ACOUSTIC METAMATERIAL SYSTEMS

Abstract

Disclosed herein are systems using acoustic metamaterial surfaces comprising arrangements of unit cells arranged to introduce time delays to an incident acoustic wave. In embodiments the relative positions of two or more acoustic metasurfaces (81, 82) is selected or adjusted to control the acoustic output of the system such that the acoustic output of the system is a non-linear combination of the respective operations performed by the plurality of acoustic metasurfaces (81, 82), the non-linear combination being a convolution of the respective operations performed by the plurality of acoustic metasurfaces that is determined as a function of the relative positioning between the acoustic metasurfaces (81, 82). Also disclosed are applications of such acoustic metasurfaces in noise-reducing structures.

Claims

1. A method for designing or constructing a system for manipulating an incident acoustic wave to generate an acoustic output, the method comprising: providing a plurality of acoustic metasurfaces, each acoustic metasurface comprising an arrangement of unit cells, with at least some of the unit cells being configured to introduce time delays to an incident acoustic wave at the respective positions of the unit cells within the acoustic metasurface, such that the unit cells define an arrangement of time delays to thereby define a spatial delay distribution for manipulating an incident acoustic wave, and such that each acoustic metasurface performs a respective operation on an incident acoustic wave based on its spatial delay distribution; and selecting or adjusting the relative positioning between the acoustic metasurfaces to control the acoustic output of the system such that the acoustic output of the system is a non-linear combination of the respective operations performed by the plurality of acoustic metasurfaces, the non-linear combination being a convolution of the respective operations performed by the plurality of acoustic metasurfaces that is determined as a function of the relative positioning between the acoustic metasurfaces.

2. The method of claim 1, comprising selecting or adjusting the mutual distance between the acoustic metasurfaces to control the acoustic output of the system.

3. The method of claim 1 or 2, wherein at least one of the plurality of acoustic metasurfaces comprises an acoustic lens, and preferably wherein the system comprises two or more acoustic lenses.

4. The method of claim 3, comprising selecting or adjusting the relative positioning of the acoustic metasurfaces to control a magnification and/or focus of the system.

5. The method of any preceding claim, wherein the relative positioning between the acoustic metasurfaces can be adjusted to change the acoustic output of the system.

6. The method of any preceding claim, wherein at least one of the acoustic metasurfaces is configured as an intensity filter or intensity modulator.

7. The method of any preceding claim, comprising at least one acoustic metasurface that is configured as an acoustic lens, and wherein the relative positioning between the acoustic metasurfaces is selected or controlled to focus acoustic waves of two different wavelengths to the same focal plane.

8. The method of any preceding claim, wherein at least one of the acoustic metasurfaces is configured to perform a noise reducing operation wherein an intensity for acoustic waves passing into and/or through the acoustic metasurface is reduced.

9. The method of any preceding claim, comprising selecting or adjusting the relative positioning between the acoustic metasurfaces to selectively attenuate an acoustic source.

10. A system for manipulating an incident acoustic wave to generate an acoustic output comprising: a plurality of acoustic metasurfaces, each acoustic metasurface comprising an arrangement of unit cells, with at least some of the unit cells being configured to introduce time delays to an incident acoustic wave at the respective positions of the unit cells within the acoustic metasurface, such that the unit cells define an arrangement of time delays to thereby define a spatial delay distribution for manipulating an incident acoustic wave, and such that each acoustic metasurface performs a respective operation on an incident acoustic wave based on its spatial delay distribution; wherein the relative positions of the acoustic metasurfaces are selected or adjusted to control the acoustic output of the system such that the acoustic output of the system is a non-linear combination of the respective operations performed by the plurality of acoustic metasurfaces, the non-linear combination being a convolution of the respective operations performed by the plurality of acoustic metasurfaces that is determined as a function of the relative positioning between the acoustic metasurfaces.

11. The system of claim 10, wherein the position of at least one of the acoustic metasurfaces can be adjusted to change the acoustic output of the system.

12. The system of claim 11, comprising a feedback circuit, wherein the position of at least one of the acoustic metasurfaces is adjusted automatically using the feedback circuit.

13. The system of any of claims 10 to 12, wherein at least one of the acoustic metasurfaces is configured as an acoustic lens, preferably wherein the system comprises two or more acoustic lenses.

14. The system of any of claims 10 to 13, wherein at least one of the acoustic metasurfaces is configured as an intensity filter.

15. The system of any of claims 10 to 14, comprising at least one acoustic metasurface that is configured as an acoustic lens, and wherein the relative positioning between the acoustic metasurfaces is selected or controlled to focus acoustic waves of two different wavelengths to the same focal plane.

16. The system of any of claims 10 to 15, wherein at least one of the acoustic metasurfaces is configured to perform a noise reducing operation wherein an intensity for acoustic waves passing into and/or through the acoustic metasurface is reduced.

17. The system of any of claims 10 to 16, wherein two or more of the acoustic metasurfaces are configured as an acoustic telescope.

18. The system of any of claims 10 to 17, wherein two or more of the acoustic metasurfaces are configured as an acoustic microscope.

19. The system of any of claims 10 to 18, wherein two or more of the acoustic metasurfaces are configured as an acoustic zoom or autozoom lens.

20. An acoustic collimator comprising a system as claimed in any of claims 10 to 19.

21. A haptic interface device comprising a system as claimed in any of claims 10 to 20.

22. The system of any of claims 10 to 21, comprising an acoustic source, wherein the plurality of acoustic metasurfaces are arranged to manipulate acoustic waves generated by the acoustic source in order to provide the acoustic output.

23. The system of any of claims 10 to 21, comprising an acoustic detector, wherein the plurality of acoustic metasurfaces are arranged to manipulate acoustic waves towards the acoustic detector to provide the acoustic output.

24. A method of using the system of any of claims 10 to 23, comprising selecting or adjusting the relative positions of the acoustic metasurfaces to provide a desired acoustic output.

25. A noise reducing system that is configured to reduce an intensity associated with an incident acoustic wave, the system comprising a first acoustic metasurface including an arrangement of unit cells, with at least some of the unit cells being configured to introduce time delays to an incident acoustic wave at the respective positions of the unit cells within the acoustic metasurface, such that the unit cells define an arrangement of time delays to thereby define a spatial delay distribution for manipulating an incident acoustic wave, preferably wherein the arrangement of unit cells comprises an alternating pattern of two or more different time delays.

26. The system of claim 25, wherein the arrangement of unit cells for the first acoustic metasurface is designed to reduce an intensity associated with an incident acoustic wave, preferably wherein the arrangement of unit cells comprises an alternating pattern of open unit cells and unit cells that are arranged to introduce a phase delay of π for incident acoustic waves at least at a selected operating wavelength.

27. The system of claim 25 or 26, comprising a second acoustic metasurface provided parallel to the first acoustic metasurface, and preferably having a complimentary alternating pattern to the first acoustic metasurface, such that the second acoustic metasurface can be rotated or otherwise moved relative to the first acoustic metasurface to selectively attenuate incident acoustic waves.

