The period map for pulse propagation in nonlinear optical DM fibres
A. V. Mikhailov, V. Yu. Novokshenov*
University of Leeds, UK and
L. D. Landau Institute for Theoretical Physics RAS, 117940 Moscow, Russia
*Institute of Mathematics RAS, 450025 Ufa, Russia
PACS: 74.50.+r, 74.80.Fp
We have derived a simple recursion formula for the amplitude and
chirp of the optical pulse propagating over a Dispersion Managed fibre with
zero mean dispersion. We neglect dissipation and assume the dispersion to be
constant along the adjacent legs of the waveguide, thus providing the
applicability of the integrable nonlinear Schrödinger models within each leg. Choosing the legs
to be long enough to ensure the formation of a self-similar profile we apply
the well-known asymptotic formulas for the non-soliton initial pulses.
Matching them through the interfaces of the legs we get recursion formulas
for the pulse amplitude and chirp. Our analytical results are well justified
by numerical simulations.