7th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics – Metamaterials 2013 Bordeaux, France, 16-21 September 2013

Experimental Demonstration of Acoustic and Electromagnetic Metamaterials with Conical Dispersion

Jensen Li1, Zixian Liang2, Tinhua Feng2, Chi Hou Chan3, Seunghoon Han4 and Sangyoon Lee4

1 School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, UK 2 Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue,

Kowloon Tong, Kowloon, Hong Kong, China 3 State Key Laboratory of Millimeter Waves, City University of Hong Kong, Tat Chee Avenue,

Kowloon, Hong Kong, China 4 Samsung Advanced Institute of Technology, Samsung Electronics, Yongin, Gyeonggi 446-712, South Korea

email: j.li@bham.ac.uk

Abstract – We experimentally demonstrate metamaterials with extreme dispersions by coiling up space with curled channels. An acoustic metamaterial is constructed with conical dispersion, supporting negative refraction with airborne sound. We have also demonstrated a double-negative microwave metamaterial by guiding through the cutoff-free TEM mode between two curled conducting wires. Field mappings and effective medium extraction confirm our studies.

I. INTRODUCTION

Double-negative metamaterials are usually constructed with subwavelength structural units with individually

tuned resonances in the two constitutive parameters. Alternative routes in achieving negative refraction through mechanisms including chirality, photonic crystals and time reversal are also being sought [1-3]. It may give a larger operational bandwidth, a lower loss, or a larger scalability to bulk metamaterials. Here, we experimentally demonstrate a geometric route in achieving double negativity and extreme indices through space coiling. By delaying the propagation phase using curled channels to mimic a two-dimensional array of high-index elements, band folding occurs at small frequencies to obtain an effective medium even above the bandgap and gives extreme effective material parameters [4,5]. It gives rise to a conical dispersion and the associated negative refractive index.

II. EXPERIMENTAL RESULTS

Fig. 1. (a) The acoustic metamaterial with unit cell size a = 2.33cm. The curled air channels guide the sound waves in zig-zag paths. (b) The microwave metamaterial with unit cell size a = 0.76cm. Copper wire patterns are the same on each layer of printed circuit board with foam spacers in between to guide EM waves in a curled fashion similar to the acoustic counterpart.

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7th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics – Metamaterials 2013 Bordeaux, France, 16-21 September 2013

Figure 1(a) shows a slab of the fabricated acoustic metamaterial within our current scheme. Each unit contains a curled air channel within aluminum (regarded as hard solid for airborne sound) to guide acoustic waves at low frequencies and without cut-off, effectively equivalent to a straight channel with a high refractive index. The high-index elements are assembled into a two-dimensional network and the resultant metamaterial gives rise to a conical dispersion at wavelengths much larger than the unit cell size (a = 2.33cm). Figure 2(a) shows the experimentally extracted refractive index n (in crosses, normalized to index the one in air). It agrees very well with the theory in solid line, varying continuously from -1 to 1 from around 2.7 to 3.7 kHz. The associated conical dispersion is plotted in Fig. 1b, with nearly linear dispersion, a constant group velocity (~6.7 in our case) around the Γ point with 2D isotropy. We have extracted both the effective density and bulk modulus applying the S-parameter retrieval method on the experimentally measured complex transmission and reflection coefficients within a waveguide and they become both negative below 3.12kHz, the center of the cone. As we have mentioned, the same principle in coiling up the space also applies to electromagnetic waves. Figure 1(b) shows a slab of the fabricated microwave metamaterial. The same pattern (as in the acoustic case) becomes copper wire layers printed on circuit boards. The patterns on each layer are identical and are stacked in the vertical direction separated by foam spacers of subwavelength thickness. In this case, the electromagnetic waves work in the H-polarization with H-field perpendicular to the patterns and propagating direction on the same plane of the patterns. The cut-off free wave guiding here is supported by the TEM mode between two adjacent wires and waves are curled in a similar manner. Figure 2(c) and (d) shows the corresponding index and dispersion with good agreement between theory and experiment. The index varies from 1 to 1 from 6.54 to 7.95 GHz, again indicating the occurrence of band folding at a very low frequency. Due to the presence of the foam spacer, a spectral gap now opens up from 7.1 to 7.4 GHz (a distinct phase of Re(n) ~ 0 in Fig. 2(c)). The size of the gap can be tuned by varying the thickness of the foam spacer and it will diminish to become the ideal conical dispersion again when the thickness of the foam spacer goes to zero.

Fig. 2. Negative indices and conical dispersion for acoustic ((a), (b)) and EM space-coiling metamaterial ((c), (d)). Solid line / crosses is simulation / experimental results

The effective medium obtained can be used to represent the metamaterial when the units are assembled into different configurations. We have constructed a prism and a slab from the acoustic metamaterial units. By putting the sample in a two-dimensional waveguide with an acoustic beam shining towards them, we can map out the pressure field patterns in the region after the beam exits and they are showed in Fig. 3. In Fig. 3(a), the beam at 2.7kHz shining horizontally undergoes negative refraction at the exit interface of the prism at an index around -1. In Fig. 3(b), a beam incident at 30 degrees away from the normal has a negative beam shift at the same frequency, indicating negative refraction which results from a negative refractive index. Fig. 4(a) shows the experimental and theoretical results if we only show the field intensity along one line, indicating a negative beam shift at 2.7kHz (n ~ -1) and a positive beam shift at 3.7 kHz (n ~ 1). For the electromagnetic wave sample,

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7th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics – Metamaterials 2013 Bordeaux, France, 16-21 September 2013

a beam is also shined at 30 degrees towards the slab and negative beam shift at 6.54GHz (n ~ -1, black color), comparing to the positive beam shift at 7.95 GHz (n ~ 1, purple color) showed in Fig. 4(b).

Fig. 3. Experimental acoustic field-mappings (pressure-field snapshots) showing negative refraction. (a) A 45-degree prism with 4 units in width and (b) a slab of two rows of the metamaterial units. An acoustic beam is shined from the left in both cases. Red/blue color indicates positive and negative values.

Fig. 4. Field intensity along a single line at exit of the metamaterial slab for the (a) acoustic sample and (b) electromagnetic wave sample. The solid line is theoretical results from full-wave simulations. Experimental results are showed as triangles at the frequency with index -1 and crosses at the frequency with index +1. Position 0 differentiates between negative and positive refraction.

III. CONCLUSION We have experimentally demonstrated a geometric approach through coiling up space to construct both

acoustic and electromagnetic metamaterials. Conical dispersion and the associated negative indices are achieved. The investigations are potentially useful to designing metamaterials with larger ratio of wavelength to lattice constant, or with a large group velocity in a wide frequency range. The effective medium parameters may also be useful for employment in the framework of transformation acoustics or optics.

This work is supported by the GRO program of Samsung Advanced Institute of Technology and the Research

Grants Council of Hong Kong (Project No. HKUST2/CRF/11G).

REFERENCES

[1] S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski and C. Simovski, "Waves and Energy in Chiral Nihility," J. Electromagn. Waves. Appl. 17, 695 (2003).

[2] J. B. Pendry, "A chiral route to negative refraction," Science 306, 1353 (2004). [3] J. B. Pendry, "Time reversal and negative refraction," Science 322, 71 (2008). [4] Z. Liang and J. Li, "Extreme acoustic metamaterial by coiling up space," Phys. Rev. Lett. 108, 114301 (2012). [5] Z. Liang et. al., "Space-coiling metamaterials with double negativity and conical dispersion,", Sci. Rep. 3, 1614 (2013).

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