Acoustic negative refractions with backward-wave (BW) effects were both theoretically and experimentally established in the second band of a two-dimensional (2D) triangular sonic crystal (SC). Intense Bragg scatterings result in the extreme deformation of the second band equifrequency surface (EFS) into two classes: one around the K point and the other around the Г point of the reduced Brillouin zone. The two classes can lead to BW negative refractions (BWNRs) but with reverse negative refraction dependences on frequencies and incident angles. Not only BWNR but BW positive refraction can be present at EFSs around the K point, so it is possible to enhance the resolution of acoustic waves with a subdiffraction limit regardless of refractions, which is no analogy in both left-handed material and SCs' first band. These abundant characters make refractions in the second band distinguished.

Negative refractions of acoustic waves in a two-dimensional (2D) sonic crystal were studied both experimentally and theoretically. By calculating the acoustic band structure and equifrequency surfaces, we theoretically analyzed the acoustic single-beam negative refraction in the first band operating in the ultrasonic regime. A 2D square sonic crystal was constructed with 2.0-mm-diam steel cylinders arranged as square arrays of 2.5mm lattice constant. A scanning transmission measurement of spatial distribution was carried out to establish the acoustic refraction of a single Gaussian beam. It was demonstrated that the negative refraction is strongly dependent on both frequencies and incident angles, which shows great potential in acoustic devices.

A two-dimensional square photonic crystal sPCd with magnetically active semiconductor constituents, for example GaAs, is proposed to realize tunable negative refractions. By the Voigt effect, the magnetic-dependent permittivity of the semiconductor, then PC's band structure and equifrequency surface could be tuned by an external magnetic field. Taking a real model into consideration with absorption, the calculation reveals that the refraction could be manipulated from positive to negative, and then to positive by the applied fields. With the tunable negative refraction, tunable superlenses with all angle negative refraction could be established by a relatively small magnetic field s0.262-0.315Td, which might lead to great potential applications in photoelectronic devices.