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Abstract In modern short‐pulse fiber lasers, there is significant pulse breathing over each round trip of the laser loop. Consequently, averaged models cannot be used for quantitative modeling and design. Instead, lumped models, which are obtained by concatenating models for the various components of the laser, are required. As the pulses in lumped models are periodic rather than stationary, their linear stability is evaluated with the aid of the monodromy operator obtained by linearizing the round‐trip operator about the periodic pulse. Conditions are given on the smoothness and decay of the periodic pulse that ensure that the monodromy operator exists on an appropriate Lebesgue function space. A formula for the essential spectrum of the monodromy operator is given, which can be used to quantify the growth rate of continuous wave perturbations. This formula is established by showing that the essential spectrum of the monodromy operator equals that of an associated asymptotic operator. Since the asymptotic monodromy operator acts as a multiplication operator in the Fourier domain, it is possible to derive a formula for its spectrum. Although the main results are stated for a particular experimental stretched pulse laser, the analysis shows that they can be readily adapted to a wide range of lumped laser models.
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Computation and Stability Analysis of Periodically Stationary Pulses in a Short Pulse Laser
A significant challenge in the modeling of short pulse fiber lasers is that with each successive generation there has been a dramatic increase in the amount by which the pulse varies over each round trip. Therefore, lumped rather than averaged models are required to accurately compute the periodically stationary (breather) solutions generated by these lasers. We use a spectral method to assess the linear stability of periodically stationary pulses in lumped models. This approach extends previous work by Menyuk and Wang on stationary pulses in averaged models. We first present a gradient based optimization method inspired by the work of Ambrose and Wilkening to compute periodically stationary pulses. Then, we use Floquet theory to characterize the linear stability of the pulses obtained using optimization in terms of the spectrum of the monodromy operator,M, obtained by linearization of the round trip operator about a periodically stationary pulse.
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- Award ID(s):
- 1807272
- PAR ID:
- 10326042
- Date Published:
- Journal Name:
- Twelfth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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