We show from an elementary symmetry analysis that, in dispersion-compensated systems for which a lossless model is valid, nonlinearity requires a chirp-free point at the center of symmetry (if such exists) of the map for any kind of unique periodic solution. We also present an example of a more-complex map when the periodic solution is not unique.
© 1999 Optical Society of America
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.1450) Nonlinear optics : Bistability
(260.2030) Physical optics : Dispersion
S. K. Turitsyn, J. H. B. Nijhof, V. K. Mezentsev, and N. J. Doran, "Symmetries, chirp-free points, and bistability in dispersion-managed fiber lines," Opt. Lett. 24, 1871-1873 (1999)