Self-similar evolutions of parabolic, Hermite-Gaussian, and hybrid optical pulses: Universality and diversity.

Three novel types of self-similar solutions, termed parabolic, Hermite-Gaussian, and hybrid pulses, of the generalized nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption are obtained. The properties of the self-similar evolutions in various nonlinear media are confirmed by numerical simulations. Despite the diversity of their formations, these self-similar pulses exhibit many universal features which can facilitate significantly the achievement of well-defined linearly chirped output pulses from an optical fiber, an amplifier, or an absorption medium, under certain parametric conditions. The other intrinsic characteristics of each type of self-similar pulses are also discussed.