Dual pumped microresonator frequency combs

A study is made of the nonlinear dynamics of dual pumped microresonator Kerr frequency combs described by a driven and damped nonlinear Schr\"odinger equation, with an additional degree of freedom in the form of the modulation frequency. A truncated four wave model is derived for the pump modes and the dominant sideband pair which is found to be able to describe much of the essential dynamical behaviour of the full equation. The stability of stationary states within the four wave model is investigated and numerical simulations are made to demonstrate that a large range of solutions, including cavity solitons, are possible beyond previously considered low intensity patterns.Comment: 7 pages, 9 figures, submitted to Phys. Rev.

A Coherent State Path Integral for Anyons

We derive an $su(1,1)$ coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to a $su(1,1)$ version of the Holstein-Primakoff transformation.Comment: Latex 6 pages, USITP-94-1

The QCD Trace Anomaly as a Vacuum Effect (The vacuum is a medium is the message!)

We use arguments taken from the electrodynamics of media to deduce the QCD trace anomaly from the expression for the vacuum energy in the presence of an external color magnetic field.Comment: 18 pages, USITP 94-1

Dynamics of the Modulational Instability in Microresonator Frequency Combs

A study is made of frequency comb generation described by the driven and damped nonlinear Schr\"odinger equation on a finite interval. It is shown that frequency comb generation can be interpreted as a modulational instability of the continuous wave pump mode, and a linear stability analysis, taking into account the cavity boundary conditions, is performed. Further, a truncated three-wave model is derived, which allows one to gain additional insight into the dynamical behaviour of the comb generation. This formalism describes the pump mode and the most unstable sideband and is found to connect the coupled mode theory with the conventional theory of modulational instability. An in-depth analysis is done of the nonlinear three-wave model. It is demonstrated that stable frequency comb states can be interpreted as attractive fixed points of a dynamical system. The possibility of soft and hard excitation states in both the normal and the anomalous dispersion regime is discussed. Investigations are made of bistable comb states, and the dependence of the final state on the way the comb has been generated. The analytical predictions are verified by means of direct comparison with numerical simulations of the full equation and the agreement is discussed.Comment: 9 pages, 6 figures, submitted to Phys. Rev.

Modulational instability of nonlinear polarization mode coupling in microresonators

We investigate frequency comb generation in the presence of polarization effects induced by nonlinear mode coupling in microresonator devices. A set of coupled temporal Lugiato-Lefever equations are derived to model the propagation dynamics, and an in-depth study is made of the modulational instability of their multistable homogeneous steady-state solutions. It is shown that new kinds of instabilities can occur for co-propagating fields that interact through nonlinear cross-phase modulation. These instabilities display properties that differ from their scalar counterpart, and are shown to result in the generation of new types of incoherently coupled frequency comb states.Comment: 8 pages, 7 figure

On the numerical simulation of Kerr frequency combs using coupled mode equations

It is demonstrated that Kerr frequency comb generation described by coupled mode equations can be numerically simulated using Fast Fourier Transform methods. This allows broadband frequency combs spanning a full octave to be efficiently simulated using standard algorithms, resulting in orders of magnitude improvements in the computation time.Comment: 3 pages, 1 figure, submitted to Optics Communication