Amplitude–energy fluctuations of optical pulses and statistics of the exit distance

We consider the propagation of an isolated optical pulse in the presence of additive noise. We apply an approach based on the Fokker–Planck equation to determine the probability distribution functions of the propagation distance at which the pulse energy and the pulse amplitude leave a certain region. ► Amplified spontaneous emission yields spurious jitter in the soliton parameters. ► Soliton parameters leave a certain range after a certain propagation distance (the exit distance). ► Fluctuations of the soliton parameters are described by the probability density function. ► The probability density function satisfies the Fokker–Planck equation. ► The statistics of the exit distance is expressed in terms of the probability density function.