Metamaterials displaying negative refractive index has remarkable potential to facilitate the manipulation of incident waves for wide variety of applications such as cloaking, superlensing and the like. Space-coiling approach is a recently explored technique to achieve extreme properties. The space coiling phenomena cause less energy absorption as compared to local resonating phenomena for obtaining extreme parameters. Here we show extreme properties in doubly negative 3D space coiling acoustic metamaterials. Frequency dispersive spectrum of extreme constitutive parameters has been calculated for 2D maze and 3D space coiling labyrinthine structure. This is in good agreement to the calculated acoustic band dispersion.

Metamaterials are engineered materials that offer the flexibility to manipulate the incident waves leading to exotic applications such as cloaking, extraordinary transmission, sub-wavelength imaging and negative refraction. These concepts have largely been explored in the context of electromagnetic waves. Acoustic metamaterials, similar to their optical counterparts, demonstrate anomalous effective elastic properties. Recent developments have shown that coiling up the propagation path of acoustic wave results in effective elastic response of the metamaterial beyond the natural response of its constituent materials. The effective response of metamaterials is generally evaluated using the ‘S’ parameter retrieval method based on amplitude of the waves. The phase of acoustic waves contains information of wave pressure and particle velocity. Here, we show using finite-element methods that phase reversal of transmitted waves may be used to predict extreme acoustic properties in space coiling metamaterials. This change is the difference in the phase of the transmitted wave with respect to the incident wave. This method is simpler when compared with the more rigorous ‘S’ parameter retrieval method. The inferences drawn using this method have been verified experimentally for labyrinthine metamaterials by showing negative refraction for the predicted band of frequencies.

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