We have fabricated sonic crystals, based on the idea of localized resonant structures, that exhibit spectral gaps with a lattice constant two orders of magnitude smaller than the relevant wavelength. Disordered composites made from such localized resonant structures behave as a material with effective negative elastic constants and a total wave reflector within certain tunable sonic frequency ranges. A 2-centimeter slab of this composite material is shown to break the conventional mass-density law of sound transmission by one or more orders of magnitude at 400 hertz.

Using a plane-wave expansion method, we have solved Maxwell’s equations for the propagation of electromagnetic waves in a periodic lattice of dielectric spheres (dielectric constant ${\mathrm{\epsilon }}_{\mathit{a}}$) in a uniform dielectric background (${\mathrm{\epsilon }}_{\mathit{b}}$). Contrary to experiment, we find that fcc dielectric structures do not have a ‘‘photonic band gap’’ that extends throughout the Brillouin zone. However, we have determined that dielectric spheres arranged in the diamond structure do possess a full photonic band gap. This gap exists for refractive-index contrasts as low as 2.

We show here the existence of acoustic metamaterial, in which both the effective density and bulk modulus are simultaneously negative, in the true and strict sense of an effective medium. Our double-negative acoustic system is an acoustic analogue of Veselago’s medium in electromagnetism, and shares many unique consequences, such as negative refractive index. The double negativity in acoustics is derived from low-frequency resonances, as in the case of electromagnetism, but the negative density and modulus are derived from a single resonance structure as distinct from electromagnetism in which the negative permeability and negative permittivity originates from different resonance mechanisms.