No abstract

The speed of light in air is dependent on the air's instantaneous density. Since air density is modulated by sound, sound in the air can be observed and measured using optical methods. One such optical method is Laser Doppler Vibrometry (LDV). Most commonly, LDVs measure the mechanical velocity of a surface. However, by placing a rigid reflector beneath a sound beam in air, it is possible to measure the time rate-of-change of optical refractive index and thus to measure dynamic changes in air density, or sound. In prior demonstrations, this method has been used to visualize sound fields in the audible frequency range and ultrasonic range underwater. Here, we present the first measurements of high-intensity airborne ultrasound beams in the frequency range spanning 100 kHz–300 kHz. We observe accumulated distortion, wave steepening, and weak shock formation as high intensity sound beams propagate. LDV measurements are compared against numerical simulations of the sound field. Advantages of the LDV technique are discussed, and we also attempt to quantify limitations of the technique which include spatial averaging of the measurand along and normal to the optical beam path.

The majority of reported measurements on high intensity ultrasound beams in air are below 40 kHz and performed on standing waves inside of a guide. Here, experimental characterization of high intensity progressive and divergent sound beams in air at 300 kHz are presented. Measurements in this frequency range are challenging. Accurate characterization of high intensity sound beams requires a measurement bandwidth at least ten times the beam's primary frequency, as high intensity soundwaves steepen and form shocks and, therefore, contain significant signal power at harmonic frequencies. Hence, a measurement bandwidth of at least 3 MHz is required. Calibrated measurement microphones are generally not available in this frequency range. This limitation has been overcome by using a hydrophone with a calibrated response from 250 kHz to 20 MHz. A narrowband piezoelectric transducer is used as the source in this study, and it is capable of generating tone burst waveforms centered at 300 kHz with 160 dB sound pressure level surface pressure. Cumulative wave steepening and shock formation are observed in on-axis measurements. The source's surface vibration profile is measured using a scanning laser Doppler vibrometer, and the vibration profile is imported into a numerical wide-angle Khokhlov-Zabolotskaya-Kuznetsov simulation for comparison against measured on-axis waveforms.

The majority of reported measurements on high intensity ultrasound beams in air are below 40 kHz and are performed on standing waves inside a guide. Here we present experimental characterization of high intensity progressive and divergent sound beams in air at 300 kHz. Measurements in this frequency range are challenging. Accurate characterization of high intensity sound beams requires a measurement bandwidth at least 10x the beam's primary frequency, as high intensity soundwaves steepen and form shocks, and therefore contain significant signal power at harmonic frequencies. A measurement bandwidth of at least 3 MHz is therefore required. Calibrated measurement microphones are generally not available in this frequency range. We have overcome this limitation by using a hydrophone with a calibrated response from 250 kHz—20 MHz. A narrowband piezoelectric transducer is used as the source in this study. The source is capable of generating tone burst waveforms centered at 300 kHz and with 160 dB SPL surface pressure. Cumulative wave steepening and shock formation are observed in on-axis measurements. The source's surface vibration profile is measured using a scanning LDV, and the vibration profile is imported into a numerical wide-angle KZK simulation for comparison against measured on-axis waveforms.

Current interest in focused vortex beams is motivated by the ability to trap particles axially and laterally using the resulting radiation force. A simple closed-form solution is obtained in the Fresnel approximation for a sound beam radiated by a Gaussian source with time dependence e−iωt , focal length d, amplitude distribution exp(− r 2/ a 2), and azimuthal phase dependence einθ , where θ is the angle in the plane perpendicular to the beam axis, and the integer n is the topological charge, referred to here as the vorticity. The solution is in good agreement with the pressure field predicted in the paraxial region by numerical evaluation of the Rayleigh integral. Of interest in optics as well as acoustics is the distance from the minimum along the beam axis to the first local maximum, referred to as the vortex ring. The present solution yields rn  =  ηn d/ ka for the vortex ring radius in the focal plane, where k is the wavenumber, and ηn  = 1.69 + 0.965( n−1) for vorticities in the range 1 ≤  n <  O(20). Within this range the radius rn thus increases linearly with the vorticity. Results are also presented for dependence of the focusing gain on the vorticity. [CAG was supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]