Nonlinear interactions between vibration modes with vastly different eigenfrequencies

Nonlinear interactions between modes with eigenfrequencies that differ by orders of magnitude are ubiquitous in various fields of physics, ranging from cavity optomechanics to aeroelastic systems. Simplifying their description to a minimal model and grasping the essential physics is typically a system-specific challenge. We show that the complex dynamics of these interactions can be distilled into a single generic form, namely, the Stuart-Landau oscillator. With our model, we study the injection locking and frequency pulling of a low-frequency mode interacting with a blue-detuned high-frequency mode, which generate frequency combs. Such combs are tunable around both the high and low carrier frequencies. By discussing the analogy with a simple mechanical system model, we offer a minimalistic conceptual view of these complex interactions originating the frequency combs, together with showcasing their frequency tunability. Nonlinear interactions between modes with eigenfrequencies that differ by orders of magnitude occur in several physical systems. This article provides a simple conceptual model of these interactions, and uses this model to design tunable frequency combs.

Automated summary

This article provides a simplified conceptual model to describe and design the nonlinear interactions between modes with different characteristic frequencies, and the generation of tunable frequency comb structures.