Negative Refraction and Energy Funneling by Hyperbolic Materials: An Experimental Demonstration in Acoustics

Victor M. García-Chocano, Johan Christensen, and José Sánchez-Dehesa

Phys. Rev. Lett. 112, 144301 – Published 10 April 2014

Abstract

This Letter reports the design, fabrication, and experimental characterization of hyperbolic materials showing negative refraction and energy funneling of airborne sound. Negative refraction is demonstrated using a stack of five holey Plexiglas plates where their thicknesses, layer separation, hole diameters, and lattice periodicity have been determined to show hyperbolic dispersion around 40 kHz. The resulting hyperbolic material shows a flat band profile in the equifrequency contour allowing the gathering of acoustic energy in a broad range of incident angles and its funneling through the material. Our demonstrations foresee interesting developments based on both phenomena. Acoustic imaging with subwavelength resolution and spot-size converters that harvest and squeeze sound waves irradiating from many directions into a collimated beam are just two possible applications among many.

Received 17 January 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.144301

Authors & Affiliations

Victor M. García-Chocano¹, Johan Christensen², and José Sánchez-Dehesa^1,*

¹Wave Phenomena Group, Department of Electronics Engineering, Universitat Politècnica de València, Camino de Vera s.n. (Edificio 7F), ES-46022 Valencia, Spain
²Department of Photonics Engineering, Technical University of Denmark, Orsteds Plads, Building 343, DK-2800 Kongens Lyngby, Denmark

^*Corresponding author. jsdehesa@upv.es

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Vol. 112, Iss. 14 — 11 April 2014

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Images

Figure 1
(a) Frontal and (b) lateral views of the fabricated sample. It consists of a stack of holey Plexiglas plates with thickness $t = 7.27 mm$ and separation $s = 3.18 mm$ . The holes of diameter $D = 2.7 mm$ are drilled in a square distribution with lattice period $a_{x} = a_{y} = 4.54 mm$ . The hole periodicity along the normal is $a_{z} = t + s = 10.45 mm$ . (c) Scheme (not to scale) of the experimental setup. The rectangle defined by the dashed lines defines the area scanned by the receiver-transducer. The sample represented consists of five holey plates (gray rectangles) with total thickness $L$ .
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Figure 2
Calculated propagating angle $ϕ_{ref}$ inside the hyperbolic material described in Fig. 1 as a function of the incident angle $ϕ_{ref}$ . The inset shows the equifrequency curves corresponding to airborne sound propagating in free space (circle of radius $k_{0} = 2 π / λ_{0}$ ) and inside a hyperbolic material with an infinite number of layers. $k_{| |}$ and $k_{z}$ are the components of the wave-vector parallel and perpendicular, respectively, to the stack of Plexiglas layers. In terms of wavelength, $λ / D = 3.2$ , $λ / d_{x} = λ / d_{y} = 1.9$ , and $λ / d_{z} = 0.8$ . The vertical dashed line is a guide for the eye indicating the conservation of $k_{| |}$ .
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Figure 3
(a) Calculated pressure map (real part) obtained from finite element simulations showing negative refraction. The cylindrical beam with frequency 40 kHz is transmitted through five layers of holey Plexiglas plates (see Fig. 1). The white arrows indicate the directions of the beam. (b) Experimental data showing the pressure map measured in the rectangular area enclosed by dashed lines in part (a). The continuous lines are guides for the eye representing the directions followed by the beam. The horizontal dashed line defines the normal to the sample passing through the point contact of the impinging beam. The dotted line $A A^{'}$ is perpendicular to the direction of the transmitted beam.
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Figure 4
Frequency dependence of the normalized pressure amplitude taken along the line $A A^{'}$ represented in Fig. 1. (a) Calculated propagating angle, $ϕ_{ref}$ , inside the hyperbolic material. (b) Measured angle. Both results are obtained considering that the direction of the incident beam is fixed at $ϕ_{inc} = 45 °$ , as in Fig. 3. The white curves follows the level with maximum amplitude. The horizontal lines define the zero.
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Figure 5
Experimental data showing the frequency dependence of the pressure amplitude measured at $P_{1}$ as a function of the incident direction [see Fig. 1]. The inset depicts the profile taken at 41 kHz. Experiments have been performed using a sample made of nine holey plates.
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Figure 6
Pressure profile of the beam transmitted through a sample made of nine holey plates. The frequency dependence of the beam profile is measured along the $y$ axis separated 2 cm from the back surface. The inset shows the profiles taken at 41 kHz with (yellow line) and without (white line) the sample.
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