In many laser systems, frequency combs whose output is frequency-modulated (FM) can form, producing light whose frequency sweeps linearly. While this intriguing result has been replicated experimentally and numerically, a compact description of the core physics has remained elusive. By creating a mean-field theory for active cavities analogous to the Lugiato–Lefever equation, we show that these lasers are described by a nonlinear Schrödinger equation with a potential proportional to the phase of the electric field. This equation can be solved analytically and produces a field with quasi-constant intensity and piecewise quadratic phase. We refer to these nondispersive waves as extendons, and they describe both fundamental FM combs and harmonic states. Our results apply to many lasers, explaining the ubiquity of this phenomenon, and our new theory unifies many experimental observations.

中文翻译：

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利用有源腔平均场理论揭示调频梳的起源

在许多激光系统中，会形成输出频率经过调频（FM）的频率梳，从而产生频率线性扫描的光。虽然这个有趣的结果已经通过实验和数值进行了复制，但对核心物理的紧凑描述仍然难以捉摸。通过为活动腔创建类似于Lugiato-Lefever方程的平均场理论，我们表明这些激光器由非线性Schrödinger方程描述，其电势与电场相位成正比。该方程可以解析地求解，并产生具有准恒定强度和分段二次相位的场。我们将这些非色散波称为扩展子，它们描述了基本的FM梳和谐波状态。我们的结果适用于许多激光器，解释了这种现象的普遍性，我们的新理论统一了许多实验观察结果。