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Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces.

Li Y, Liang B, Gu ZM, Zou XY, Cheng JC - Sci Rep (2013)

Bottom Line: Here, we theoretically demonstrate that the generalized Snell's law can be achieved for reflected acoustic waves based on ultrathin planar acoustic metasurfaces.The metasurfaces are constructed with eight units of a solid structure to provide discrete phase shifts covering the full 2π span with steps of π/4 by coiling up the space.Our results could open up a new avenue for acoustic wavefront engineering and manipulations.

View Article: PubMed Central - PubMed

Affiliation: 1] Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, P. R. China [2] State Key Laboratory of Acoustics, Chinese Academy of Sciences, Beijing 100190, P. R. China.

ABSTRACT
The introduction of metasurfaces has renewed the Snell's law and opened up new degrees of freedom to tailor the optical wavefront at will. Here, we theoretically demonstrate that the generalized Snell's law can be achieved for reflected acoustic waves based on ultrathin planar acoustic metasurfaces. The metasurfaces are constructed with eight units of a solid structure to provide discrete phase shifts covering the full 2π span with steps of π/4 by coiling up the space. By careful selection of the phase profiles in the transverse direction of the metasurfaces, some fascinating wavefront engineering phenomena are demonstrated, such as anomalous reflections, conversion of propagating waves into surface waves, planar aberration-free lens and nondiffracting Bessel beam generated by planar acoustic axicon. Our results could open up a new avenue for acoustic wavefront engineering and manipulations.

No MeSH data available.


Related in: MedlinePlus

An acoustic metasurface for generalized Snell's law.(a) The schematic diagram of an acoustic metasurface made of two stiff corrugated beams with a channel coiling up the space. The coiling structure has a width p = 1 cm and length a (a = 0.8 cm in this example). The width of the channel is d = 0.067p. The width of the beams is w = 0.03p, and the corrugation length is l = a − 2w − d. Sound hard boundary conditions are imposed to the left boundaries (red line) to mimic the fact that the metasurface is actually coated on a stiff plate. The light blue and dark red arrows refer to the propagation direction of incident and reflected waves, respectively. The label “1”, “2” and “3” refer to the three outlets of each element. (b) The phase of the reflected waves, as a function of the length a of the metasurface, with incident wavelength λ = 19.6p. The black dots refer to specific a values for eight units to fulfill the desired discrete phase shifts. (c) Schematic diagram of the eight units with the specific a values shown in (b) with black dots. The gap between each unit is , with a1 and a2 denoting the length of the two adjacent coiling structures. (d) The pressure strips of the reflected waves by the eight units. The high maps of pressure field are utilized to clearly show the different phase shifts by each unit.
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f1: An acoustic metasurface for generalized Snell's law.(a) The schematic diagram of an acoustic metasurface made of two stiff corrugated beams with a channel coiling up the space. The coiling structure has a width p = 1 cm and length a (a = 0.8 cm in this example). The width of the channel is d = 0.067p. The width of the beams is w = 0.03p, and the corrugation length is l = a − 2w − d. Sound hard boundary conditions are imposed to the left boundaries (red line) to mimic the fact that the metasurface is actually coated on a stiff plate. The light blue and dark red arrows refer to the propagation direction of incident and reflected waves, respectively. The label “1”, “2” and “3” refer to the three outlets of each element. (b) The phase of the reflected waves, as a function of the length a of the metasurface, with incident wavelength λ = 19.6p. The black dots refer to specific a values for eight units to fulfill the desired discrete phase shifts. (c) Schematic diagram of the eight units with the specific a values shown in (b) with black dots. The gap between each unit is , with a1 and a2 denoting the length of the two adjacent coiling structures. (d) The pressure strips of the reflected waves by the eight units. The high maps of pressure field are utilized to clearly show the different phase shifts by each unit.

