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In this brief opinionated article, I present a personal perspective on metamterials with high degrees of freedom and dimensionality and discuss their potential roles in enriching light–matter interaction in photonics and related fields.

A class of metamaterials designed with low permittivity provides a platform for developing optical devices with unconventional properties. In most wave phenomena, the interplay between the spatial and temporal features of a wave is influenced by the medium in which the wave propagates. For example, the wavelength λ (a spatial feature) and the frequency f (a temporal feature) of a propagating signal are related via the phase velocity v of the wave in the medium as v = f λ. For electromagnetic waves such as radio, microwave, and optical waves, the phase velocity is determined by the medium's electromagnetic parameters of permittivity ε and permeability µ, which is then given as √εμ. When a wave interacts with a structure embedded in a host medium, both these temporal and spatial features play key roles in determining the scattering response of the structure. The recent development of a class of metamaterials in which the electric (ε) and magnetic (µ) properties can be tuned by design is providing a platform to engineer optical devices with unconventional properties.

Metamaterials and transformation optics play substantial roles in various branches of optical science and engineering by providing schemes to tailor electromagnetic fields into desired spatial patterns. We report a theoretical study showing that by designing and manipulating spatially inhomogeneous, nonuniform conductivity patterns across a flake of graphene, one can have this material as a one-atom-thick platform for infrared metamaterials and transformation optical devices. Varying the graphene chemical potential by using static electric field yields a way to tune the graphene conductivity in the terahertz and infrared frequencies. Such degree of freedom provides the prospect of having different \"patches\" with different conductivities on a single flake of graphene. Numerous photonic functions and metamaterial concepts can be expected to follow from such a platform.

Deflecting and changing the direction of propagation of electromagnetic waves are needed in multiple applications, such as in lens–antenna systems, point-to-point communications and radars. In this realm, metamaterials have been demonstrated to be great candidates for controlling wave propagation and wave–matter interactions by offering manipulation of their electromagnetic properties at will. They have been studied mainly in the frequency domain, but their temporal manipulation has become a topic of great interest during the past few years in the design of spatiotemporally modulated artificial media. In this work, we propose an idea for changing the direction of the energy propagation of electromagnetic waves by using time-dependent metamaterials, the permittivity of which is rapidly changed from isotropic to anisotropic values, an approach that we call temporal aiming. In so doing, here, we show how the direction of the Poynting vector becomes different from that of the wavenumber. Several scenarios are analytically and numerically evaluated, such as plane waves under oblique incidence and Gaussian beams, demonstrating how proper engineering of the isotropic—anisotropic temporal function of εr(t) can lead to a redirection of waves to different spatial locations in real time.Metamaterials: temporal beam steeringTheoretical analysis shows that beam-steering of electromagnetic waves can be accomplished by temporally changing the permittivity of metamaterials between isotropic to anisotropic values. The approach, called “temporal aiming”, has been formulated by Victor Pacheco-Peña from Newcastle University, UK and Nader Engheta from University of Pennsylvania in the US. In principle, it could open new opportunities for the flow of information around integrated photonic circuits, with flat metamaterial elements deflecting electromagnetic waves to specific targets or receivers on an optical chip as desired. Simulations performed with the software COMSOL with both plane, monochromatic waves and more complex Gaussian beams confirm the feasibility of the approach. It is proposed that the required temporal changes in the metamaterial’s relative permittivity could be achieved by the use of tunable metasurfaces or transmission lines with time-varying circuit elements.

In the search for improved computational capabilities, conventional microelectronic computers are facing various problems arising from the miniaturization and concentration of active electronics. Therefore, researchers have explored wave systems, such as photonic or quantum devices, for solving mathematical problems at higher speeds and larger capacities. However, previous devices have not fully exploited the linearity of the wave equation, which as we show here, allows for the simultaneous parallel solution of several independent mathematical problems within the same device. Here we demonstrate that a transmissive cavity filled with a judiciously tailored dielectric distribution and embedded in a multi-frequency feedback loop can calculate the solutions of a number of mathematical problems simultaneously. We design, build, and test a computing structure at microwave frequencies that solves two independent integral equations with any two arbitrary inputs and also provide numerical results for the calculation of the inverse of four 5 x 5 matrices. Optical analog computing has so far been mostly limited to solving a single instance of a mathematical problem at a time. Here, the authors show that the linearity of the wave equation allows to solve several problems simultaneously, and demonstrate it using an MW transmissive cavity.