28. The system of claim 25, comprising first and second parallel acoustic metasurfaces that can be rotated or otherwise moved relative to each other into at least a first configuration wherein the combination of the first and second acoustic metasurfaces acts to reduce an intensity of an incident acoustic wave.

29. The system of claim 25, comprising first and second parallel and spaced-apart acoustic metasurfaces, wherein the mutual distance between the first and second parallel acoustic metasurfaces can be adjusted to selectively reduce an intensity of incident acoustic waves.

30. A system for generating an acoustic output, the system comprising: an acoustic source; and one or more acoustic metasurface(s), wherein an acoustic metasurface comprises an arrangement of unit cells, with at least some of the unit cells being configured to introduce time delays to an incident acoustic wave at the respective positions of the unit cells within the acoustic metasurface, such that the unit cells define an arrangement of time delays to thereby define a spatial delay distribution for manipulating an incident acoustic wave, and such that each acoustic metasurface performs a respective operation on an incident acoustic wave based on its spatial delay distribution, wherein the acoustic source and the acoustic metasurface(s) are arranged within a common housing or structure such that acoustic waves generated from the acoustic source are provided to and operated on by the acoustic metasurface(s) to generate an acoustic output or wherein the acoustic metasurface(s) comprises a surface of the acoustic source.

31. The system of claim 30 wherein the acoustic metasurface(s) are provided in line in front of the acoustic source.

32. The system of claim 30 or 31, wherein the relative positioning, e.g. mutual distance, between the acoustic metasurface(s) and the acoustic source is adjustable to control the acoustic output.

33. The system of claim 30 wherein the acoustic metasurface(s) defines a surface of the housing and/or of the acoustic source.

34. The system of claim 33, wherein the acoustic source comprises a diaphragm or cone, wherein the diaphragm or cone is patterned with an arrangement of unit cells, and thereby defines an acoustic metasurface.

35. A loudspeaker having a diaphragm that is moved in use in order to generate an acoustic output, wherein the diaphragm is patterned with an arrangement of unit cells, with at least some of the unit cells being configured to introduce time delays to an incident acoustic wave at the respective positions of the unit cells on the diaphragm, such that the unit cells define an arrangement of time delays to thereby define a spatial delay distribution for controlling the acoustic output.

36. A noise reducing structure comprising a plurality of unit cells arranged into one or more acoustic metasurface(s), at least some of the unit cells being configured to introduce time delays to an incident acoustic wave at the respective positions of the unit cells, such that the plurality of unit cells define an arrangement of time delays to thereby define a spatial delay distribution that is configured to cause an incident acoustic wave passing into and/or through the structure to at least partially destructively interfere with itself to generate an acoustic output with a reduced intensity.

37. The structure of claim 36, wherein at least some of the unit cells are arranged into one or more array(s), each array defining an alternating pattern of two or more time delays that causes an incident acoustic wave passing into and/or through the array to at least partially destructively interfere with itself to generate an acoustic output with a reduced intensity.

38. The structure of claim 36, comprising a plurality of acoustic metasurfaces, each acoustic metasurface comprising an arrangement of unit cells defining an arrangement of time delays to thereby define a spatial delay distribution for manipulating an incident acoustic wave, wherein the plurality of acoustic metasurfaces act in combination to generate an acoustic output with a reduced intensity.

39. The structure of any of claims 36 to 38, comprising two or more acoustic metasurfaces, each acoustic metasurface comprising an arrangement of unit cells defining an arrangement of time delays to thereby define a spatial delay distribution for manipulating an incident acoustic wave, wherein the relative orientation and/or mutual distance between the acoustic metasurfaces is selected to control a noise reducing operation performed by the structure.

40. The structure of claim 39, wherein the unit cells of the two or more acoustic metasurfaces are arranged such that by moving one of the acoustic metasurfaces relative to the other or another acoustic metasurface the structure can be adjusted between a noise-reducing configuration wherein an incident acoustic wave is substantially attenuated and a noise-permitting configuration wherein the incident acoustic wave is substantially transmitted through the structure.

41. A method of reducing noise using a structure as claimed in any of claims 36 to 40, comprising positioning the structure in front of one or more source(s) of noise to attenuate at least some of the noise generated thereby.

42. A method comprising providing a first noise reducing acoustic metasurface in front of one or more source(s) of noise to attenuate at least some of the noise generated thereby; and further comprising positioning a second acoustic metasurface relative to the first noise reducing acoustic metasurface to allow at least some of the noise attenuated by the first noise reducing acoustic metasurface to be transmitted.

43. A noise reducing structure comprising a cavity or passage, wherein a surface of the cavity or passage is provided with a plurality of unit cells, each unit cell with at least some of the unit cells being configured to introduce time delays to an incident acoustic wave at the respective positions of the unit cells along the surface of the cavity or passage, wherein the unit cells are arranged to provide a noise reducing effect for acoustic waves passing into and/or through the cavity or passage.

44. The structure of claim 43, wherein the cavity or passage defines a flow channel that is at open to allow air, or another fluid, to flow through the cavity or passage, and wherein the unit cells are provided on a surface of flow channel.

45. The structure of claim 44, wherein the flow channel comprises a substantially cylindrical pipe.

46. An appliance comprising a structure as claimed in any of claim 43, 44 or 45, wherein the structure is arranged to reduce noise associated with an operation of the appliance.

47. The appliance of claim 46, wherein the appliance comprises a: (i) vacuum cleaner; (ii) fan; or (iii) hair dryer.

48. The structure of claim 44, wherein the flow channel is formed in an external surface of the structure.

49. A tyre or an item of clothing comprising the structure of claim 48.

50. The structure of claim 43 wherein the cavity or passage defines a closed channel containing an incompressible fluid.

51. An anechoic tile for a submarine comprising the structure of claim 50.

52. The invention of any of claims 43 to 51 wherein the cavity has a longitudinal axis along which a fluid can flow in use, and wherein the central channels of at least some of the unit cells are arranged substantially parallel to the longitudinal axis of the flow channel.

53. The invention of any of claims 43 to 52, wherein two or more sets of unit cells are provided that are spaced-apart along the cavity or passage.

54. The invention of claim 53, wherein the two or more sets of unit cells are configured to operate at different, but overlapping, frequency ranges, and wherein the distance between the sets of unit cells is selected to increase the frequency range of operation of the structure.

55. The invention of preceding claim, wherein at least some of the unit cells comprise a central channel extending through the unit cell, wherein the central channel is structured to increase the effective path length for acoustic waves passing through the unit cell.

56. A method of designing a structure comprising providing a first acoustic metasurface that is configured to operate at a first frequency range and providing a second acoustic metasurface that is configured to operate at a second frequency range, wherein the first and second frequency ranges overlap, the method further comprising selecting the mutual distance between the first and second acoustic metasurfaces.

