Shape controlling of self-similar evolution in optical fibers

We numerically demonstrate controlled self-similar evolution of optical pulses in fibers. In so doing, we utilize the nonlinear Schrödinger equation with constant gain to which we add a linear forcing term, which we call an optical potential in analogy to other optical media, which acts as the shape forming mechanism; this term, in earlier studies is added in the form of a periodically placed filter. Here, we show that a distributed equation not only makes the modelling and analysis of the system simpler but also allows for initial Gaussian shaped pulses to grown self-similarly, under evolution, to rectangular or triangular shaped localized structures.