Friday, April 22, 2022 11am to 12pm
Fiber lasers generate ultra-short pulses of light for applications such as accurate measurement of time and frequency, the detection of exo-planets, and precision surgery. These lasers are modeled by nonlinear partial differential equations similar to the nonlinear Schroedinger equation and which have both stationary and periodic pulse solutions. This talk will address the mathematical modeling of laser systems, the existence, dynamics, and stability of pulse solutions, and the performance of the systems in the presence of noise.
In the case of periodic pulses, we use semigroup theory to establish the existence of the monodromy operator associated with the linearization of the system about the pulse. We establish a formula for the essential spectrum of the monodromy operator which quantifies whether noise perturbations far from the pulse lead to instabilities. 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, Erika Gallo, Yuri Latushkin, Chris Jones, Jeremy Marzuola, and Curtis Menyuk
ECSW 1.315 JO 4.614
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