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Using the known solutions of the Lugiato-Lefever equation, we derive universal trends of Kerr frequency combs. In particular, normalized properties of temporal cavity soliton solutions lead us to a simple analytic estimate of the maximum attainable bandwidth for given pump-resonator parameters. The result is validated via comparison with past experiments encompassing a diverse range of resonator configurations and parameters.
A single closed-form analytical solution of the driven nonlinear Schr{o}dinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, dark-solitons, and a large class of periodic wavetrains.
Kerr optical frequency combs with multi-gigahertz spacing have previously been demonstrated in chip-scale microresonators, with potential applications in coherent communication, spectroscopy, arbitrary waveform generation, and radio frequency photoni
We use numerical simulations based on an extended Lugiato-Lefever equation (LLE) to investigate the stability properties of Kerr frequency combs generated in microresonators. In particular, we show that an ensemble average calculated over sequences o
Recent experiments have demonstrated the generation of widely-spaced parametric sidebands that can evolve into clustered optical frequency combs in Kerr microresonators. Here we describe the physics that underpins the formation of such clustered comb
Using numerical simulations of an extended Lugiato-Lefever equation, we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators taking into account third-order dispersion effects. We show