On the Generation of Stable Kerr Frequency Combs in the Lugiato-Lefever Model of Periodic Optical Waveguides
On the Generation of Stable Kerr Frequency Combs in the Lugiato-Lefever Model of Periodic Optical Waveguides
复制标题
周期性光波导Lugiato-Lefever模型中稳定克尔频率梳的生成
DOI：
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发表时间：
2018
影响因子：
1.9
通讯作者：
A. Stefanov
中科院分区：
文献类型：
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作者：
S. Hakkaev;M. Stanislavova;A. Stefanov
我们考虑光纤的Lugiato-Lefever（LL）模型。我们构造了一个双参数的定态解族，即Kerr频率梳，当泵浦参数h>0，失谐参数α>0时.这些是O（1）波，因为它们是由三次NLS的标准椭圆余弦解分支而成的。我们确定的谱稳定的，更准确地说，我们表明，谱的线性化运营商包含的特征值0，-2 α $，而其余的是一个子集的$ {mu：Remu=-alpha }$。这与有效阻尼哈密顿系统（如LL模型）的预期一致。
We consider the Lugiato-Lefever (LL) model of optical fibers. We construct a two parameter family of steady state solutions, i.e. Kerr frequency combs, for small pumping parameter $h>0$ and the correspondingly (and necessarily) small detuning parameter, $alpha>0$. These are $O(1)$ waves, as they are constructed as bifurcation from the standard cnoidal solutions of the cubic NLS. We identify the spectrally stable ones, and more precisely, we show that the spectrum of the linearized operator contains the eigenvalues $0, -2alpha$, while the rest of it is a subset of $ {mu: Remu=-alpha }$. This is in line with the expectations for effectively damped Hamiltonian systems, such as the LL model.
DOI：
10.1137/16m1066221
发表时间：
2016-03
期刊：
SIAM J. Appl. Math.
影响因子：
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作者：
Rainer Mandel;W. Reichel
通讯作者：
Rainer Mandel;W. Reichel