Parabolic similariton pulses in high gain fiber amplifiers with arbitrary longitudinal gain profiles

Summary form only given. The first experiments studying self-similar propagation of linearly-chirped parabolic pulses have recently been reported in a normal dispersion Yb:amplifier (Fermann et al, Proc. OSA 2000, CLEO Tech. Digest paper CME2, p. 21, 2000). Parabolic pulses are of fundamental interest since they are a new class of solution to the nonlinear Schrodinger equation (NLSE) with constant gain and have wide-ranging practical significance since they are efficiently compressed. In this paper we generalize the work of Fermann et al (Phys. Rev. Lett. vol. 84, p. 6010, 2000) to show that parabolic pulses are solutions to the NLSE for any gain profile, and determine the optimal profile to achieve minimum duration pulses after compression.