Mentions: The acoustic metasurface, as shown in Fig. 1(a), is constructed by immersing identical thin rigid beams (width w and length l) in air in a way that forms fluid channels (width d). It has been proven that the coiling structure (width p and length a) could behave as an effective medium with extremely high refractive index1835, such that the reflected waves can be delayed heavily after the incident waves impinge on the structure and propagate within the zigzag path. It is therefore reasonable to infer that the phase of the reflected waves could be controlled at will by appropriately selecting the geometrical parameters of the structure, and will be demonstrated later. In order to ensure a planar structure, the length a of the metasurfaces associated to the length l of the rigid corrugations are tailored to yield the desired phase shifts, while the values of w, d and p are fixed in the calculations. The phase of the reflected waves as a function of a with free space wavelength λ = 19.6 cm is plotted in Fig. 1(b). It should be noted that, since acoustic waves, as scalar waves, can propagate within the channels freely, the reflected waves at the right-edge of the metasurface (containing three channels labeled with “1”, “2” and “3” in Fig. 1(a)) can be considered as the accumulated field of three sources, resulting in the inhomogeneous pressure distribution at the right edge of the metasurface. Therefore, the phase information at the right edge of the metasurface is retrieved by integration along extra line λ/8 (not shown in Fig. 1(a)) away from the edge. From Fig. 1(b), it is sufficient to frame eight units that could realize discrete phase shifts covering the full 2π span with steps of π/4. The exact values of a for achieving these discrete phase shifts are also illustrated with black dots in Fig. 1(b). Schematic diagrams of these eight units with different values of a are shown in Fig. 1(c). Planar acoustic metasurfaces are obviously constructed because the lengths of the units in x direction are entirely identical. To further verify the discrete phase shifts, the reflected waves by these eight units are shown in Fig. 1(d). The strips refer to the pressure filed patterns p(x,y) at the same time instant. The peak of the pressure field can shift up to a wavelength, which provide solid support that the phase shifts cover the whole 2π range. It therefore could be concluded that desirable discrete phase shifts can be realized by the eight units. The metasurfaces constructed by the eight units are ultrathin with the thickness approximately equal to λ/19.6, revealing that the metasurface is good candidate to realize acoustic devices easy for integration. It is worth pointing out that fascinating features of the coiling metamaterials such as negative refractions and zero refractive index are first presented theoretically and later verified experimentally183637. Recently we have proved that by coiling up space it is possible to change the propagating phase of acoustic wave and thereby focus the waves, but the phase delay in that work is too limited to cover 2π range35. In what follows we will further demonstrate the potential of coil-up acoustic metamaterials to design a more general metasurface that has an ultrathin structure and is capable of controlling reflected acoustic waves arbitrarily.


Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces.

Li Y, Liang B, Gu ZM, Zou XY, Cheng JC - Sci Rep (2013)

An acoustic metasurface for generalized Snell's law.(a) The schematic diagram of an acoustic metasurface made of two stiff corrugated beams with a channel coiling up the space. The coiling structure has a width p = 1 cm and length a (a = 0.8 cm in this example). The width of the channel is d = 0.067p. The width of the beams is w = 0.03p, and the corrugation length is l = a − 2w − d. Sound hard boundary conditions are imposed to the left boundaries (red line) to mimic the fact that the metasurface is actually coated on a stiff plate. The light blue and dark red arrows refer to the propagation direction of incident and reflected waves, respectively. The label “1”, “2” and “3” refer to the three outlets of each element. (b) The phase of the reflected waves, as a function of the length a of the metasurface, with incident wavelength λ = 19.6p. The black dots refer to specific a values for eight units to fulfill the desired discrete phase shifts. (c) Schematic diagram of the eight units with the specific a values shown in (b) with black dots. The gap between each unit is , with a1 and a2 denoting the length of the two adjacent coiling structures. (d) The pressure strips of the reflected waves by the eight units. The high maps of pressure field are utilized to clearly show the different phase shifts by each unit.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3756345&req=5

