Self-similar propagation and amplification of parabolic pulses in optical fibers

Ultrashort pulse propagation in high gain optical fiber amplifiers with nor mal dispersion is studied by self-similarity analysis of the nonlinear Schr odinger equation with gain. An exact asymptotic solution is found, correspo nding to a linearly chirped parabolic guise which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numeri cal simulations and experiments studying propagation in a Yb-doped fiber am plifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.