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.