Numerical models of single- and double-negative metamaterials including viscous and thermal losses

Negative index acoustic metamaterials are artificial structures made of subwavelength units arranged in a lattice, whose effective acoustic parameters, bulk modulus and mass density, can be negative. In these materials, sound waves propagate inside the periodic structure, assumed rigid, showing extraordinary properties.

We are interested in two particular cases: a double-negative metamaterial, where both parameters are negative at some frequencies, and a single-negative metamaterial with negative bulk modulus within a broader frequency band. In previous research involving the double-negative metamaterial, numerical models with viscous and thermal losses were used to explain that the extraordinary behavior, predicted by analytical models and numerical simulations with no losses, disappeared when the metamaterial was measured in physical setups.

The improvement of the models is allowing now a more detailed understanding on how viscous and thermal losses affect the setups at different frequencies. The modeling of a simpler single-negative metamaterial also broadens this overview. Both setups have been modeled with quadratic BEM meshes. Each sample, scaled at two different sizes, has been represented with a detailed frequency step.

The influence of viscous and thermal losses as a function of the scale has been studied at two different scales, in both metamaerials. It is shown that the effect of losses on the scale is not the same for the different regimes of the metamaterials. Special attention is also given to the double-negative frequency band, where a fine frequency step of the simulation reveals details about the Fabry-Perot resonances in the metamaterial slab.

The numerical model with losses, which is computationally very demanding, will also be commented.