Fisher Information on the Phase Transition from Regular to Flat Top Optical Pulse in Cubic-Quintic Nonlinear Media

We study the properties of optical pulses in cubic-quintic nonlinear media using Fisher information. The nonlinear media can support regular (sharp top) and flat top pulses depending on the type of quintic nonlinearity and the frequency of the pulse. For defocusing quintic nonlinearity, it holds both regular and flat top solitons. We find that the Fisher information suddenly drops near the transition from sharp to flat top pulses. This is also reflected in the linear stability curve where it is seen that the power of the pulse starts to grow rapidly near the point of transition. However, the solution is linearly stable according to Vakhitov-Kolokolov criterion. We examine that, in the case of focusing nonlinearity, the change from linearly stable to unstable solitons is imperceptible through Fisher information.