A Lossless Sink Based on Complex Frequency Excitations

The creation of a sink in a lossless wave-bearing medium is achieved using complex frequency signals-harmonic excitations that exponentially grow in time. The wave sink, where incident waves are confined to a point, has attracted interest for imaging and sensing since it may lead to arbitrarily small hotspots that surpass the diffraction limit. However, most methods of creating sinks require careful tuning, such as by impedance matching the sink to free space through the inclusion of loss, which imposes constraints on emerging applications. An alternative method, proposed here, relies on complex frequency excitations, bypassing the need to modify the scattering system by instead shaping the input signal. Eigenvalue zeros derived from a scattering formalism extended to the complex frequency plane reveal operating conditions that induce complete energy trapping under steady-state conditions in a framework generally applicable to 2D and 3D media. To support the developed theory, an experiment is performed where a sink is realized using elastic waves on a plate with a circular cutout. These findings may lead to imaging and sensing applications relying on subwavelength focal points and nonlinear wave generation due to the high amplitudes achieved over short timescales.