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Passive Cancellation and
Directional Cloaking
More "traditional" techniques have been proposed using passive sound cancellation. The idea is to coat an object with a layer that eliminates the scattered sound. In the long wavelength, low frequency limit, this can be achieved by eliminating the monopole and dipole scattered terms, which amounts to making the cloak plus the target have effective density and compressibility of water (Zhou and Hu, 2007; Guild et al., 2011) so the scatterer behaves as a "neutral acoustic inclusion." Omnidirectional cancellation can be achieved at finite frequencies using optimization methods to determine the coating properties (Guild et al., 2011). Martin and Orris (2012) proposed a hybrid design combining TA with scattering cancellation and showed that it outperforms both a cancellation layer and a discretized TA design over a broad frequency range in cloaking an Aluminium cylinder in water.
Guild et al. (2014) used the fact that cancellation eliminates the scattering in the exterior fluid without removing the field inside the object, to consider non-scattering sensors. This would enable the sensor to detect sound without disrupting the acoustic field. Simulations of a scattering cancellation cloak made of two fluid layers surrounding a piezoelectric sensor showed a 20-to-50 dB scattering strength reduction compared to the uncloaked sensor over the typical frequen- cy range of operation.
Directional cloaking (as opposed to omnidirectional) can be achieved for specific directions of incidence using simpler cancellation designs. Thus, García-Chocano et al. (2011) demonstrated a 2D narrow band cloak in air comprising 120 aluminum cylinders of 1.5 cm diameter surrounding the cloaked cylinder of diameter 22.5 cm. The 120 positions were determined by optimization at an operating frequency of 3061 Hz, yielding good cloaking over a bandwidth of 100 Hz. Sanchis et al. (2013) used the same design strategy to experimentally characterize a 3D acoustic cloak in air that significantly reduces scattering for a unique incidence di- rection. The cloak consists of 60 tori made by 3D printing, arranged concentrically around the 4 cm radius cloaked sphere. Measurements show an approximately ten-fold scattering reduction at operating frequency 8600 Hz with a bandwidth of 200 Hz.
Urzhumov et al. (2012) proposed a uni-directional cloak comprising a spherical shell of isotropic (i.e. normal) acous- tic material. The cloak, designed to operate in transmission
mode, uses a conformal mapping (the only case of TA that does not require anisotropy) to yield an eikonal cloak, a cloak which partially preserves the ray structure of TA in the desired direction but without the necessary impedance. Conversely, Hu et al. (2013) designed and tested a 2D uni- directional cloak that specifically reduces backscattering by surrounding an object with layers of perforated plates that make the target appear narrow in reflection. Measurements show at least 20 dB reduction in sound pressure level near the backscatter direction over a frequency range 1500 to 2200 Hz.
Cloaking of Elastic and Other Waves
Elastic waves present a greater challenge for cloaking be- cause of the two wave types as compared with one in acous- tics. Theoretical analyses (Brun et al., 2009; Norris and Shu- valov, 2011) show that even more exotic material properties are required for TA in the presence of waves with transverse and longitudinal polarization. The cloak material must dis- play significant stress asymmetry, which is not found in natural solids and difficult to achieve with microstructure. Asymmetric stress is a feature of small-on-large elasticity, the type of linear elasticity found in hyperelastic solids after large static strain, offering one possible cloaking mechanism (Norris and Parnell, 2012).
One area of elastic waves has seen practical cloaking: flexur- al (or bending) waves in thin plates are polarized in a single direction (normal to the plate) and satisfy a Helmholtz-like equation similar to acoustics. Stenger et al. (2012) adapted the TA design proposed by Farhat et al. (2009) to make a flex- ural wave cloak comprising 20 concentric rings of PVC and PDMS machined into a 1 mm thin PVC plate. The cloak was demonstrated at acoustic frequencies (Figure 7). This de- vice exhibits the largest measured relative bandwidth (more than one octave) of reported free-space acoustic cloaks.
Cloaking has been demonstrated for gravity waves in water (Farhat et al., 2008) which satisfy a wave equation amenable to TA. Modifications of acoustic cloak design to include con- vective effects for moving objects and cloaks was considered by Huang et al. (2014). Thermal effects have even been pro- posed for 2D acoustic cloaking in air. García-Chocano et al. (2012) simulated cylindrically layered anisotropic density by controlled heating or cooling of cylinders. Numerical results showed reduced acoustic backscatter in certain frequency bands using this exotic mechanism.
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