Self-Similar Propagation and Amplification of Parabolic Pulses in Optical Fibers

Abstract

Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.

Real-time measurement of long parabolic optical similaritons

“…Output temporal width can be continuously varied over a wide range, from 50 ps to 250 ps. The experimental results are in good agreement with a fit based on a E ini 1/3 function which is typical of the selfsimilar analytical evolution of the parabolic pulses [1]. However let us note that for pulse durations below 100 ps, the asymptotic parabolic profile is not fully reached.…”

“…Experimental demonstrations have been carried out both in rare-earth doped fibres (with Ytterbium [1] and Erbium [2] dopants) as well as in Raman fibre amplifiers [3]. The use of frequency resolved optical gating (FROG) technique based on iterative algorithms has enabled a precise but indirect intensity and phase characterisation of the amplified pulses which exhibit a parabolic intensity profile combined with a strictly linear chirp.…”

“…Since their first experimental demonstration in 2000 [1], parabolic similaritons have stimulated a growing interest in the field of fibre amplification of high-power ultrashort pulses. This new type of optical pulse is asymptotically generated in an amplifier as the result of the combined interaction of normal dispersion, Kerr nonlinearity and gain.…”

Active Mamyshev regenerator

“…The characteristic parameters of the similariton (peak power, temporal and spectral widths) then undergo an exponential increase with the propagation distance. A remarkable feature that constitutes a clear advantage for regeneration purpose 29) is that this asymptotic profile does only depend on the initial pulse energy and not on the details of the initial pulse shape 30,34) .…”

“…Indeed, it has been demonstrated that any initial waveform propagating under conditions of normal dispersion, non-linearity and distributed gain will evolve asymptotically into a similariton, a pulse characterized by a parabolic intensity profile with a linear positive chirp [30][31][32] . Once this typical parabolic profile is obtained, it propagates self-similarly, i.e.…”