It is characterized by two types of vector-field degrees of freedom, i.e., a velocity field and a microrotation field. Unlike previous spin-sustaining acoustic fields 19, 20, 22, the transverse sound is spin-1 in nature and carries the properties of elastic waves. In this work, we show that airborne sound can behave as a transverse wave with well-defined polarization in an acoustic metamaterial that goes beyond the Cauchy elasticity and follows a micropolar elasticity theory 23. In other words, sound is characterized by a scalar pressure field p and a vector velocity field v, whereas light is characterized by two vector fields E and H. Despite this discovery of acoustic spin, SOIs remain beyond reach in sound, a fact that mainly owes to the lack of degrees of freedom. In a homogenous medium, however, the spatial integration of acoustic spin density for a localized wave must vanish, in agreement with its spin-0 nature 20. Such an acoustic spin can emerge locally in nonuniform acoustic fields 20, 21 and has recently been observed in experiments 19, 22. Recent studies show that an engineered sound field can possess a locally rotational velocity field v that may be regarded as acoustic spin 19, 20, 21, similar to electric spin deriving from the local rotation of electric field. This is because although longitudinal waves such as airborne sound can carry OAM 14, 15, 16, 17, 18, they are spin-0 in nature. SOIs are unique to transverse waves such as light and are absent for longitudinal waves. The couplings between spin and OAM, referred to as spin–orbit interactions (SOIs), can give rise to intriguing phenomena and applications in optics 2, 3, 4, 5, 6, 7, 8, such as photonic spin-Hall effect 9, 10, 11 and spin-dependent vortex generation 12, 13. OAM originates from the spatial phase gradient (scalar degree of freedom) of waves and manifests as a helical wave front 1. Spin is associated with circular polarization (vector degrees of freedom) of waves and is characterized by the local rotation of a vector field. Spin and orbital angular momentum (OAM) are intrinsic properties of classical waves. The acoustic SOIs can provide new perspectives and functionalities for sound manipulations beyond the conventional scalar degree of freedom and may open an avenue to the development of spin-orbit acoustics. In addition, we show that the scattering of the transverse sound by a dipole particle can generate spin-dependent acoustic vortices via the geometric phase effect. We demonstrate that acoustic activity of the metamaterial can induce coupling between the spin and linear crystal momentum k, which leads to negative refraction of the transverse sound. This enables the realization of acoustic SOIs with rich phenomena beyond those in conventional acoustic systems. Here, we theoretically and experimentally demonstrate that airborne sound can possess artificial transversality in an acoustic micropolar metamaterial and thus carry both spin and orbital angular momentum. However, it is counterintuitive that SOIs can exist for sound, which is a longitudinal wave that carries no intrinsic spin. These interactions usually occur in homogenous crystals, or in birefringent crystals cut appropriately.Spin-orbit interactions (SOIs) endow light with intriguing properties and applications such as photonic spin-Hall effects and spin-dependent vortex generations. There is no change in polarization associated with the interaction. This is a situation of great symmetry and the angle of incidence is found to match the angle of diffraction. In such a situation, the acoustic wave travels longitudinally in the crystal and the incident and diffracted laser beams see the same refractive index. While these all share the basic principles of momentum and energy conservation, these different modes of operation have very different performances - as shall be seen.Īn isotropic interaction is also referred to as a longitudinal-mode interaction. These can be heard described by terms such as longitudinal- and shear-mode, isotropic and anisotropic. This ∽oppler shift can generally be neglected since F<<F d or F i, but can be of great interest in heterodyning applications.Īcousto-optic components use a range of different materials in a variety of configurations. So, the optical frequency of the diffracted beam is by an amount equal to the frequency of the acoustic wave. n i and n d are the refractive indexes experienced by the incident and diffracted beams (these are not necessarily the same).Įnergy conservation leads to : F d = F i +/- F Here F is the frequency of the acoustic wave traveling at velocity v.
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