Complex frequency sink

Abstract

As the time-reversed analog of the source, the sink is an abstraction of a device that can absorb incident symmetrical waves at a point. Such a device is useful for its ability to create an arbitrarily small focusing spot, surpassing the conventional diffraction limit. Sinks have been created using impedance matching and active cancellation; however, these techniques require the introduction of tailored loss or gain into the system. Here, we demonstrate a new method for creating a sink that requires no loss or gain but instead relies on complex frequency excitations, harmonic excitations that exponentially grow or decay in time. Recent work has shown how complex frequency excitations in Hermitian systems enable phenomena such as PT symmetry and perfect absorption that are typically only associated with non-Hermitian systems. We will discuss the theory of the complex frequency sink and analyze the case of a sink in a thin elastic plate. We will present experimental results where the scattering of a symmetric scatterer is minimized by complex frequency waves launched by piezoelectric patches. Laser-doppler vibrometer measurements of the plate shows the resonator’s curious behavior as a loss and gain free sink.