Dynamics of the modulational instability in microresonator frequency combs

The generation of optical Kerr frequency combs by microresonators has attracted much interest in the last few years [1]. The equidistant and highly resolved spectral lines of these combs are expected to help facilitate numerous applications such as optical clocks, sensing and spectroscopy. The theoretical descriptions of microresonator frequency combs has to date mostly been carried out using a modal expansion approach, which describes the slow evolution of the comb spectrum using time-domain rate equations [2]. However, this approach has several disadvantages when it comes to modelling of temporal structures and is also computationally expensive to use when applied to broadband combs, which in the case of octave spanning combs can comprise thousands of resonant modes. An alternative description of microresonator frequency combs has recently been proposed [3] that allows the comb to be described in the time-domain under quite general conditions, by means of a mean-field Lugiato-Lefever equation, which is a driven and damped nonlinear Schrödinger equation that has previously been applied to great success in the description of fiber-ring lasers [4].