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Spin-orbit interactions (SOIs) endow light with intriguing properties and applications such as photonic spin-Hall effects and spin-dependent vortex generations. However, it is counterintuitive that SOIs can exist for sound, which is a longitudinal wave that carries no intrinsic spin. 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. This enables the realization of acoustic SOIs with rich phenomena beyond those in conventional acoustic systems. 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. 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. 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.

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Significance Vectorial optical holography, as a scheme to control the polarization distributions of light in the Fourier space, has been experimentally demonstrated in the linear optical regime. However, its nonlinear optical counterpart, which can generate the holographic images at different frequencies to that of the incident light, remains unexplored. Here, we demonstrate nonlinear vectorial holography through the second harmonic generation process on a quad-atom plasmonic metasurface, which consists of gold meta-atoms with threefold rotational symmetry. The proposed metasurface platform may have important applications in vectorial polarization nonlinear optical source, high-capacity optical information storage, and optical encryption.