Two-stage linear-nonlinear shaping of an optical frequency comb as rogue nonlinear-Schrödinger-equation-solution generator

We report a wave generator of complex solutions of the nonlinear Schrodinger equation (NLSE) combining both intensity and phase spectral shaping of an initial optical frequency comb with subsequent nonlinear propagation in an optical fiber. We apply the explicit analytical form of the two-breather solutions of the NLSE as a linear spectral filter to shape ideal modulation of a continuous wave. The additional nonlinear propagation of the tailored wave provides experimental evidence of both the growth and decay of the fundamental second-order periodic breather solution. The temporal and spectral profiles of the higher-order breather are in excellent agreement with the corresponding analytical solution.