Metastructures hold the potential to bring a new twist to the field of spatial-domain optical analog computing: migrating from free-space and bulky systems into conceptually wavelength-sized elements. We introduce a metamaterial platform capable of solving integral equations using monochromatic electromagnetic fields. For an arbitrary wave as the input function to an equation associated with a prescribed integral operator, the solution of such an equation is generated as a complex-valued output electromagnetic field. Our approach is experimentally demonstrated at microwave frequencies through solving a generic integral equation and using a set of waveguides as the input and output to the designed metastructures. By exploiting subwavelength-scale light-matter interactions in a metamaterial platform, our wave-based, material-based analog computer may provide a route to achieve chip-scale, fast, and integrable computing elements.

The process of diffusion is central to the ever increasing entropic state of the universe and is fundamental in many branches of science and engineering. Although non-reciprocal metamaterials are well developed for wave systems, the studies of diffusive metamaterials have been limited by their characteristic spatial inversion symmetry and time inversion antisymmetry. Here, we achieve large spatial asymmetric diffusion characteristics inside a metamaterial whose material parameters are space- and time-modulated. Inside such a spatiotemporal metamaterial, diffusion occurs as if the material had an intrinsic flow velocity, whose direction is dictated by the relative phase between the modulations of the conductivity and capacity. This creates dramatic out-of-equilibrium concentrations and depletions, which we demonstrate experimentally for the diffusion of electric charges in a one-dimensional electrical system composed of an array of space-time-modulated variable capacitors and switches. These results may offer exciting possibilities in various fields, including electronics, thermal management, chemical mixing, etc. Being able to manipulate the temporal evolution and spatial distribution of diffusive quantities would provide exciting possibilities for applications. Here, the authors show that one can achieve large spatial asymmetric diffusion characteristics inside a metamaterial whose material parameters are space- and time-modulated.

Materials with designed electromagnetic response have a wide range of exotic applications Since the beginning of metamaterial research, the electrodynamic properties of media with a refractive index near zero have attracted the interest of the scientific community because of the intriguing wave phenomena that they are expected to exhibit ( 1 – 3 ). As the refractive index approaches zero, the wavelength expands, and the spatial and temporal field variations effectively decouple ( 1 , 3 ). This gives access to a new regime of wave dynamics in which geometry-invariant wave phenomena can take place. For example, waves can tunnel through deformed waveguides ( 2 ), resonators can preserve their resonance frequency independently of the geometry of their external boundary ( 4 ), and light can be trapped in small three-dimensional (3D) regions, even if open to an unbounded environment ( 5 , 6 ). Recent experimental progress is also pushing forward the applied aspects of near-zero-index (NZI) media, leading to a generation of technologies with the potential to revolutionize different aspects of nanophotonics and other physical systems.

Optical materials with a dielectric constant near zero have the unique property that light advances with almost no phase advance. Although such materials have been made artificially in the microwave and far-infrared spectral range, bulk three-dimensional epsilon-near-zero (ENZ) engineered materials in the visible spectral range have been elusive. Here, we present an optical metamaterial composed of a carefully sculpted parallel array of subwavelength silver and silicon nitride nanolamellae that shows a vanishing effective permittivity, as demonstrated by interferometry. Good impedance matching and high optical transmission are demonstrated. The ENZ condition can be tuned over the entire visible spectral range by varying the geometry, and may enable novel micro/nanooptical components, for example, transmission enhancement, wavefront shaping, controlled spontaneous emission and superradiance. Silver and silicon nitride metamaterial structures with dielectric permittivities close to zero are demonstrated at visible wavelengths. In such materials, the optical phase advance during propagation can be very small.

Structured optical materials create new computing paradigms using photons, with transformative impact on various fields, including machine learning, computer vision, imaging, telecommunications, and sensing. This Perspective sheds light on the potential of free-space optical systems based on engineered surfaces for advancing optical computing. Manipulating light in unprecedented ways, emerging structured surfaces enable all-optical implementation of various mathematical functions and machine learning tasks. Diffractive networks, in particular, bring deep-learning principles into the design and operation of free-space optical systems to create new functionalities. Metasurfaces consisting of deeply subwavelength units are achieving exotic optical responses that provide independent control over different properties of light and can bring major advances in computational throughput and data-transfer bandwidth of free-space optical processors. Unlike integrated photonics-based optoelectronic systems that demand preprocessed inputs, free-space optical processors have direct access to all the optical degrees of freedom that carry information about an input scene/object without needing digital recovery or preprocessing of information. To realize the full potential of free-space optical computing architectures, diffractive surfaces and metasurfaces need to advance symbiotically and co-evolve in their designs, 3D fabrication/integration, cascadability, and computing accuracy to serve the needs of next-generation machine vision, computational imaging, mathematical computing, and telecommunication technologies. Optical computing via free-space-based structured optical materials allows to access optical information without the need for preprocessing or optoelectronic conversion. In this Perspective, the authors describe opportunities and challenges in their use for optical computing, information processing, computational imaging and sensing.