Title: The essential spectrum of periodically stationary pulses in femtosecond fiber lasers
Abstract: In recent generations of experimental fiber lasers, light pulses exhibit significant pulse breathing but return to the same shape once per round trip. We investigate the linear stability of such periodically stationary pulses with the aid of a lumped model in which the fiber amplifier in the system is modeled using the nonlinear Schroedinger equation with saturable gain and spectral filtering. With the aid of semigroup theory, we define the monodromy operator associated with the linearization of the system about a periodically stationary pulse. We establish a formula for the essential spectrum of the monodromy operator and show that this portion of the spectrum is stable provided that loss exceeds gain away from the pulse. We validate these results using numerical simulations of an experimental laser in which we discover periodically stationary pulses by numerically optimizing a Poincare map functional.
This is joint work with Vrushaly Shinglot, Yuri Latishkin, Chris Jones, Jeremy Marzuola, and Curtis Menyuk