Description

DESCRIPTION OF THE FIGURES

[0174] Various embodiments will now be described, by way of example only, and with reference to the accompanying drawings in which:

[0175] FIG. 1 shows schematically an assembly for modulating sound according to various embodiments of the present disclosure;

[0176] FIG. 2 shows schematically a unit cell construction for introducing a phase delay to an incident acoustic wave;

[0177] FIG. 3 illustrates how the unit cell construction shown in FIG. 2 may be designed to introduce different phase delays to an incident acoustic wave;

[0178] FIG. 4 shows a set of unit cells configured to introduce phase delays spanning the range 0 to 2π in discrete intervals of π/8;

[0179] FIG. 5 shows schematically an example of how a set of metamaterial unit cells may be arranged to construct a converging acoustic lens;

[0180] FIG. 6A shows an example of how a parabolic acoustic lens may be designed and FIG. 6B illustrates how the unit cells may be operable at a number of different frequencies;

[0181] FIG. 7 shows a determined relationship between the focal length of an acoustic lens designed according to the present disclosure and the curvature of the lens;

[0182] FIG. 8 shows a system of acoustic lenses that may be used to provide a varifocal lens;

[0183] FIG. 9 shows another example of a system of acoustic lenses having a variable focal length;

[0184] FIG. 10 shows an example of a system of acoustic lenses that may be used to provide an automatic zoom lens;

[0185] FIG. 11 illustrates how the structure of a unit cell can be designed to control both the transmission (intensity) and phase delay values for that unit cell;

[0186] FIG. 12 shows an example of an acoustic metasurface window having a noise reducing effect;

[0187] FIG. 13 illustrates how a system of two noise reducing acoustic metasurfaces can be used to provide a selective filtering of noise;

[0188] FIG. 14 shows another example of a selective noise reducing system;

[0189] FIG. 15 shows another example of how the distance between two acoustic metasurfaces may be varied in order provide a noise reducing effect;

[0190] FIG. 16 shows the effect of varying the distance between two metasurfaces of the type shown in FIG. 13;

[0191] FIG. 17 shows an exemplary approach for possible way of realising noise cancellation (as a function of distance) using two metasurfaces with a gradient phase profile;

[0192] FIG. 18 shows an example of a speaker system having a diaphragm incorporating a metamaterial surface;

[0193] FIG. 19 shows an example of a surface channel having an arrangement of metamaterial unit cells patterned along the sides of the channel;

[0194] FIG. 20 shows an example of a cylindrical channel whose internal surfaces are patterned with metamaterial unit cells; and

[0195] FIG. 21 shows an example of a metasurface system comprising a plurality of metasurfaces incorporated along a surface.

DETAILED DESCRIPTION

[0196] The concepts described herein generally relate to approaches for spatially manipulating sound using acoustic metamaterials. Thus, in embodiments a device for manipulating acoustic waves (hereinafter, a “sound modulation device”) may be provided. In particular, a plurality of unit cells each capable of encoding a particular time or phase delay, or plurality of time or phase delays, are arranged together in an array in order to construct an acoustic “metasurface” (or, metamaterial layer). The time delay or phase distribution of the acoustic metasurface may thus be quantised in the spatial domain according to the positions and sizes of the unit cells. The spatial distribution of the time or phase delays across the acoustic metasurface generally determines how an acoustic wave incident on the metasurface will be transformed or manipulated as it passes through and interacts with the unit cells of the metasurface. The arrangement of unit cells within the metasurface may be configured for performing various different acoustic transformations or manipulations. A sound modulation device can then be provided comprising a system of a plurality of such metasurfaces.

[0197] Various non-limiting examples and embodiments will now be described to help illustrate these concepts.

[0198] FIG. 1 shows schematically an assembly for modulating sound according to various embodiments of the present disclosure. The assembly comprises an acoustic source 10 which as shown in FIG. 1 may generally comprise a transducer or array of transducers driven in phase and a sound modulation device 20 for manipulating the acoustic wave generated by the acoustic source 10. The sound modulation device 20 may be positioned over the acoustic source 10 at a certain fixed distance from the plane of the acoustic source 10 so that the acoustic waves generated by the acoustic source 10 are passed towards and through the sound modulation device 20. However, it will be appreciated that the sound modulation device 20 need not be positioned directly over the acoustic source 10 in the manner shown in FIG. 1, and in embodiments desirably may not be, so long as the acoustic waves generated by the acoustic source 10 are directed towards and through the sound modulation device 20.

[0199] It will be appreciated that the acoustic source 10 itself does not itself need to perform any spatial modulation as this functionality may be completely devolved to the separate sound modulation device 20. That is, the spatial sound modulation device 20 can act independently to the acoustic source 10, and can act on the incident acoustic waves in whatever form they are provided. Thus, the acoustic source 10 may typically be arranged to generate substantially uniform acoustic waves normal to the surface of the spatial sound modulation device 20 so that the spatial modulation can be controlled completely by the sound modulation device 20. In other embodiments, the acoustic source may already provide a directional or focussed acoustic wave. In this case, the spatial sound modulation device may perform an additional manipulation on the field. In whatever form they are provided, the sound modulation device 20 acts to shape or otherwise spatially transform or manipulate the incident acoustic waves in order to generate a desired acoustic output field 30.

[0200] By way of example, FIG. 1 shows the generation of a ‘bottle’ type acoustic field 30 suitable for acoustic levitation. However, as explained further below, the spatial sound modulation device 20 may be configured to generate different acoustic fields 30 as desired.

[0201] The sound modulation device 20 is generally composed of a plurality of acoustic metasurfaces 21, 22 with each acoustic metasurface comprising a substantially flat and two-dimensional arrangement of unit cells each capable of encoding a particular time or phase delay. The positions of the unit cells (and their associated time or phase delays) thus define the spatial delay distribution for each of the acoustic metasurfaces 21,22, which are effectively quantised according to the positions and dimensions of the unit cells. By controlling the positions and/or delays of the unit cells within the acoustic metasurfaces 21,22 of the sound modulation device 20, the sound modulation device 20 may be selectively configured to perform various manipulations or transformations of an incident acoustic wave to generate an acoustic output.

[0202] Although the acoustic metasurfaces 21,22 are shown in FIG. 1 as being substantially flat and two-dimensional, it is also contemplated that the sound modulation device 20, or at least an upper or lower surface thereof, may be curved or profiled. For instance, the upper or lower surface of the sound modulation device 20 may be substantially convex or concave. In this way, the shape of the surface may also in part contribute to the transformation applied to the incident acoustic waves.

[0203] As discussed above, it will be appreciated that the manipulation of the acoustic wave may advantageously be performed solely by the sound modulation device 20. That is, the spatial manipulation or modulation may be independent of and disconnected from the acoustic source 10. The acoustic source 10 may thus be used solely for generating the incident acoustic waves, and may typically therefore generate a substantially uniform acoustic wave perpendicular to the surface of the sound modulation device 20. This means that the modulation does not need to draw any power from the power supply of the acoustic source 10. In this way the power requirements for the acoustic source and the modulation may be kept relatively simple (or low), e.g. compared to conventional phased transducer array approaches, and independent from each other.

