A venting resonator emitting monochromatic periodic traveling waves in dispersive media

Abstract

Dynamically stable traveling periodic waves are notoriously difficult to realize experimentally. Manifestations of such waves inherently become unstable in any dispersive medium, whether it be at continuum length scales in fluid mechanics, in electrodynamics, or in nonlinear optics. Here, a simple experimental system is proposed where Stokes waves are emitted from a resonator whose cavity accommodates standing waves of same wavelength that is emitted out. A single characteristic wavelength is found for each driving frequency despite the coexistence of standing and traveling waves, external noise, and potentially parasitic reflections. The system's response is shown to be reliable at very small values of quality factor. A unique utility of this model system is suggested in that such a venting resonator can be used as an inhibitor of modulation instability in dispersive medium where an engineering application demands stable periodic traveling waves. Some parallels are drawn with other unbounded resonators found in society, whereby their leakiness is central to their application, such as the role of air-filled cavity to achieve impedance matching in stringed musical instruments, or energy harvesting from oscillating fluid columns in nature.