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.

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.

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.

Sounds to Astound: An acoustics outreach show.

Sounds to Astound is an acoustics demonstration show, produced for the community twice yearly by the Brigham Young University Student Chapter of the Acoustical Society of America. The free, interactive demonstration show explores the science of sound for a target audience of fifth- to eighth-grade students. Introductory acoustics concepts, such as longitudinal wave motion, wave properties, propagation effects, and standing waves, are taught with live demonstrations, animations, and videos. The goal of this paper is to inspire and encourage readers in their outreach efforts by describing the purposes of Sounds to Astound and technical details of several entertaining and educational demonstrations. Lessons learned from a decade of these student-produced shows serve as an aid for future efforts and highlight the benefits of outreach efforts, particularly for the students involved.

Nonlinear characteristics of high amplitude focusing using time reversal in a reverberation chamber.

Time reversal (TR) signal processing is an effective tool to exploit a reverberant environment for the intentional focusing of airborne, audible sound. A previous room acoustics TR study found preliminary evidence that above a certain focal amplitude the focal waveform begins to display signs of nonlinearity [Willardson, Anderson, Young, Denison, and Patchett, J. Acoust. Soc. Am. 143(2), 696-705 (2018)]. This study investigates that nonlinearity further by increasing the focal peak amplitudes beyond that previously observed. This increases the nonlinear characteristics, allowing for a closer inspection of their properties. An experiment is conducted using eight horn loudspeaker sources and a single receiver in a reverberation chamber. A maximum peak focal amplitude of 214.8 kPa (200.6 dBpk) is achieved. The focus signal waveforms are linearly scaled to observe and characterize the nonlinear amplification of the waveform. Frequency spectra of the peak focal amplitudes are plotted to observe changes in frequency content as the signals become nonlinear. A one-dimensional spatial scan of the focal region is conducted to observe properties of the converging and diverging waves. A proposal for a possible explanation involving free-space Mach stem formation is given.

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.

High-amplitude time reversal focusing of airborne ultrasound to generate a focused nonlinear difference frequency.

Time reversal (TR) focusing of airborne ultrasound in a room is demonstrated. Various methods are employed to increase the amplitude of the focus. These methods include creating a small wooden box (or chamber) to act as a miniature reverberation chamber, using multiple sources, and using the clipping processing method. The use of a beam blocker to make the sources more omnidirectional is also examined, and it is found that for most source/microphone orientations, the use of a beam blocker increases the amplitude of the focus. A high-amplitude focus of 134 dB peak re 20 µPa sound pressure level with a center frequency of about 38 kHz is generated using TR. Using four sources centered at 36.1 kHz and another four sources centered at 39.6 kHz, nonlinear difference frequency content centered at 3.5 kHz is observed in the focus signal. The difference frequency amplitude grows quadratically with increasing primary frequency amplitude. When using beam blockers, the difference frequency content propagates away from the focal location with higher amplitude than when beam blockers are not used. This is likely due to the differences in the directionality of the converging waves during TR focusing.

The performance of time reversal in elastic chaotic cavities as a function of volume and geometric shape of the cavity.

Time reversal is used as an energy-focusing technique in nondestructive evaluation applications. Here, it is often of interest to evaluate small samples or samples that do not lend themselves to the bonding of transducers to their surfaces. A reverberant cavity, called a chaotic cavity, attached to the sample of interest provides space for the attachment of transducers as well as an added reverberant environment, which reverberation is critical to the quality of time reversal focusing. The goal of this research is to explore the dependence of the quality of the time reversal focusing on the size and geometric shape of the chaotic cavity used. An optimal chaotic cavity will produce the largest focusing amplitude, best spatial resolution, and linear focusing of the time reversed signal. Ultrasonic elastic-wave experiments are performed on a rectangular, cylindrical, and three-dimensional Sinai billiard prism samples, and experiments are repeated each time these samples are successively cut down to smaller volumes. As the size of the cavity decreases, the peak amplitude may increase or decrease depending on the normalization scheme employed. The higher the degree of ergodicity of the cavity, the higher the amplitude and quality focusing achieved.

Solving one-dimensional acoustic systems using the impedance translation theorem and equivalent circuits: A graduate level homework assignment.

The natural frequency resonances and sound radiation from one-dimensional acoustic systems are of great interest in the study of musical instruments, human vocal tract effects on speech, automotive exhaust pipes, duct systems for temperature control in buildings, and more. The impedance translation theorem is an approach that may be used to solve for the input impedance and therefore the resonance frequencies of one-dimensional systems. Equivalent circuits offer another approach to solving one-dimensional systems, though with equivalent circuits you can also solve for the response at any location in the system, including the radiated sound pressure. At Brigham Young University, there are two graduate level courses that teach these two techniques. One of the most challenging and memorable homework assignments from these courses is based on using one of these techniques to analyze a particular acoustic system and compare its response with the real thing. This paper discusses the basics of these two techniques and applies them to an analysis of phonemes produced by altering the human vocal tract. Details about the homework assignments are also given.

A comparison of impulse response modification techniques for time reversal with application to crack detection.

