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Recent advances in twistronics of low-dimensional materials, such as bilayer graphene and transition-metal dichalcogenides, have enabled a plethora of unusual phenomena associated with moiré physics. However, several of these effects require demanding manipulation of superlattices at the atomic scale, such as the careful control of rotation angle between two closely spaced atomic lattices. Here, we study moiré hyperbolic plasmons in pairs of hyperbolic metasurfaces (HMTSs), unveiling analogous phenomena at the mesoscopic scale. HMTSs are known to support confined surface waves collimated towards specific directions determined by the metasurface dispersion. By rotating two evanescently coupled HMTSs with respect to one another, we unveil rich dispersion engineering, topological transitions at magic angles, broadband field canalization, and plasmon spin-Hall phenomena. These findings open remarkable opportunities to advance metasurface optics, enriching it with moiré physics and twistronic concepts.

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Optical metasurfaces are assemblies of subwavelength, artificially designed inclusions forming planarized devices with unprecedented capabilities to manipulate electromagnetic waves and facilitate multiple functionalities. Recent topical efforts in this research area have been focused on pushing forward the frontiers of enhanced light-matter interactions exploiting new concepts and fabrication capabilities. In this context, layered and twisted metasurfaces have showcased interesting features, including flexibility and tunability in manipulating light, contributing to the development of moiré physics for light. Here, we provide an overview on the state-of-art layered and stacked moiré metasurfaces. Freespace multifunctional metadevices are first discussed, followed by recent discoveries in polaritonics and twistronics for twisted hyperbolic metasurface bilayers. We conclude with a discussion on recent advances in the nanofabrication of moiré metasurfaces and remark on their future potential applications. Emerging Strategies for Advanced Optical Metasurfaces Using Twisting and StackingOptical metasurfaces (see Glossary), commonly recognized as the 2D counterpart of bulk metamaterials, are composed of subwavelength planarized inclusions [1,2]. Unlike metamaterials, metasurfaces usually have a thickness smaller than the operational wavelength in free space, holding the promise for next-generation multifunctional, compact, and integrated functional optical devices. Their ultrathin nature can significantly ease nanofabrication requirements compared with metamaterials, making them compatible for mass production in the semiconductor industry. One essential step in designing metasurfaces is to control light interactions with its local functional composites, so-called meta-atoms, thus enabling unprecedented control of the local scattering processes in terms of phase, amplitude, polarization, frequency, dispersion, and more [3][4][5][6]. In this way, a designer metasurface can be endowed with unprecedented control in tailoring the impinging light. This process inherently requires resonant light-matter interactions in meta-atoms, given the small light-matter interaction length. Tremendous efforts have been made in searching for better materials and novel metasurface designs for improved performance. For composite materials, metals can support enhanced photonic local density of states due to plasmonic phenomena, but may suffer from large Ohmic loss [7][8][9]. On the contrary, all-dielectric materials have significantly lower loss, but typically require a larger thickness, in the order of the wavelength in the material, limiting the field localization and enhancement of light-matter interactions [10]. Various geometries have been explored to realize metasurfaces, including split ring resonators, nanorods, and V-shape nanoantennas, supporting optical resonances in subwavelength meta-atoms [7,10]. These designs typically rely on heavy optimization techniques to obtain the best responses, requiring computational resources and tim...

Recently, it has been shown that a new class of particle chains that support the simultaneous interplay of two-type rotations-geometric and electromagnetic-may possess strong nonreciprocity and one-way guiding effects. Here, we use the Z transform to develop a rigorous Green's function theory for these one-way chains. A study of the chain's spectra and its analytic properties in the complex spectral (Z) plane, where each and every singularity (e.g., pole, branch cut, etc.) represents a distinct wave phenomenon, reveals all the wave constituents that may be excited. We explore the breach of symmetry of the complex Z plane singularities and their manifestations as the symmetry breaking wave mechanisms that underly the one-way guiding effects. It is shown that this breach of symmetry in particle chains is possible only when both rotations-geometric and electromagnetic-are simultaneously present. It is also shown that the continuous spectrum (e.g., branch singularity) plays a pivotal role in suppressing the radiation into the "forbidden" direction.