The essential spectrum of periodically stationary pulses in lumped models of short-pulse fiber lasers

TL;DR

This paper analyzes the essential spectrum of periodically stationary pulses in lumped models of short-pulse fiber lasers, providing a formula to assess pulse stability and growth of perturbations.

Contribution

It introduces a method to compute the essential spectrum of the monodromy operator in lumped laser models, applicable to various experimental setups.

Findings

Derived a formula for the essential spectrum of the monodromy operator.

Showed the spectrum can be obtained from an asymptotic operator acting as a multiplication operator.

Applicable to a wide range of lumped laser models.

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. Since 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 which 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.