f1: An acoustic metasurface for generalized Snell's law.(a) The schematic diagram of an acoustic metasurface made of two stiff corrugated beams with a channel coiling up the space. The coiling structure has a width p = 1 cm and length a (a = 0.8 cm in this example). The width of the channel is d = 0.067p. The width of the beams is w = 0.03p, and the corrugation length is l = a − 2w − d. Sound hard boundary conditions are imposed to the left boundaries (red line) to mimic the fact that the metasurface is actually coated on a stiff plate. The light blue and dark red arrows refer to the propagation direction of incident and reflected waves, respectively. The label “1”, “2” and “3” refer to the three outlets of each element. (b) The phase of the reflected waves, as a function of the length a of the metasurface, with incident wavelength λ = 19.6p. The black dots refer to specific a values for eight units to fulfill the desired discrete phase shifts. (c) Schematic diagram of the eight units with the specific a values shown in (b) with black dots. The gap between each unit is , with a1 and a2 denoting the length of the two adjacent coiling structures. (d) The pressure strips of the reflected waves by the eight units. The high maps of pressure field are utilized to clearly show the different phase shifts by each unit.
Mentions: The acoustic metasurface, as shown in Fig. 1(a), is constructed by immersing identical thin rigid beams (width w and length l) in air in a way that forms fluid channels (width d). It has been proven that the coiling structure (width p and length a) could behave as an effective medium with extremely high refractive index1835, such that the reflected waves can be delayed heavily after the incident waves impinge on the structure and propagate within the zigzag path. It is therefore reasonable to infer that the phase of the reflected waves could be controlled at will by appropriately selecting the geometrical parameters of the structure, and will be demonstrated later. In order to ensure a planar structure, the length a of the metasurfaces associated to the length l of the rigid corrugations are tailored to yield the desired phase shifts, while the values of w, d and p are fixed in the calculations. The phase of the reflected waves as a function of a with free space wavelength λ = 19.6 cm is plotted in Fig. 1(b). It should be noted that, since acoustic waves, as scalar waves, can propagate within the channels freely, the reflected waves at the right-edge of the metasurface (containing three channels labeled with “1”, “2” and “3” in Fig. 1(a)) can be considered as the accumulated field of three sources, resulting in the inhomogeneous pressure distribution at the right edge of the metasurface. Therefore, the phase information at the right edge of the metasurface is retrieved by integration along extra line λ/8 (not shown in Fig. 1(a)) away from the edge. From Fig. 1(b), it is sufficient to frame eight units that could realize discrete phase shifts covering the full 2π span with steps of π/4. The exact values of a for achieving these discrete phase shifts are also illustrated with black dots in Fig. 1(b). Schematic diagrams of these eight units with different values of a are shown in Fig. 1(c). Planar acoustic metasurfaces are obviously constructed because the lengths of the units in x direction are entirely identical. To further verify the discrete phase shifts, the reflected waves by these eight units are shown in Fig. 1(d). The strips refer to the pressure filed patterns p(x,y) at the same time instant. The peak of the pressure field can shift up to a wavelength, which provide solid support that the phase shifts cover the whole 2π range. It therefore could be concluded that desirable discrete phase shifts can be realized by the eight units. The metasurfaces constructed by the eight units are ultrathin with the thickness approximately equal to λ/19.6, revealing that the metasurface is good candidate to realize acoustic devices easy for integration. It is worth pointing out that fascinating features of the coiling metamaterials such as negative refractions and zero refractive index are first presented theoretically and later verified experimentally183637. Recently we have proved that by coiling up space it is possible to change the propagating phase of acoustic wave and thereby focus the waves, but the phase delay in that work is too limited to cover 2π range35. In what follows we will further demonstrate the potential of coil-up acoustic metamaterials to design a more general metasurface that has an ultrathin structure and is capable of controlling reflected acoustic waves arbitrarily.

Bottom Line: Here, we theoretically demonstrate that the generalized Snell's law can be achieved for reflected acoustic waves based on ultrathin planar acoustic metasurfaces.The metasurfaces are constructed with eight units of a solid structure to provide discrete phase shifts covering the full 2π span with steps of π/4 by coiling up the space.Our results could open up a new avenue for acoustic wavefront engineering and manipulations.

View Article: PubMed Central - PubMed

Affiliation: 1] Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, P. R. China [2] State Key Laboratory of Acoustics, Chinese Academy of Sciences, Beijing 100190, P. R. China.

ABSTRACT
The introduction of metasurfaces has renewed the Snell's law and opened up new degrees of freedom to tailor the optical wavefront at will. Here, we theoretically demonstrate that the generalized Snell's law can be achieved for reflected acoustic waves based on ultrathin planar acoustic metasurfaces. The metasurfaces are constructed with eight units of a solid structure to provide discrete phase shifts covering the full 2π span with steps of π/4 by coiling up the space. By careful selection of the phase profiles in the transverse direction of the metasurfaces, some fascinating wavefront engineering phenomena are demonstrated, such as anomalous reflections, conversion of propagating waves into surface waves, planar aberration-free lens and nondiffracting Bessel beam generated by planar acoustic axicon. Our results could open up a new avenue for acoustic wavefront engineering and manipulations.

No MeSH data available.


Related in: MedlinePlus