Wave breaking in dispersion-decreasing fiber with normal group-velocity dispersion

We show wave breaking (WB) can occur in a dispersion decreasing fiber with normal group-velocity dispersion preceding the parabolic pulse formation (PPF), and the distance where it happens can be described by two equations. Based on the transformation of a nonlinear Schr dinger equation with the typical decreasing dispersion into the form of the uniform dispersion and “equivalent” gain, the first equation is obtained to determine the virtual WB distance. The corresponding real distance can then be acquired from the second equation derived from the fiber dispersion distribution function. Both the analytical results are confirmed by the numerical simulations of the two forms NLSE, and illustrated by the chirp oscillations appeared in the pulse edges, respectively. We further demonstrate that the spectral broadening of the pulse is quite different from that of the pulse temporal evolution during the PPF process. In the initial stage, the spectral broadening is dominated by the expansion of ripples in the central part of pulse caused by self-phase modulation (SPM); while in the last stage, it is dominated by the widening of sidelobe in the pulse wings caused by four-wave mixing (FWM). These facts reveal that FWM also plays an important role in the process of PPF besides SPM while the WB point is the very threshold that FWM begins to take effect.