[0204] This is in direct contrast to known approaches utilising phased transducer arrays, where the same elements i.e. transducers are used for generating the acoustic wave and for shaping it. These known approaches typically require relatively complex and expensive electronics for re-configuring the acoustic output field. Furthermore, any switching or re-configuring of the phased transducer array results in a loss of power. Since the spatial sound modulation techniques described in the present application allow the sound power to be disconnected from the modulator, the device may have much lower power requirements that conventional phased transducer arrays. By decoupling the manipulation from the acoustic source, the devices according to the present disclosure may also allow for a faster switching or re-configuration than conventional phase transducer arrays.

[0205] In embodiments, the unit cells are each pre-configured to encode a particular, fixed time delay. The unit cells effectively therefore become, in isolation, the building blocks of the acoustic metamaterial layers or metasurfaces, whereby the individual unit cells can be assembled on-demand into arrays or layers having a desired delay distribution. For instance, the pre-configured unit cells may be interconnected together, or inserted into a frame, to form a two-dimensional array or metamaterial layer. The unit cells may then be released, or removed from the frame, and then re-configured into a different arrangement to perform a different transformation.

[0206] Because each of the unit cells forming the layer or metasurface is pre-configured to encode a single, specific time delay or intensity, the array or layer of unit cells quantised in both the spatial and time delay domains. Various spatial delay distributions suitable for generating a great number of acoustic output fields may be encoded by selecting the appropriate unit cell (i.e. time delay) for each position within the array or layer. The accuracy at which the sound modulation device 20 can generate a desired arbitrarily complex acoustic wave may in general be increased by increasing the number of unit cells within the array and/or decreasing the size of the unit cells within the array (i.e. so that the spatial delay distribution is quantised with a higher resolution), or by increasing the number of different types of unit cells available (i.e. the number of available time delays and hence the resolution of the time delays) so that the time delay at each position may be chosen to better match that for the desired field.

[0207] The unit cells may take various suitable forms so long as they act to introduce a well-defined time delay to an incident acoustic wave. Generally, the unit cells may be designed to introduce a local phase shift at least within the range 0 to 2π for a selected operating frequency. In order to form a desired acoustic wave with the required accuracy, and in order to avoid spatial aliasing effects, the unit cells desirably hold sub-wavelength resolution. The unit cells should also be able to transmit sound effectively with minimal energy losses, particularly where it is desired to stack the unit cells or layers.

[0208] For instance, in embodiments, the unit cells may define a central channel through which acoustic waves pass from one side of the unit cell to the other. The central channel may further comprise various sub-wavelength structures or features that act to slow down the acoustic waves and/or increase the effective path length travelled by the acoustic waves through the channel thereby introducing a phase delay. For example, the channels may include a substantially labyrinthine, or meandered, structure, or a multi-slit, coil, helical, or Helmholtz resonator-type structure. One suitable structure is illustrated by way of example in FIG. 2 which shows in cross section an example of a labyrinth structure with meanders defined by four bars extending into an open channel.

[0209] The effective path length, L.sub.eff, for acoustic waves travelling through the unit cell is given by L.sub.eff=h+ΔL, where h is the height on the unit cell, and ΔL is the additional path length introduced by the structure of the unit cell. This additional path length introduces a phase delay φ=e.sup.ik.Leff where k is the wavenumber (k=2π/λ) of the acoustic wave.

[0210] The shape and/or dimensions of the unit cells may generally be selected to introduce a desired phase delay for acoustic waves of a particular wavelength. That is, the design of unit cells may be substantially optimised or configured for use with a particular operating wavelength, such that a desired phase delay is provided for incident acoustic waves at the operating wavelength, λ.sub.0. In embodiments, the device may be designed for use substantially only at a single operating wavelength, such that there is little or no response or transmission at other wavelengths. In other embodiments it is contemplated that the device may be designed for use with a range of wavelengths, such as a range of wavelengths around a central operating wavelength. It is also contemplated that the device may be configured to operate at a number of different operating wavelengths.

[0211] FIG. 3 illustrates how the exemplary unit cell construction shown in FIG. 2 may be designed to encode a range of different phase delays. The unit cells shown in FIG. 3 are generally in the form of a rectangular cuboid with a square base shape of side λ.sub.0/2 and height of λ.sub.0. Thus, the unit cells allow the acoustic metamaterial layers to be quantised with a resolution of λ.sub.0/2. This may be a good compromise between ease-of-manufacture and the need to realise diffraction-limited fields without spatial aliasing. Indeed, it has been found that it may be advantageous to keep the size of the unit cells (in the plane of the metamaterial layers) smaller than the wavelength corresponding to the Nyquist frequency. Thus, when designing a device that is optimised or configured for use at an operating wavelength, λ.sub.0, the unit cells may suitably have a dimension of λ.sub.0/2, or smaller.

[0212] As shown in FIG. 3, and as mentioned above in relation to FIG. 2, the unit cells each comprise an open central channel having a structure that delays the incident wave, hence shifting the relative phase of the output. In particular, the open central channel is provided with a labyrinthine or meandered structure by a plurality of bars extending into the channel. The length of, b.sub.l, and spacing between, b.sub.s, the meanders may then be varied in order to provide a range of effective path lengths as shown in FIG. 3. In FIG. 3, the thickness of the walls relative to the configured operating wavelength, λ.sub.0, is λ.sub.0/40 and the thickness of the meanders is λ.sub.0/20. However, these values may be selected as desired e.g. to achieve a desired strength or robustness, or based on manufacturing constraints.

[0213] FIG. 4 shows in cross-section 16 different unit cells that are pre-configured to introduce phase delays spanning the range 0 to 2π in discrete steps of π/8. It can be seen from FIG. 4 how varying the lengths and spacing of the bars allows the phase delay to be adjusted.

[0214] The 16 different unit cells shown in FIG. 4 represent a set of 16 unique quanta. The illustrated set of unit cells are uniformly spaced in phase and FIG. 4 thus represents a uniform 4-bit control (i.e. 16=2.sup.4). It has been found that any focussed field can be reproduced with an error of less than 0.1 dB using such uniform 4-bit control. Using fewer quanta, or lower bit control, generally increases the error. For instance, the error may increase to about 1 dB for a uniform 3-bit control (8 quanta), or about 3 dB with uniform 2-bit control (4 quanta). The error may be determined by comparing the analogue field that is desired to be reproduced with the field generated by the spatial sound modulation device.

[0215] Although the example set of unit cells shown in FIG. 4 are uniformly spaced in the phase domain (in discrete intervals of π/8) it will be appreciated that a set of unit cells need not be uniformly spaced, and in embodiments, the set of unit cells may advantageously be non-uniformly spaced in the phase domain. For instance, by selecting an appropriate non-uniform set of quanta (i.e. phase delay values), practically any focussed field may be reproduced with similar error to the uniform 4-bit control mentioned above but using fewer quanta. For instance, it has been found that a non-uniform 3-bit control may provide similar results to a uniform 4-bit control.

