Novel negative mass density resonant metamaterial unit cell
Introduction
The term metamaterial refers to a medium composed of sub-wavelength unit cells, specifically engineered to exhibit unusual properties in relation to wave propagation, generally not found in nature. Most research in this area has been dedicated to electromagnetic metamaterials, which offer the possibility of engineering effective permeability and permittivity, resulting in phenomena such as negative phase velocity, superlensing and cloaking [1], [2], [3], [4], [5], [6], [7], [8], [9]. However, in recent years a lot of attention has also been given to the study of acoustic metamaterials, where specific design is deployed to control the values of effective compressibility and mass density [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22].
Negative values of effective mass density have so far been achieved using composites [13], [14], [15], [16], [17], or exploiting the equivalence to the transmission-line-approach to metamaterials [18], [19], [20], [21]. In the latter case the frequency dependence of the effective density of unit cells exhibits the Drude behaviour, while no attempt has been made so far to design a unit cell with effective mass density of the Lorentzian type. In this paper we propose such a unit cell, derive a closed analytical formula for its effective mass density, and demonstrate evanescent and left-handed propagation of acoustic waves. Finally, we propose a dual-band version of the unit cell, capable of operating at two independently chosen frequencies.
Section snippets
Theory
In the electromagnetic (EM) case, the most typical unit cell exhibiting Lorentzian-type permeability is the split-ring resonator (SRR) placed next to a microstrip. With the aim of obtaining a novel Lorentzian-type density acoustic unit cell, i.e. the acoustic counterpart of such an EM unit cell, we design its physical structure so as to match its lumped-element equivalent circuit to the one of the SRR-loaded microstrip, given in [23].
Namely, in the EM case the equivalent circuit features a
Results
To illustrate the versatility of the proposed unit cell, we first use it to design an evanescent bandstop acoustic medium. This structure is designed by cascading unit cells loading the host duct, as shown in Fig. 3(a). The bandwidth of such a medium can be controlled by conventional filter design methods, i.e. by varying the number of unit cells used and by tuning their mutual coupling. The medium composed of four unit cells, analyzed in Fig. 3(b), exhibits stopband attenuation of more than 30
Conclusions
In summary, we have demonstrated that the acoustic metamaterial unit cell based on a simple electro-acoustic analogy with the typical resonant-permeability unit cell from the domain of electromagnetic metamaterials is an efficient means to provide negative mass density to acoustic metamaterials. A closed analytical formula for the effective density has been developed, confirming that at a range of frequencies the value of this parameter is indeed negative. The versatility of the proposed
Acknowledgements
This research was supported in part by the European Commission (grant no. PIRSES-GA-2009-247532).
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