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The recently proposed digital coding metasurfaces make it possible to control electromagnetic (EM) waves in real time, and allow the implementation of many different functionalities in a programmable way. However, current configurations are only space-encoded, and do not exploit the temporal dimension. Here, we propose a general theory of space-time modulated digital coding metasurfaces to obtain simultaneous manipulations of EM waves in both space and frequency domains, i.e., to control the propagation direction and harmonic power distribution simultaneously. As proof-of-principle application examples, we consider harmonic beam steering, beam shaping, and scattering-signature control. For validation, we realize a prototype controlled by a field-programmable gate array, which implements the harmonic beam steering via an optimized space-time coding sequence. Numerical and experimental results, in good agreement, demonstrate good performance of the proposed approach, with potential applications to diverse fields such as wireless communications, cognitive radars, adaptive beamforming, holographic imaging. Current digital coding metasurfaces are only space-encoded. Here, the authors propose space-time modulated digital coding metasurfaces to obtain simultaneous manipulations of electromagnetic waves and present harmonic beam steering, beam shaping, and scattering-signature control as application examples.

Multisection quarter-wave impedance transformers are widely applied in microwave engineering and optics to attain impedance-matching networks and antireflection coatings. These structures are mostly designed in the spatial domain (time harmonic) by using geometries of different materials. Here, we exploit such concepts in the time domain by using time-varying metamaterials. We derive a formal analogy between the spectral responses of these structures and their temporal analogs, i.e., time-varying stepped refractive-index profiles. We show that such space-time duality grants access to the vast arsenal of synthesis approaches available in microwave engineering and optics. This allows, for instance, the synthesis of temporal impedance transformers for broadband impedance matching with maximally flat or equi-ripple responses, which extend and generalize the recently proposed quarter-wave design as an antireflection temporal coating. Our results, validated via full-wave numerical simulations, provide new insights and deeper understanding of the wave dynamics in time-varying media, and may find important applications in space-time metastructures for broadband frequency conversion and analog signal processing.

Nonlocality is a fundamental concept in photonics. For instance, nonlocal wave-matter interactions in spatially modulated metamaterials enable novel effects, such as giant electromagnetic chirality, artificial magnetism, and negative refraction. Here, we investigate the effects induced by spatial nonlocality in metamaterials, i.e., media with a dielectric permittivity rapidly modulated in time. Via a rigorous multiscale approach, we introduce a general and compact formalism for the nonlocal effective medium theory of temporally periodic metamaterials. In particular, we study two scenarios: (i) a periodic temporal modulation, and (ii) a temporal boundary where the permittivity is abruptly changed in time and subject to periodic modulation. We show that these configurations can give rise to peculiar nonlocal effects, and we highlight the similarities and differences with respect to the spatial-metamaterial counterparts. Interestingly, by tailoring the effective boundary wave-matter interactions, we also identify an intriguing configuration for which a temporal metamaterial can perform the first-order derivative of an incident wavepacket. Our theoretical results, backed by full-wave numerical simulations, introduce key physical ingredients that may pave the way for novel applications. By fully exploiting the time-reversal symmetry breaking, nonlocal temporal metamaterials promise a great potential for efficient, tunable optical computing devices.

Spatial tailoring of the material constitutive properties is a well-known strategy to mold the local flow of given observables in different physical domains. Coordinate-transformation-based methods (e.g., transformation optics) offer a powerful and systematic approach to design anisotropic, spatially inhomogeneous artificial materials (metamaterials) capable of precisely manipulating wave-based (electromagnetic, acoustic, elastic) as well as diffusion-based (heat) phenomena in a desired fashion. However, as versatile as these approaches have been, most designs have thus far been limited to serving single-target functionalities in a given physical domain. Here, we present a step towards a “transformation multiphysics” framework that allows independent and simultaneous manipulation of multiple physical phenomena. As a proof of principle of this new scheme, we design and synthesize (in terms of realistic material constituents) a metamaterial shell that simultaneously behaves as a thermal concentrator and an electrical “invisibility cloak.” Our numerical results open up intriguing possibilities in the largely unexplored phase space of multifunctional metadevices, with a wide variety of potential applications to electrical, magnetic, acoustic, and thermal scenarios.

