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Modelling of Kerr frequency combs: successes and challenges

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Date and time:��

Tuesday, November 4, 2014 - 4:30pm

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ECOT 226

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An optical microresonator exhibits many optical resonance frequencies (modes) that are nearly equidistantly spaced. Coupling a single-frequency high-power laser into such a resonator leads to coupling between these modes via the Kerr nonlinearity and results in the generation of an optical Kerr frequency comb, which corresponds to light consisting of equidistantly spaced frequencies.

Optical frequency combs are of great interest for a wide variety of applications, particularly for time and frequency metrology and spectroscopy. The invention of the optical frequency comb has been awarded with the Nobel prize in physics in 2005. In the past few years, 2 models have been proposed to describe these Kerr frequency combs, one being the Fourier transform of the other. The first model is based on a modal expansion of the electromagnetic field in the optical cavity, and leads to an infinite number of equations coupled through a nonlinear and global interaction, the four-wave mixing. In the time-domain, these equations can be transformed into a partial differential equation similar to a nonlinear Schrödinger equation with additional terms: damping, detuning and driving. This equation is also analogous to a Lugiato-Lefever equation in one dimension.

These models have successfully described a large number of experimental results; however, we recently found at NIST a variety of peculiar Kerr comb states that we have not been able to completely explain. These combs show interesting properties: they all appear in the same small region of the parameter space, they are all “phase-locked”, and some of them present phase alignments with very well-defined pi-shifts. Since these states were observed in different types of resonators and materials, we believe there exists a fundamental explanation in terms of nonlinear dynamics or phase synchronization to the existence of these combs.