Controllable Optical Similaritons in GRIN by Tailoring of Tapered Profile

In this chapter, we describe the controllable behavior of the intensity of self-similar waves for different tapering profiles, in a graded-index nonlinear waveguide. By utilizing the isospectral Hamiltonian approach with the crucial observation that the equation governing the tapering profile can be transformed into a Schrödinger-like equation, we detail the procedure to tailor \(\textrm{sech}^{2}\) -type and parabolic tapering profiles of such waveguides. We demonstrate that this technique yields a wide class of tapering profiles, for the effective control of similariton structure and their dynamical behavior. We exhibit that this novel technique may be profitably exploited to model different tapering profiles that find practical applications.