle Kobakhidze, Tiernan R. Cartwright, Joshua P. Lourdesamy, Antoine F. J. Runge, Tristram J. Alexander, C. Martijn de Sterke
Abstract
Optical temporal solitons, arising from self-phase modulation and negative quadratic (${\ensuremath{\beta}}_{2}$) 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 (${\ensuremath{\beta}}_{4}$) dispersion, for which a change in group velocity necessarily leads to nonzero quadratic and cubic (${\ensuremath{\beta}}_{3}$) dispersion. Analyzing the generalized nonlinear Schr\"odinger 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.