The essential spectrum of periodically stationary pulses in lumped models of short‐pulse fiber lasers
The essential spectrum of periodically stationary pulses in lumped models of short‐pulse fiber lasers
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DOI：
10.1111/sapm.12538
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发表时间：
2022-11
影响因子：
2.7
通讯作者：
Vrushaly Shinglot;J. Zweck
中科院分区：
文献类型：
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作者：
Vrushaly Shinglot;J. Zweck
在现代短脉冲光纤激光器中，在激光回路的每一次往返中都存在明显的脉冲呼吸。因此，平均模型不能用于定量建模和设计。相反，需要的是集总模型，该模型是通过将激光的各个部件的模型串联起来得到的。由于集总模型中的脉冲是周期性的而不是平稳的，因此利用周期脉冲的往返算子线性化得到的一元算子来评估其线性稳定性。给出了周期脉冲的平滑性和衰减性的条件，保证了单算子在适当的勒贝格函数空间上存在。给出了单算子的本质谱的一个公式，该公式可用于量化连续波扰动的增长率。这个公式是通过证明单算子的本质谱等于一个相关的渐近算子的本质谱来建立的。由于渐近单算子在傅里叶域中充当乘法算子，因此可以推导出其谱的公式。虽然主要结果是针对特定的实验拉伸脉冲激光器，但分析表明，它们可以很容易地适应于广泛的集总激光模型。
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.