Restricting angles of incidence to improve super resolution in time reversal focusing that uses metamaterial properties of a resonator array.

Focusing waves with a spatial extent smaller than a half wavelength (i.e., super resolution or sub diffraction limit) is possible using resonators placed in the near field of time reversal (TR) focusing. While a two-dimensional (2D) Helmholtz resonator array in a three-dimensional reverberant environment has limited ability to produce a high-resolution spatial focus in the TR focusing of audible sound, it is shown that acoustic waves propagating out-of-plane with the resonator array are not as strongly affected by the smaller effective wavelength induced by the resonator array, partially negating the effect of the resonators. A physical 2D waveguide is shown to limit the out-of-plane propagation, leading to improved resolution. It is also shown that post processing using an orthogonal particle velocity decomposition of a spatial scan of the focusing can filter out-of-plane particle motion in the near field of the array, which bypasses the effect of the unwanted third spatial dimension of propagation. The spatial resolution in a reverberant environment is shown to improve in the presence of a 2D Helmholtz resonator array and then further improve by adding a 2D waveguide. The resolution among the resonator array is better still without using a waveguide and instead using the partial-pressure reconstruction.

Time reversal imaging of complex sources in a three-dimensional environment using a spatial inverse filter.

Time reversal focusing above an array of resonators creates subwavelength-sized features when compared to wavelengths in free space. Previous work has shown the ability to focus acoustic waves near the resonators with and without time reversal with an array placed coplanar with acoustic sources, principally using direct sound emissions. In this work, a two-dimensional array of resonators is studied with a full three-dimensional aperture of waves in a reverberation chamber and including significant reverberation within the time reversed emissions. The full impulse response is recorded, and the spatial inverse filter is used to produce a focus among the resonators. Additionally, images of complex sources are produced by extending the spatial inverse filter to create focal images, such as dipoles and quadrupoles. Although waves at oblique angles would be expected to degrade the focal quality, it is shown that complex focal images can still be achieved with super resolution fidelity when compared to free space wavelengths.

Numerical modeling of Mach-stem formation in high-amplitude time-reversal focusing.

In acoustics, time-reversal processing is commonly used to exploit multiple scatterings in reverberant environments to focus sound to a specific location. Recently, the nonlinear characteristics of time-reversal focusing at amplitudes as high as 200 dB have been reported [Patchett and Anderson, J. Acoust. Soc. Am. 151(6), 3603-3614 (2022)]. These studies were experimental in nature and suggested that converging waves nonlinearly interact in the focusing of waves, leading to nonlinear amplification. This study investigates the nonlinear interactions and subsequent characteristics from a model-based approach. Utilizing both finite difference and finite-element models, it is shown that nonlinear interactions between high-amplitude waves lead to free-space Mach-wave coalescence of the converging waves. The number of waves used in both models represents a small piece of the full aperture of converging waves experimentally. Limiting the number of waves limits the number of Mach-stem formations and reduces the nonlinear growth of the focus amplitudes when compared to experiment. However, limiting the number of waves allows the identification of individual Mach waves. Mach wave coalescence leading to Mach-stem formation appears to be the mechanism behind nonlinear amplification of peak focus amplitudes observed in high-amplitude time-reversal focusing.

Super-resolution within a one-dimensional phononic crystal of resonators using time reversal in an equivalent circuit model.

An equivalent circuit model has been developed to model a one-dimensional waveguide with many side-branch Helmholtz resonators. This waveguide constitutes a phononic crystal that has been shown to have decreased phase speed below the resonance frequency of an individual resonator. This decreased phase speed can be exploited to achieve super-resolution using broadband time reversal focusing techniques. It is shown that the equivalent circuit model is capable of quantifying this change in phase speed of the crystal and also the small-scale wave-resonator interactions within the crystal. The equivalent circuit model enables the parameterization of the physical variables and the optimization of the focusing bandwidth by balancing the combination of increasing resolution and decreasing amplitude near the resonance frequency. It is shown that the quality factor-in this case, the quality factor determined by the geometric shape of each resonator-controls the range of frequencies that are strongly affected by the Helmholtz resonators.

The physics of knocking over LEGO minifigures with time reversal focused vibrations for use in a museum exhibit.

Time reversal (TR) is a method of focusing wave energy at a point in space. The optimization of a TR demonstration is described, which knocks over one selected LEGO minifigure among other minifigures by focusing the vibrations within an aluminum plate at the target minifigure. The aim is to achieve a high repeatability of the demonstration along with reduced costs to create a museum exhibit. By comparing the minifigure's motion to the plate's motion directly beneath its feet, it is determined that a major factor inhibiting the repeatability is that the smaller vibrations before the focal event cause the minifigure to bounce repeatedly and it ends up being in the air during the main vibrational focal event, which was intended to launch the minifigure. The deconvolution TR technique is determined to be optimal in providing the demonstration repeatability. The amplitude, frequency, and plate thickness are optimized in a laboratory setting. An eddy current sensor is then used to reduce the costs, and the impact on the repeatability is determined. A description is given of the implementation of the demonstration for a museum exhibit. This demonstration illustrates the power of the focusing acoustic waves, and the principles learned by optimizing this demonstration can be applied to other real-world applications.

The impact of room location on time reversal focusing amplitudes.

Time reversal (TR) is a signal processing technique often used to generate focusing at selected positions within reverberant environments. This study investigates the effect of the location of the focusing, with respect to the room wall boundaries, on the amplitude of the focusing and the uniformity of this amplitude when focusing at various room locations. This is done experimentally with eight sources and two reverberation chambers. The chambers are of differing dimensions and were chosen to verify the findings in different volume environments. Multiple spatial positions for the TR focusing are explored within the rooms' diffuse field, against a single wall, along a two-wall edge, and in the corners (three walls). Measurements of TR focusing at various locations within the room show that for each region of study, the peak amplitude of the focusing is quite uniform, and there is a notable and consistent increase in amplitude for each additional wall that is adjacent to the focal location. A numerical model was created to simulate the TR process in the larger reverberation chamber. This model returned results similar to those of the experiments, with spatial uniformity of focusing within the room and increases when the focusing is near adjacent walls.

Time reversal in a phononic crystal using finite-element modeling and an equivalent circuit model.

A phononic crystal acts as a dispersive medium with a phase speed that is lower than the bulk wave speed at frequencies below the resonance of a single resonator. Time reversal is used to compensate for the phase shifts caused by individual resonators as the waves enter the medium and enable focusing of acoustic waves among the crystal. An equivalent circuit, which can predict the dispersion and attenuation of the crystal model, is shown and compared to a full-wave finite-element simulation in frequency and time. The phase shift due to a single resonator is also depicted.