Temporal metamaterials, based on time-varying constitutive properties, offer new exciting possibilities for advanced field manipulations. In this study, we explore the capabilities of anisotropic temporal slabs, which rely on abrupt changes in time from isotropic to anisotropic response (and vice versa). Our findings show that these platforms can effectively manipulate the wave-spin dimension, allowing for a range of intriguing spin-controlled photonic operations. We demonstrate these capabilities through examples of spin-dependent analog computing and spin–orbit interaction effects for vortex generation. These results provide new insights into the field of temporal metamaterials, and suggest potential applications in communications, optical processing and quantum technologies.

In analogy with spatial multilayers, we put forward the idea of Herpin equivalence in temporal metamaterials characterized by step-like time variations of the constitutive parameters. We show that, at a given frequency, an arbitrary temporal multistep exhibiting mirror symmetry can be replaced by an equivalent temporal slab with suitable refractive index and travel-time. This enables the synthesis of arbitrary values of the refractive index, in a way that differs fundamentally from the effective-medium approach, and adds new useful analytical machinery to the available toolbox for the study and design of temporal metamaterials, with potentially intriguing applications to anti-reflection coatings and filters.

Supersymmetry has been shown to provide a systematic and effective framework for generating classes of isospectral optical structures featuring perfectly-phase-matched modes, with the exception of one (fundamental) mode which can be removed. More recently, this approach has been extended to non-Hermitian scenarios characterized by spatially-modulated distributions of optical loss and gain, in order to allow the removal of higher-order modes as well. In this paper, we apply this approach to the design of non-Hermitian optical couplers with higher-order mode-selection functionalities, with potential applications to mode-division multiplexing in optical links. In particular, we highlight the critical role of the coupling between non-Hermitian optical waveguides, which generally induces a phase transition to a complex eigenspectrum, thereby hindering the targeted mode-selection functionality. With the specific example of an optical coupler that selects the second-order mode of a given waveguide, we illustrate the aforementioned limitations and propose possible strategies to overcome them, bearing in mind the practical feasibility of the gain levels required.

Within the overarching framework of space-time metastructures, digital metasurfaces based on spatio-temporal coding are emerging as powerful and versatile architectures for complex field manipulations, also in view of their inherently programmable nature. Here, we provide a compact survey of our recent results and ongoing studies in this research area. Examples of field manipulations include harmonic beam steering and/or shaping and programmable nonreciprocal effects. Possible applications are abundant and range from wireless communications to radars and imaging.

We introduce the concept of metamaterial analog computing, based on suitably designed metamaterial blocks that can perform mathematical operations (such as spatial differentiation, integration, or convolution) on the profile of an impinging wave as it propagates through these blocks. Two approaches are presented to achieve such functionality: (i) subwavelength structured metascreens combined with graded-index waveguides and (ii) multilayered slabs designed to achieve a desired spatial Green's function. Both techniques offer the possibility of miniaturized, potentially integrable, wave-based computing systems that are thinner than conventional lens-based optical signal and data processors by several orders of magnitude.

In solid-state physics, “doping” is a pivotal concept that allows controlling and engineering of the macroscopic electronic and optical properties of materials such as semiconductors by judiciously introducing small concentrations of impurities. Recently, this concept has been translated to two-dimensional photonic scenarios in connection with host media characterized by vanishingly small relative permittivity (“epsilon near zero”), showing that it is possible to obtain broadly tunable effective magnetic responses by introducing a single, nonmagnetic doping particle at an arbitrary position. So far, this phenomenon has been studied mostly for lossless configurations. In principle, the inevitable presence of material losses can be compensated via optical gain. However, taking inspiration from quantum (e.g., parity−time) symmetries that are eliciting growing attention in the emerging fields of non-Hermitian optics and photonics, this suggests considering more general gain−loss interactions. Here, we theoretically show that the photonic doping concept can be extended to non-Hermitian scenarios characterized by tailored distributions of gain and loss in either the doping particles or the host medium. In these scenarios, the effective permeability can be modeled as a complex-valued quantity (with the imaginary part accounting for the gain or loss), which can be tailored over broad regions of the complex plane. This enables a variety of unconventional optical responses and waveguiding mechanisms, which can be, in principle, reconfigured by varying the optical gain (e.g., via optical pumping). We envision several possible applications of this concept, including reconfigurable nanophotonics platforms and optical sensing, which motivate further studies for their experimental validation.