[0216] As best shown in FIG. 3, the base portions of the bars defining the meanders may have ‘shoulders’ such that they gradually taper into the channel to the desired end thickness (e.g. λ.sub.0/20). These ‘shoulders’ may help to increase robustness and stability during manufacture and/or may help contribute to impedance matching. In particular, the geometry of the unit cells may be selected so that the effective acoustic impedance of each unit cell is matched to that of the ambient medium within which the device is operating (e.g. air or water), thereby increasing the efficiency of transmission (and suppressing reflection).

[0217] It is emphasised again that FIGS. 1 to 4 merely illustrate one example of a suitable unit cell for introducing a time delay, and that the unit cells may generally take various forms including, but not limited to, other types of labyrinthine or meandered structures, multi-slit, helical or coiled structures, or Helmholtz resonator-type structures.

[0218] Also, whilst FIGS. 1 to 4 illustrate pre-configured unit cells, it is also contemplated that the unit cells themselves are each re-configurable between a plurality of different time delay values. Thus, in embodiments, the unit cells may be fixed in position within the array or layer, but are re-configured in situ to encode a plurality of different phase delays. Naturally, it is also possible that in a given sound modulation device or metamaterial layer some of the unit cells may be both removable and re-configurable, or that some of the unit cells may be fixed in both position and phase. Furthermore, in embodiments, it is contemplated that a single sound modulation device or metamaterial layer may contain a mixture of pre-configured and re-configurable unit cells.

[0219] The arrangement of the unit cells within an acoustic metasurface will determine how an acoustic wave incident on, and passing through, the acoustic metasurface will be manipulated. Thus, it is possible to design a vast range of acoustic metasurfaces that are arranged to perform various different acoustic manipulations.

[0220] For instance, in basic terms, there are four steps involved in designing an acoustic metasurface according to the present disclosure to perform a certain function: (1) choosing the desired function (i.e. the operation performed by the acoustic metasurface); (2) transforming this information into an analogue phase/intensity distribution on the acoustic metasurface; (3) selecting the unit cells to use to best reproduce the required phase/intensity distribution; and (4) fabricating the acoustic metasurface, taking into account any constraints in terms of its spatial and frequency response. It will be appreciated that this process essentially involves moving from a desired analogue field that is to be reproduced to a discrete spatial delay distribution within the plane of the metasurface, with the delay distribution being quantised according to the positions of the unit cells in the metasurface.

[0221] Various techniques for designing and constructing such metasurfaces are described, for example, in International (PCT) Patent Publication number WO 2018/146489. In particular, various approaches are described wherein the required analogue phase/intensity distribution is quantised to match the possible unit cells. The acoustic metasurfaces of the present disclosure can thus be fabricated similarly, although other arrangements may of course be possible.

[0222] The operation that is performed by an acoustic metasurface is generally defined in terms of how an acoustic wave is manipulated, both spatially and in terms of its intensity, after it has passed through the acoustic metasurface.

[0223] For example, by appropriately arranging the unit cells (time delays) within an acoustic metasurface, the acoustic metasurface may be arranged to perform a focussing transformation, and thus configured as an acoustic “lens”. That is, the metasurface may be configured to focus an incident acoustic wave towards a certain focal point (i.e. defined in terms of the focal length of the lens).

[0224] A converging lens is generally characterised by two quantities: its focal length and its physical extension (i.e. for an acoustic metasurface, how many unit cells it contains). So, once a desired focal length F has been set along the axis of the acoustic lens, the phase distribution φ(x,y) for the metasurface (i.e. in the z=0 plane) can then be obtained, e.g. by imposing that all the contributions from the unit cells arrive in phase at a position (0,0,F). For example, the basic focussing transformation for a converging lens may be described by the analogue phase distribution: φ(x, y)=ϕ.sub.0−2π/λ.sub.0(√{square root over (r.sup.2+F.sub.0.sup.2)}−F.sub.0), where r.sup.2=x.sup.2+y.sup.2, ϕ.sub.0 is a phase value, λ.sub.0 is the operating wavelength and F.sub.0 is the focal length.

[0225] FIG. 5 illustrates an example of an acoustic metamaterial layer that is configured to provide a converging focussing transformation at 40 kHz. In particular, the metamaterial layer shown in FIG. 5 is formed of 16 different phase values, e.g. corresponding to the 16 phase values between 0 and 2π in steps of π/8 shown in FIG. 4, with the unit cells (or blocks of unit cells) at each discrete position (i,j) within the metamaterial layer being selected or configured to have a phase value that closely matches the desired phase as defined by the analogue phase distribution φ(x,y). For the surface shown in FIG. 5, that means the unit cells at each position are selected to have a phase value selected from the 16 available phase values that most closely matches the desired phase. The acoustic metamaterial layer thus contains a quantised representation φ.sub.i,j of the analogue phase distribution φ(x,y). To account for the presence of the frame, etc. the phases assigned to the unit cells may be taken as the phase according to the analogue phase distribution φ(x,y) corresponding to an imaginary point at the centre of each unit cell. However, it will be appreciated that the layer may equally use alternative arrangements of unit cells that may be either pre-configured or re-configurable, and may be either uniformly or non-uniformly spaced in the phase domain.

[0226] FIG. 5 also shows pressure plots illustrating the acoustic wave in the vertical plane moving away from the surface of the metamaterial layer and in the horizontal plane at a position 100 mm from the surface. It can be seen that the spatial sound modulation device performs as expected by focussing the acoustic wave.

[0227] It has also been found that the size of the focal region perpendicular to the axis depends on the lateral dimensions of the acoustic metamaterial layer. In particular, the larger the lateral dimensions of the acoustic metamaterial layer, the tighter the focus. Again, this is not necessarily expected when working with acoustic waves, but has been found to result from the unit cell metamaterial-based approaches described herein.

[0228] Although FIG. 5 shows one example of a converging lens, it will be appreciated that other suitable arrangements are also possible. For example, it would also be possible to design an acoustic lens having a parabolic phase profile, i.e.: φ(x,y)=φ.sub.0−A.sup.2(x.sup.2+y.sup.2), where φ(x,y) is local phase (assigned to a unit cell), A is a constant related to the local curvature of the phase profile, and φ.sub.0 is an arbitrary constant. For instance, this phase profile may allow for more compact acoustic lenses to be realised, and allows the parameter A to be easily related to the “curvature” of the lens. In particular, as shown in FIG. 6A, a larger value of A corresponds to a more focussing lens.

[0229] So, as mentioned above, once the required phase distribution φ(x,y) for the metasurface is known, whatever this is, a set of unit cells must then be chosen for reproducing this. Preferably the unit cells are of the type above (although it will be appreciated that other types of unit cells may also be used). These unit cells are designed to have a maximum transmission (e.g. of approximately 97%) at a particular operating wavelength (corresponding to 40±1 kHz). However, the unit cells may still be used at other wavelengths. In particular, for this type of unit cell, substantially the same transmission at the designed operating wavelength is also achieved at a set of other frequencies: f.sub.j=f.sub.0−j.Math.c.sub.0/L.sub.eff, where L.sub.eff is a design parameter of the specific unit cell wherein j=0, 1, 2, . . . , N, with N being the integer number of times that L.sub.eff contains the wavelength. As shown in FIG. 6B, it is thus possible to operate the unit cells at one of these frequencies, maintaining a similar transmission to the one in f.sub.0 (but considering that the phase encoded at f.sub.j is different from the one at f.sub.0, so a suitable look-up table may be used).

