Several particles demonstrate a collective mechanical behavior of bunching together in a light field. This effect is called optical binding, and it is advantageous for a great scope of applications. Structured interfaces can provide an additional flexibility in tailoring scattering channels of the particles via a predesigned dispersion of surface and bulk modes. Here, we investigate capabilities of hyperbolic metamaterials substrates in application to optical binding. In contrary to free-space binding scenarios, a hyperbolic metamaterial substrate opens additional interaction channels, mediated by surface and volumetric modes. It is shown that metamaterial substrate provides an enhancement of optical binding stiffness, while the periodicity of optical binding is highly dependent on the thickness of the substrate and can be either deeply subwavelength or long-range. Here we discuss a possibility to achieve long-range optical binding due to the volumetric modes of a hyperbolic metamaterial slab.

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