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This work presents a multiple scattering formulation of two dimensionalacoustic metamaterials. It is shown that in the low frequency limit multiplescattering allows us to define frequency-dependent effective acousticparameters for arrays of both ordered and disordered cylinders. Thisformulation can lead to both positive and negative acoustic parameters, wherethe acoustic parameters are the scalar bulk modulus and the tensorial massdensity and, therefore, anisotropic wave propagation is allowed with bothpositive or negative refraction index. It is also shown that the surface fieldson the scatterer are the main responsible of the anomalous behavior of theeffective medium, therefore complex scatterers can be used to engineer thefrequency response of the effective medium, and some examples of application todifferent scatterers are given. Finally, the theory is extended toelectromagnetic wave propagation, where Mie resonances are found to be theresponsible of the metamaterial behavior. As an application, it is shown thatit is possible to obtain metamaterials with negative permeability andpermittivity tensors by arrays of all-dielectric cylinders and that anisotropiccylinders can tune the frequency response of these resonances.

Multiple Scattering Formulation of Two Dimensional Acoustic and Electromagnetic Metamaterials