[0230] The present Applicants have further developed some design tools that can be used to model such acoustic metasurface lenses. This discovery simplifies the realisation of metamaterial based devices and leads to solving some of the limitations of current metamaterial-based approaches.

[0231] In particular, it has been found that the focal length of an acoustic metasurface lens can be related to the positions of the source and the image using a relationship of the form: 1/p+1/q=1/f, where f is the focal length of the lens, p is the distance between the source and the lens, q the distance between the lens and the image of the source. This equation is based on the same hypotheses used to design the metasurface and has been found to apply directly at least when the metasurface thickness is smaller than the wavelength. Remarkably, despite the different nature of acoustic and electromagnetic waves, this equation is of the same general form as the thin lens equation that can be applied to optical systems. FIG. 7 is a plot essentially confirming the validity of this relationship for a parabolic acoustic lens and in particular showing how the focal point varies with the curvature of the lens (i.e. with the parameter A).

[0232] The discovery of this relationship leads naturally to the design of systems including various arrangements of acoustic lenses such as acoustic telescopes or microscopes. For instance, for a system of two acoustic metasurface lenses, the focal length is then given by: 1/F=1/f.sub.1+1/f.sub.2−D/(f.sub.1.Math.f.sub.2), where f.sub.1 and f.sub.2 are the focal lengths of the two lenses and D is the mutual distance between the two lenses.

[0233] By appropriately selecting the mutual distance between two such acoustic metasurface lenses, it is thus possible to control the acoustic output. For instance, FIG. 8 shows a system comprising two acoustic metasurface lenses whose mutual distance can be varied in order to vary an acoustic output.

[0234] For instance, in FIG. 8, a system is provided comprising a first acoustic metamaterial lens 81 and a second acoustic metamaterial lens 82 that are provided in front of an acoustic source in the form of a speaker 83. Acoustic waves from the speaker 83 are thus transmitted through the acoustic metamaterial lenses and acted on accordingly in order to generate a certain acoustic output.

[0235] A suitable mechanism is also provided for adjusting the mutual distance between the first and second acoustic metamaterial lenses. For instance, in FIG. 8, a drive means 84 is provided that allows the mutual distance to be adjusted in order to vary the acoustic output (i.e. to vary the magnification and/or focus of the acoustic output). However, various other possibilities would be provided. For example, the acoustic metamaterial lenses may be translated along suitable guide rails, or a screw mechanism may be provided to allow the mutual distance to be adjusted. However, various other arrangements would of course be possible.

[0236] For instance, in another embodiment, rather than providing some mechanism for incrementally adjusting the mutual distance between the first and second acoustic metamaterial lenses, the first and second acoustic metamaterial lenses may be stacked at different positions within a housing, as shown in FIG. 9. For instance, the housing 90 may comprise a plurality of axial slots to allow acoustic metamaterial lenses 91, 92 to be arranged in a suitable stack with the mutual distance between the acoustic metamaterial lenses being determined by the position of the acoustic metamaterial lenses within the stack.

[0237] In embodiments, the mutual distance between the acoustic metamaterial lenses may be set or controlled by a user. However, it is also contemplated that the mutual distance between the acoustic metamaterial lenses may be controlled automatically. For example, by providing a suitable feedback circuit, it would be possible to automatically focus the acoustic output towards a moving target. An example of this is shown in FIG. 10. FIG. 10 thus shows a sound delivery system designed to be able to track a moving target. The system of FIG. 10 is based on the device illustrated in FIG. 8. However, n FIG. 10, a position sensor 85 is provided (that may comprise a camera, or any other suitable position sensor) that is able to determine the distance to a target object. The target position information is then passed to a suitable processing circuit and used to adjust the distance between the acoustic metamaterial lenses appropriately to track the target and continue to deliver focussed sound to the target as it moves towards/away from the speaker. As shown, the processing circuit may generally comprise any suitable circuitry. For instance, in some embodiments, the processing circuit may comprise a dedicated microprocessor 86 that is able to directly control the spacing based on the information obtained from the position sensor. This may provide sufficient control for some sensors. However, in the illustrated embodiment, the control may be performed by a computer 87. Thus, the information from the position sensor 85 is processed by the computer 87 which in turn causes the microprocessor 86 to control the mechanics to vary the spacing between the two acoustic metamaterial lenses 81, 82. For example, this may be the case where the sensor is a camera and the image tracking is performed on a computer or a Raspberry-Pi microprocessor.

[0238] Of course the device can also work in reception. For instance, rather than providing an audio spotlight that can track and deliver sound to a moving target (as shown in FIG. 10), a zoom microphone could be realised that automatically tracks a moving acoustic source. In such an auto zoom system (operating in detection) the speaker may thus be substituted for a microphone positioned in the focal plane of the closest lens.

[0239] Thus, based on the principles set out above, it is possible to realise various novel acoustic metamaterial-based devices. Various embodiments will now be described with respect to systems of acoustic lenses. Like in modern optical objectives, it is also possible to design systems with more than two lenses.

[0240] For instance, based on the principles set out above, it is possible to build an acoustic collimator that acts to correct the geometric divergence of a source (so that the output is spatially contained in a highly directional beam). For instance, by locating an acoustic metasurface lens at a distance from the source equal to its focal length, the acoustic waves from the source can be transformed into a substantially parallel beam. By providing two such acoustic lenses, it is possible to further control the acoustic output, e.g. to reduce the divergence. Such systems can then be used to transform an arbitrary speaker into a highly directional audio spotlight.

[0241] In the same way, an acoustic collimator system could be used in detection, to transform generic acoustic sensors into highly directional ones. Indeed, although FIG. 1 shows a transmitting device, it will be appreciated that the devices substantially as described herein may also be used as part of a receiver or sensor assembly, for example, for acoustic sensing or imaging applications.

[0242] Similarly, such systems may be used to provide highly personalised audio experiences in shared spaces. For instance, an acoustic beam can be sent selectively to different areas in order to optimise or tailor the acoustic experience at different positions.

[0243] Similar considerations can be applied to smart speakers, like Google Home or Amazon Echo, whose 360 degree range of emission is provided by an array of speakers.

[0244] Various other systems would of course be possible. For instance, systems of acoustic metasurface lenses may also be used to construct acoustic magnifying glasses, or acoustic telescopes. This might find utility in various applications. For example, one possibility would be to create the image of a speaker in front of the user and thus providing the feeling that the sound is coming from a localised source. This might then provide a more immersive audio experience, analogous to a surround sound system, but without requiring an expensive speaker system (since the modulation of the acoustic output can be performed instead using the acoustic metasurface system).

