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 Schrodinger 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.