Extracting Solitons from Noisy Pulses

We describe an iterative method that extracts the underlying soliton from a noisy pulse. The method is formulated as a functional iteration: at each step, the soliton component of the difference between the noisy pulse and the current underlying soliton is determined via soliton perturbation theory; this is then added to the soliton, and the process is repeated. We show that this iteration converges if the perturbation is not too large, and we give the specific types of deviations which most easily cause the iteration to fail to converge. As an example of the method’s use, we apply it to obtain improved statistics of the amplitude, phase, frequency, and position of a soliton propagating in an optical fiber in the presence of amplifier noise.