Akhmediev breather signatures from dispersive propagation of a periodically phase-modulated continuous wave.

We investigate in detail the qualitative similarities between the pulse localization characteristics observed using sinusoidal phase modulation during linear propagation and those seen during the evolution of Akhmediev breathers during propagation in a system governed by the nonlinear Schrödinger equation. The profiles obtained at the point of maximum focusing indeed present very close temporal and spectral features. If the respective linear and nonlinear longitudinal evolutions of those profiles are similar in the vicinity of the point of maximum focusing, they may diverge significantly for longer propagation distance. Our analysis and numerical simulations are confirmed by experiments emulating an optical fibre. • Qualitative similarities between sinusoidal phase modulated waves and Akhmediev breathers exist. • Profiles at the point of focusing present very close temporal and spectral features. • The longitudinal evolutions are similar in the vicinity of the point of focusing. • The respective linear and nonlinear evolution then diverge significantly. • Our analysis and numerical simulations are confirmed by experiments. [ABSTRACT FROM AUTHOR]