Monophonic and polyphonic acoustic vortices: the foundation of acoustic tweezers

Wilson, Chris (2013) Monophonic and polyphonic acoustic vortices: the foundation of acoustic tweezers. MSc(R) thesis, University of Glasgow.

Abstract

It is well known that light is capable of carrying a component of orbital angular momentum (OAM), and that this OAM can be manipulated in such a way as to be useful in applications such as optical trapping, leading to the development of optical tweezers which now see use in many fields for the manipulation of small scale particles. Despite the advances in the field of optical OAM, relatively little research has been conducted in the field of acoustical OAM. Presented in this thesis is evidence of the equivalence of optical and acoustical OAM in several experiments that have already been proven and widely accepted for the optical case.

Demonstrated in chapter 3 is what has been dubbed an acoustic spanner, which provides a preamble to the main body of the research. In this chapter, an experiment that demonstrates how sound waves can carry a component of OAM using simple off-the-shelf equipment is discussed. An anular array of loudspeakers was constructed and a set of analogue electronics was assembled in such a way that, when driven by a signal from a laboratory signal generator, eight individual signals were
produced, identical to the driving signal, but separated by a relative phase difference of π/4. The net result is that, considered as a set, there is a difference of 2π between the first and eighth signals. These signals were sent to the eight speakers which resulted in an approximation to a l = 1 beam. A demonstration is also made of how the OAM carried by a sound beam may be transmitted to matter by observing the rotation of a styrofoam disk, and measure the total displacement from it’s equilibrium position. These reults were confirmed when the direction of the beam was reversed by reversion the direction of the phase increase.

A further experiment detailed in chapter 4 was conducted where four signals of varying frequency were superimposed upon one another before being phase shifted and sent to the speakers. This meant that instead of a beam with a single tone, as was generated in the acoustic spanner experiment, a polyphonic acoustic vortex was generated using four frequencies. Using a microphone mounted atop a translation stage, an amplitude cross-section of the vortex confirmed that there were indeed four constituent vortices in the beam. It was also confirmed that these constituent beams were not coupled to one another, and thus it was possible to stear each component of the vortex without affecting the others. This was achieved by modulating the amplitude of the signal at one speaker, and applying an equal and opposite modulation at the corresponding speaker on the opposite side of the array.

The final experiment was an investigation into the phase structure of acoustical vortices. While only first order beams were used in the acoustic spanner and polyphonic vortex experiments, high order beams were produced this time. Beams of l = ±1±2±4 were produced, and the same microphone and translation stage that was used before was used totrace a 2-dimensional cross-section through the beams and measure their phase profiles. The results for l = ±1 and ±2 were as expected, and the phase profiles for these can be seen in the figures in chapter 5. Beams for l = ±4 were expected to fail since the number of speakers used in the array did not provide enough sources for the beam to fully form into a vortex, and this was also as expected. The phase profiles are incliuded in chapter 5 to demonstrate the limitations of the experiment, and to show that in this case that it’s impossible to differentiate between a l = 4 and a l = −4 beam in the say that can be done for the others. Similarly, l = ±3 beams are not measured due to the limitations of the apparatus.

• Item Type: Thesis (MSc(R))
• Qualification Level: Masters
• Keywords: acoustic, orbital angular momentum, vortex, vortices
• Subjects: Q Science > QC Physics
• Colleges/Schools: College of Science and Engineering > School of Physics and Astronomy
• Supervisor's Name: Padgett, Prof. Miles
• Date of Award: 2013
• Depositing User: Mr Chris Wilson
• Unique ID: glathesis:2013-5092
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 15 Apr 2014 08:33
• Last Modified: 15 Apr 2014 08:36
• URI: https://theses.gla.ac.uk/id/eprint/5092