[0245] Thus, in embodiments, the techniques described herein may be used to realise a directional sound system such as an ‘audio spotlight’ used with digital signage, or displays, or kiosks for targeted advertising or announcements. A directional sound system may also be employed on consumer electronic devices e.g. for providing wireless audio devices.

[0246] As another example, the techniques may be used for wireless power transfer such as ultrasonic charging. Existing techniques for wireless ultrasonic charging using a phased transducer array require extremely high operating powers in order to provide a sufficiently strong focussed beam, and may not therefore be practical or safe. As explained above, because the power requirements for the modulator are separated from the power requirements of the source, the techniques described herein may operate at significantly lower powers than phased array techniques.

[0247] A further example would be using the acoustic wave for interactions with other objects, for instance, in the field of haptic control e.g. for consumer electronic devices, or for acoustic levitation or tractor beams. For instance, using an appropriate system of acoustic metamaterial lenses, it may be possible to extend the range of haptic devices to large distances. Similarly, the techniques may be used in virtual reality applications.

[0248] The techniques may also find a variety of application in the medical and industrial sectors. For instance, there are a variety of therapeutic and diagnostic techniques involving spatial sound modulation. One example of this would be High Intensity Focussed Ultrasound for ablating tissue. Another example would be targeted drug delivery. A typical industrial application may be in the field of non-destructive testing, or for waste manipulation.

[0249] Such acoustic metasurface lenses may also of course be used in combination with other types of acoustic metasurfaces.

[0250] For example, an acoustic metasurface lens may be used in combination with a metasurface that is arranged to generate an acoustic hologram. Such systems may thus also be used for extending the range of haptic devices, or providing moveable acoustic holograms. An application of this would be, e.g., to provide a tactile television that provides extra sensory output.

[0251] As another example, acoustic metasurface lenses may be used in combination with an intensity filter or intensity modulator. For instance, an acoustic metasurface may be configured to act as an intensity filter that provides the same phase delay for a range of different intensities. FIG. 11 illustrates this concept. More specifically, FIG. 11 shows how the transmitted intensity and phase delay for a unit cell can be adjusted by changing the structure of the unit cell (in particular by changing the geometrical parameters, i.e. the lengths b.sub.s and bi as shown in FIG. 3). In particular, FIG. 11 shows the effect of changing geometrical parameters for a unit cell geometry of the type shown in FIG. 3 with four horizontal bars (two on each side) and for acoustic waves at 5200 Hz. It can be seen that the same phase delay can be achieved using different geometry choices. Correspondingly, this means that the same phase delay can be achieved using different intensities, which would allow an intensity filter or modulator to be created.

[0252] For instance, for a given design of unit cell (i.e. having a fixed effective length), the delay is typically linear with the frequency. So, for a unit cell having a fixed area, it is possible to optimise the design for use around a certain frequency. A possible way of optimising the unit cell design is: (a) change the length and the spacing of the horizontal bars (b.sub.l and b.sub.s in FIG. 3) until the desired transmission is achieved; (b) among the configurations that give the desired transmission, select the ones that give the desired phase delay; (c) among the ones that give the desired phase delays and transmission, select those that are more “resilient” to changes of in the operating frequency, to provide a larger operating bandwidth.

[0253] Thus, it will be appreciated that the present disclosure provides various novel acoustic systems that can be realised through the appropriate combination of differently configured acoustic metasurfaces. In general each acoustic metasurface may be quantised spatially, i.e. according to the positions of the unit cells. In such systems, each unit cell thus effectively acts as a ‘control point’ (i.e. a separate acoustic source) whose output is then provided to the next acoustic metasurface in the system, and so on. The output of the system can thus generally be determined from a convolution of the operations performed by the acoustic metasurfaces within the system, with the convolution depending on the mutual orientation (e.g. spacing) between the various acoustic metasurfaces. For the case of acoustic metasurface lenses, the Applicants have recognised (and confirmed through extensive testing and device realisation) that this behaviour remarkably can be modelled using an acoustic analogue of the thin lens equation. However, the Applicants have also extended this analysis to more general systems of acoustic metasurfaces, and developed a tensor-based method for modelling and/or designing acoustic metasurface systems. In particular, it has been found that the acoustic output (or a desired acoustic output), P.sub.n, for a system of two acoustic metasurfaces may be given by a relationship of the form:

[00001]$P_n=\underset{\underset{T_{\mathrm{njk}}}{︸}}{M_{\mathrm{nl}}.Math.N_{\mathrm{jlk}}}\mathrm{.Math.}{I}_j^{\left(2\right)}.Math.I_k^{\left(1\right)}$

where M.sub.nl looks at the geometrical propagation from the second metasurface to the N control points, N.sub.lk considers the propagation from the K unit cells in the first meta-surface to the L unit cells in the second meta-surface, while I.sub.j.sup.(2) reports the change in phase and amplitude encoded by the second meta-surface and I.sub.k.sup.(1) the change in phase and amplitude encoded by the first meta-surface. The two-dimensional problem of a stack of two meta-surfaces can therefore be written using a 3.sup.rd-order tensor T.sub.njk and the problem of finding I.sub.j.sup.(2) and I.sub.k.sup.(1) can be solved with the methods of tensor factorization.

[0254] The techniques described herein thus represent a very powerful approach for designing and constructing acoustic systems that are capable of performing essentially arbitrarily complex operations on an acoustic wave, and whose acoustic output can be readily tailored through a suitable adjustment of the mutual orientation between a number of acoustic metasurfaces constituting the acoustic system.

[0255] In addition to the various applications presented above, an acoustic metasurface may also be configured to provide a reduction in intensity for incident acoustic waves, i.e. to provide a noise cancelling (or reduction) operation. This could be realised, for example, as shown in FIG. 12, by providing an acoustic metasurface 120 having an alternating checkerboard pattern of unit cells designed to introduce phase delays of 0 and π. An acoustic wave encountering these phase delays will then have its intensity reduced as a result of the interference between the components passing through the different unit cells.

[0256] This structure may be used by itself, e.g. to provide a noise cancelling window. However, this structure may also be used in combination with other acoustic metasurfaces.

[0257] For example, FIG. 13 shows an example of a system comprising two acoustic metasurfaces, each configured to provide a noise reducing effect. In particular, each acoustic metasurface has a complimentary alternating checkerboard pattern of 0 and π phase delays (see FIG. 13A). The two acoustic metasurfaces can then be slid relative to each other to control the acoustic output. For instance, in the position shown in FIG. 13B, there is a noise reduction only in some directions (the sides ones, i.e. at the edges of the device), while other acoustic waves passing through the center of the device can still pass. In the position shown in FIG. 13C, there is noise reduction in all directions. In intermediate positions the noise cancelation may be selective, or even frequency selective (e.g. if the two metasurfaces are designed to operate over different but overlapping bandwidths).

