Joint supervisors: Prof Alastair P Hibbins, Prof J Roy Sambles
External partner: Dr Ben Hodder (QinetiQ)
The ability to emit or receive sound with directional dependence is of great relevance to acoustic imaging and navigation applications. A classic example of the use of sound for navigation is echolocation employed by bats and marine mammals. If one knows the speed of sound in the medium carrying the wave, then the time elapsed between the generation and reception of the acoustic signal provides an estimate of the distance between the animal and the object that scatters the signal. Although this is useful information, a single omnidirectional source-receiver pair will only tell the distance between the two with no information about direction.
Acoustic localization is most often performed using arrays of transducers such as hydrophones and microphones. If an array of acoustic point sources are equally spaced along a line, then when all of the sources are driven to emit sound of equal magnitude at the same time, the resulting wave front propagates at an angle normal to the array. If, instead of activating all of the sources simultaneously, we impart a phase delay of ϕ across each successive element in the array, the emitted wave front is steered at an angle θ. This often requires complex electromechanical systems, post processing algorithms, and significant power. However the explosion in recent years of autonomous systems for exploration requires navigation systems that are physically smaller, with reduced energy needs.
An alternative approach is to use a single source coupled to a passive array of so-called ‘meta-atoms’. ‘Meta-atoms’ are resonant building blocks that play an analogous role to that of conventional atoms when we consider the acoustic response of natural materials. 3D arrangements of these building blocks are artificial crystals termed ‘metamaterials’, where the structure of the meta-atom, and its proximity to its neighbours, define the manner in which the crystal interacts with acoustic waves. This project will focus on the use of meta-atoms as passive resonant elements to yield highly directional radiation or detection of sound.
Our starting point will be based on some recent work on the design of leaky wave antennas (LWA) [1,2] and bullseye antennas , both concepts borrowed from the electromagnetic regime. These structures can steer acoustic energy by preferential coupling to an input frequency and can be designed to steer from backfire to end fire, including broadside. Fundamental to the operation of an acoustic LWA is that sound must “leak” out of the device into the surrounding media in a controlled manner. In this context, leaking refers to the ability of a wave in one medium that is traveling parallel to the boundary with a second medium to lose some energy to an acoustic wave radiating into the second medium. According to Snell’s law, this only occurs if the wave traveling at the interface between the media is faster than the wave in the second medium. By designing the waveguide supporting the sound to be highly dispersive, (i.e. the speed of sound varies with frequency), then we are able to generate frequency-dependent directionality. The dispersion comes from the highly resonant nature of our meta-atoms. An excellent summary of the state-of-the-art of Acoustic Leaky Wave antennas can be found in references 4 and 5.
The project will involve a mix of analytical, numerical and experimental techniques. For example, we will use transmission-line modelling based on a inductive (mass), capacitive (acoustic compliance) and loss/radiation (acoustic resistance), which is practically implemented in 1D as a rigid walled waveguide with side ducts and vibrating membranes. Full-wave numerical modelling (e.g. Comsol) will also be utilised, and experimental validation will take place either in air, or underwater, using the facilities in the Exeter labs. Similarly a 2D embodiment of LWAs can be envisaged as a centrally fed point-source surrounded by surface patterning that supports acoustic surface waves, whose energy can be re-radiated, i.e. scattered from the surface by careful design of the surface structure to yield the designed radiation pattern.
A particular research challenge will be the successful design of these antennas underwater. Although typical structural materials such as plastics and metals have an acoustic impedance that is several orders of magnitude larger than that in air (and therefore tend to appear acoustically rigid), these same materials are much closer in impedance to water, with significantly more fluid-elastic coupling. As a result, the propagation of sound directly through the waveguide and the radiation via leaky compressional waves becomes far more complicated and challenging to control.
A successful project will meet milestones and deliverables that may include • Literature review of acoustic leaky wave antennas, particularly focusing on the use of metamaterial aspects of their design, and a comparison of performance to conventional systems.
• Experimental characterisation of a rigid-waveguide based leaky wave antenna in air, and underwater. Both studies will require the design of apparatus to determine the directivity of acoustic directivity.
• Modelling, fabrication and characterisation of an acoustic bullseye leaky-surface-wave antenna in air. Consider the implementation of an anisotropic surface structure for improved performance/functionality. Demonstration of frequency-dependent directivity.
• Similar to above – an analogous study underwater, which will require a complete study of the fluid-structure interactions.
• A study of the ability for the devices above to generate acoustic vortices carrying orbital angular momentum .
• Extension of the concepts above to develop acoustic imaging / detection devices.
• Further development of the above to devise compact antennas and detectors
 W. W. Hansen, “Radiating Electromagnetic Waveguide”, No. 2, 402,. U.S. Patent, 1940  D. R. Jackson et al. “Leaky-Wave Antennas”, Proceedings of the IEEE, Volume 100 , Issue 7 , July 2012.  M. J. Lockyear et al., “Enhanced microwave transmission through a single subwavelength aperture surrounded by concentric grooves”, J. Opt. A, Volume 7, No. 2, pages S152–S158, 2005.  Naify et al., “Experimental realization of a variable index transmission line metamaterial as an acoustic leaky-wave antenna”, Appl. Phys. Lett. Volume 102, Article 203508, 2013.  Naify et al., “Acoustic Leaky Wave Antennas: Direction-Finding via Dispersion”, Acoustics Today, Fall, page 31, 2018.  C. J. Naify et al., “Generation of topologically diverse acoustic vortex beams using a compact metamaterial aperture”, App. Phys. Lett. Volume 108, Issue 22, article 223501 (2016).
The studentship is part of the UK’s Centre of Doctoral Training in Metamaterials (XM2) based in the Departments of Physics and Engineering on the Streatham Campus in Exeter. Our aim is to undertake world-leading research, while training scientists and engineers with the relevant research skills and knowledge, and professional attributes for industry and academia.
The 4 year studentship is funded 50:50 by an industrial sponsor and the College of Engineering, Mathematics and Physical Sciences at the University of Exeter. It is of value around £105,000, which includes £13,000 towards the research project (travel, consumables, equipment etc.), tuition fees, and an annual, tax-free stipend of approximately £16,500 per year for UK/EU students.
Exeter has a well-established and strong track record of relevant research, and prospective students can consider projects from a wide variety of fields:
The studentship is subject to funding availability.