Time reversal (TR) focusing used for nonlinear detection of cracks relies on the ability of the TR process to provide spatially localized, high-amplitude excitation. The high amplitude improves the ability to detect nonlinear features that are a signature of the motion of closed cracks. It follows that a higher peak focal amplitude than what can be generated with the traditional TR process will improve the detection capability. Modifying the time-reversed impulse response to increase the amplitude of later arrivals in the impulse response, while maintaining the phase information of all arrivals, increases the overall focal signal amplitude. A variety of existing techniques for increasing amplitude are discussed, and decay compensation TR, a technique wherein amplitude is increased according to the inverse of the amplitude envelope of the impulse response decay, is identified as the best modification technique for nonlinear crack detection. This technique increases the focal signal amplitude with a minor introduction of harmonic content, a drawback in two other methods studied, one-bit TR and clipping TR. A final study employs both decay compensation TR and traditional TR, focusing on a rod with stress corrosion cracking, and compares the merits of each in detecting nonlinearity from cracks in a real system.

Nonlinearity from stress corrosion cracking as a function of chloride exposure time using the time reversed elastic nonlinearity diagnostic.

The Time Reversed Elastic Nonlinearity Diagnostic (TREND) has a long history of successful nondestructive detection of cracks in solids using nonlinear indicators. Recent research implemented TREND to find stress corrosion cracking (SCC) in the heat-affected zone adjacent to welds in stainless steel. SCC development around welds is likely to occur due to the temperature and chemical exposure of steel canisters housing spent nuclear fuel. The ideal SCC detection technique would quantify the size and extent of the SCC, rather than just locating it, as TREND has been used for in the past. The current paper explores TREND's ability to detect an assumed increase in SCC over time using 13 samples exposed to a magnesium chloride (MgCl2) bath for different lengths of time. The samples are then scanned with TREND and nonlinearity is quantified for each scan point and each sample. The results suggest that TREND can be used to not only locate SCC in the heat-affected zone, but also track an increase in nonlinearity, and thereby an increase in damage, in samples exposed to the MgCl2 solution for a longer duration.

Time reversal focusing of high amplitude sound in a reverberation chamber.

Time reversal (TR) is a signal processing technique that can be used for intentional sound focusing. While it has been studied in room acoustics, the application of TR to produce a high amplitude focus of sound in a room has not yet been explored. The purpose of this study is to create a virtual source of spherical waves with TR that are of sufficient intensity to study nonlinear acoustic propagation. A parameterization study of deconvolution, one-bit, clipping, and decay compensation TR methods is performed to optimize high amplitude focusing and temporal signal focus quality. Of all TR methods studied, clipping is shown to produce the highest amplitude focal signal. An experiment utilizing eight horn loudspeakers in a reverberation chamber is done with the clipping TR method. A peak focal amplitude of 9.05 kPa (173.1 dB peak re 20 µPa) is achieved. Results from this experiment indicate that this high amplitude focusing is a nonlinear process.

Optimized phase sensing in a truncated SU(1,1) interferometer.

Homodyne detection is often used for interferometers based on nonlinear optical gain media. For the configuration of a seeded, "truncated SU(1,1)" interferometer Anderson, et al. [ Phys. Rev. A95, 063843 (2017)] showed how to optimize the homodyne detection scheme and demonstrated theoretically that it can saturate the quantum Cramer-Rao bound for phase estimation. In this work we extend those results by taking into account loss in the truncated SU(1,1) interferometer and determining the optimized homodyne detection scheme for phase measurement. Further, we build a truncated SU(1,1) interferometer and experimentally demonstrate that this optimized scheme achieves a reduction in noise level, corresponding to an enhanced potential phase sensitivity, compared to a typical homodyne detection scheme for a two-mode squeezed state. In doing so, we also demonstrate an improvement in the degree to which we can beat the standard quantum limit with this device.

Time reversal acoustics applied to rooms of various reverberation times.

Time Reversal (TR) is a technique that may be used to focus an acoustic signal at a particular point in space. While many variables contribute to the quality of TR focusing of sound in a particular room, the most important have been shown to be the number of sound sources, signal bandwidth, and absorption properties of the medium as noted by Ribay, de Rosny, and Fink [J. Acoust. Soc. Am. 117(5), 2866-2872 (2005)]. However, the effect of room size on TR focusing has not been explored. Using the image source method algorithm proposed by Allen and Berkley [J. Acoust. Soc. Am. 65(4), 943-950 (1979)], TR focusing was simulated in a variety of rooms with different absorption and volume properties. Experiments are also conducted in a couple rooms to verify the simulations. The peak focal amplitude, the temporal focus quality, and the spatial focus clarity are defined and calculated for each simulation. The results are used to determine the effects of absorption and room volume on TR. Less absorption increases the amplitude of the focusing and spatial clarity while decreasing temporal quality. Dissimilarly, larger volumes decrease focal amplitude and spatial clarity while increasing temporal quality.

Improved measurement of two-mode quantum correlations using a phase-sensitive amplifier.

We demonstrate the ability of a phase-sensitive amplifier (PSA) to pre-amplify a selected quadrature of one mode of a two-mode squeezed state in order to improve the measurement of two-mode quantum correlations that exist before degradation due to optical and detection losses. We use four-wave mixing (4WM) in 85Rb vapor to generate bright beams in a two-mode squeezed state. One of these two modes then passes through a second 4WM interaction in a PSA configuration to noiselessly pre-amplify the desired quadrature of the mode before loss is intentionally introduced. We demonstrate an enhancement in the measured degree of intensity correlation and intensity-difference squeezing between the two modes.