[0258] Other patterns of unit cells can also be used for providing such noise reductions. For instance, in FIG. 14, a selective noise reducing structure is provided that comprises two acoustic metasurfaces each comprising an alternating pattern of acoustic metasurface having an alternating checkerboard pattern of 0 and π/2 phase delays. In this case, when the patterns are rotatably aligned (such that the π/2 phase delays for the two circular metasurfaces are aligned), the combined pattern is then an alternating pattern of 0 and π phase delays, and the resulting interference thus results in a reduction in intensity for acoustic waves experiencing these phase delays. On the other hand, for any intermediate positions there will be only a partial attenuation.

[0259] This concept is further illustrated in FIG. 15 which shows how the concept of alternating 0 and π phase delays can be implemented in a single unit cell, so that sound reduction can be achieved with a metasurface formed by the same repeated unit cell. In particular, for the unit cell shown in FIG. 15A, the portion of the incoming acoustic wave passing through the central channel of the unit cell is shifted out of phase with the portion(s) of the acoustic wave passing around the external (lateral) parts of the unit cell, and the resulting interference causes a reduction in sound in a similar fashion as described above. However, by placing another similar metasurface at appropriate distances from the first one (as shown in FIG. 15B), it is possible to ‘recreate’ the original acoustic wave. This is illustrated in FIG. 15C, which is a plot of the maximum pressure obtained after passing acoustic waves through a system of two identical metasurfaces as a function of the spacing between the acoustic metasurfaces and of the frequency of the acoustic waves, for a thickness of the metasurface equal to 13 mm. It can be seen from FIG. 15C that for some frequencies and spacings the initial pressure is reproduced and even amplified (due to resonance). In this way, by varying the distance between the two acoustic metasurfaces, a device can be realised than can selectively cancel/amplify sound by pressure (i.e. with one of the metasurfaces acting like a button).

[0260] FIG. 16 shows an example of using two acoustic metasurfaces, e.g. of the type shown in FIG. 13, having an alternating arrangement of 0 and π phase delays. In this case the mutual distance may again be used to create resonant effects, so that the area of noise cancellation changes position as a function of the distance.

[0261] FIG. 17 shows another example where this concept is extended over a broader frequency range. In this case, rather than using alternating arrangements of 0 and π phase delays, two acoustic metasurfaces are provided having respective phase gradients of dφ/dx=±2π/h, where h=λ/2 is the spacing between the acoustic metasurfaces. Each acoustic metasurface is configured to reduce noise at least in a certain direction (which direction is determined based on the direction and magnitude of the delay gradient). However, by placing the two acoustic metasurfaces next to each other, the sound is transmitted through the barrier. Again, this solution may cause cancellation only when desired.

[0262] The unit cell metamaterial-based approaches described herein may also be applied to surfaces, or structures, rather than being used to provide stand-alone acoustic metasurfaces (or systems of acoustic metasurfaces, e.g. as described above). For instance, FIG. 18 shows an example of a speaker system 190 including a magnet 192 that causes a speaker diaphragm (or cone) 194 to oscillate in order to create the audio output, and wherein the speaker diaphragm 194 is patterned with a suitable arrangement of unit cells in order to control the speaker output. That is, the unit cells may be incorporated into the curved surface of the speaker diaphragm 194. In this way, the speaker may be configured as a parametric or directional speaker, with the directionality being determined by the arrangement of unit cells.

[0263] Various other arrangements would of course be possible. For example, FIG. 19 shows a channel 196 formed within a surface 199 (which may, e.g., comprise the surface of a tyre), with the inner walls 198 of the channel 196 being patterned with an arrangement of unit cells 197. In this way, sound waves passing through the cavity 196 may be manipulated, as desired, based on the arrangement of the unit cells 197. For example, the unit cells 197 may be arranged to provide a noise reduction effect. A specific example is the back box of a loudspeaker, which could be realised to be much lighter using noise-cancelling metasurfaces. Another example would be a surface patterned with grooves, like a partition wall in an open-office set-up.

[0264] FIG. 20 shows another example wherein a plurality of unit cells 201, 202, 203 are arranged around the curved inner surface of a cylindrical channel 200 in order to manipulate acoustic waves passing through the channel 200. As shown in FIG. 20, the unit cells may be spaced along the length of the channel 200. For example, the channel 200 may comprise a vacuum cleaner or fan tube, with the unit cells arranged to attenuate noise associated with the vacuum cleaner or fan while letting the air through.

[0265] However, various other arrangements would of course be possible. For example, rather than an open channel (as shown in FIG. 19 or FIG. 20), such unit cells may be used on the outside of a closed channel. An example of this might be a tyre or a submarine anechoic tile.

[0266] In general the unit cells may be incorporated into any desired structure. For example, the unit cells may be provided on an item of clothing or to form a screen. In all cases, the metasurfaces can be designed to let air/fluid flow through them, while acting as noise-cancellation filters in their range of frequencies.

[0267] FIG. 21 shows how the spacing of the unit cells along a structure (e.g. along a channel as shown in FIG. 19 or FIG. 20) may be selected to provide a multi frequency response. In particular, FIG. 21 shows a structure in which three different acoustic metasurfaces have been formed. For example, the structure may comprise any suitable material, such as rubber, or wood, with the acoustic metasurfaces then being embossed/engraved onto the surface. However, various other arrangements would of course be possible. Furthermore, although FIG. 21 shows a flat arrangement it will be appreciated that this is merely for ease of illustration and that the arrangement of unit cells may be curved, e.g. such that the unit cells are arranged around an interior of a cylindrical flow channel (as in FIG. 20), or any other desired arrangement.

[0268] Each of the acoustic metasurfaces is optimised for a different operating frequency (f1, f2, f3), and has an associated operating bandwidth (Δf1, Δf2, Δf3). In general the acoustic metasurfaces may be configured to perform any desired operation. For instance the acoustic metasurfaces may be configured to perform the same function (e.g. lensing, or noise-cancellation), or may perform different functions.

[0269] It is desired to maximise, in convolution, the bandwidth of the entire pattern (i.e. of the system including each of the acoustic metasurfaces) so that the structure performs the same function over a wider range of frequencies. Two main methods are contemplated for doing this. In a first main method, the structure of the acoustic metasurfaces (and hence the operating frequencies) may be fixed, but the distances between the acoustic metasurfaces (D1, D2) may then be adjusted in a quasi-random pattern. The Applicants have found that the mutual distances can be optimised by analytical models, e.g. similar to those described in “The Pneumatic Tire” (US Department of Transportation, DOT HS 810 561, February 2006) or numerical methods used for optical systems, e.g. as described in Wetzstein et al., “Tensor Displays: Compressive Light Field Synthesis using Multilayer Displays with Directional Backlighting” (ACM Transactions on Graphics, July 2012). Alternatively, in a second main method, the distances (D1, D2) may be fixed, with the operating frequencies being varied. This may be more effective for applications with space constraints.

[0270] Although various embodiments have been described above in relation to systems that work in transmission, it will be appreciated that similar principles as described above can also be applied to systems using reflecting metasurfaces, or other types of acoustic waves.

[0271] Thus, although the techniques presented herein have been described with reference to particular embodiments, it will be understood by those skilled in the art that various changes in form and detail may be made without departing from the scope of the inventions as set forth in the accompanying claims.