Roadmap for Optical Metasurfaces.

Metasurfaces have recently risen to prominence in optical research, providing unique functionalities that can be used for imaging, beam forming, holography, polarimetry, and many more, while keeping device dimensions small. Despite the fact that a vast range of basic metasurface designs has already been thoroughly studied in the literature, the number of metasurface-related papers is still growing at a rapid pace, as metasurface research is now spreading to adjacent fields, including computational imaging, augmented and virtual reality, automotive, display, biosensing, nonlinear, quantum and topological optics, optical computing, and more. At the same time, the ability of metasurfaces to perform optical functions in much more compact optical systems has triggered strong and constantly growing interest from various industries that greatly benefit from the availability of miniaturized, highly functional, and efficient optical components that can be integrated in optoelectronic systems at low cost. This creates a truly unique opportunity for the field of metasurfaces to make both a scientific and an industrial impact. The goal of this Roadmap is to mark this "golden age" of metasurface research and define future directions to encourage scientists and engineers to drive research and development in the field of metasurfaces toward both scientific excellence and broad industrial adoption.

Diffractive optical computing in free space.

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.

Feature issue introduction: temporal and spatiotemporal metamaterials.

Temporal modulation of material parameters provides a new degree of freedom for metamaterials, metasurfaces and wave-matter interactions as a whole. In time-varying media the electromagnetic energy may not be conserved, and the time reversal symmetry may be broken, which may lead to novel physical effects with potential applications. Currently, theoretical and experimental aspects of this field are rapidly advancing, expanding our understanding of wave propagation in such complex spatiotemporal platforms. This field promises novel possibilities and directions in research, innovation and exploration.

Effect of Epsilon-Near-Zero Modes on the Casimir Interaction between Ultrathin Films.

Vacuum fluctuation-induced interactions between macroscopic metallic objects result in an attractive force between them, a phenomenon known as the Casimir effect. This force is the result of both plasmonic and photonic modes. For very thin films, field penetration through the films will modify the allowed modes. Here, we theoretically investigate the Casimir interaction between ultrathin films from the perspective of force distribution over real frequencies for the first time. Pronounced repulsive contributions to the force are found due to the highly confined and nearly dispersion-free epsilon-near-zero (ENZ) modes that only exist in ultrathin films. These contributions persistently occur around the ENZ frequency of the film irrespective of the interfilm separation. We further associate the ENZ modes with a striking thickness dependence of a proposed figure of merit (FOM) for conductive thin films, suggesting that the motion of objects induced by Casimir interactions is boosted for deeply nanoscale sizes. Our results shed light on the correlation between special electromagnetic modes and the vacuum fluctuation-induced force as well as the resulting mechanical properties of ultrathin ENZ materials, which may create new opportunities for engineering the motion of ultrasmall objects in nanomechanical systems.

Open and Close-Packed, Shape-Engineered Polygonal Nanoparticle Metamolecules with Tailorable Fano Resonances.

A top-down lithographic patterning and deposition process is reported for producing nanoparticles (NPs) with well-defined sizes, shapes, and compositions that are often not accessible by wet-chemical synthetic methods. These NPs are ligated and harvested from the substrate surface to prepare colloidal NP dispersions. Using a template-assisted assembly technique, fabricated NPs are driven by capillary forces to assemble into size- and shape-engineered templates and organize into open or close-packed multi-NP structures or NP metamolecules. The sizes and shapes of the NPs and of the templates control the NP number, coordination, interparticle gap size, disorder, and location of defects such as voids in the NP metamolecules. The plasmonic resonances of polygonal-shaped Au NPs are exploited to correlate the structure and optical properties of assembled NP metamolecules. Comparing open and close-packed architectures highlights that introduction of a center NP to form close-packed assemblies supports collective interactions, altering magnetic optical modes and multipolar interactions in Fano resonances. Decreasing the distance between NPs strengthens the plasmonic coupling, and the structural symmetries of the NP metamolecules determine the orientation-dependent scattering response.

Four-dimensional optics using time-varying metamaterials.

Optical platforms using material parameters that change with time have diverse applications.

Solving integral equations in free space with inverse-designed ultrathin optical metagratings.

As standard microelectronic technology approaches fundamental limitations in speed and power consumption, novel computing strategies are strongly needed. Analogue optical computing enables the processing of large amounts of data at a negligible energy cost and high speeds. Based on these principles, ultrathin optical metasurfaces have been recently explored to process large images in real time, in particular for edge detection. By incorporating feedback, it has also recently been shown that metamaterials can be tailored to solve complex mathematical problems in the analogue domain, although these efforts have so far been limited to guided-wave systems and bulky set-ups. Here, we present an ultrathin Si metasurface-based platform for analogue computing that is able to solve Fredholm integral equations of the second kind using free-space visible radiation. A Si-based metagrating was inverse-designed to implement the scattering matrix synthesizing a prescribed kernel corresponding to the mathematical problem of interest. Next, a semitransparent mirror was incorporated into the sample to provide adequate feedback and thus perform the required Neumann series, solving the corresponding equation in the analogue domain at the speed of light. Visible wavelength operation enables a highly compact, ultrathin device that can be interrogated from free space, implying high processing speeds and the possibility of on-chip integration.

Mathematical operations and equation solving with reconfigurable metadevices.

Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical computations or computationally-intensive optimization. Their equation-solving capabilities are applied only to matrices with special spectral (eigenvalue) distribution. Here we report the theory and design of wave-based metastructures using tunable elements capable of solving integral/differential equations in a fully-reconfigurable fashion. We consider two architectures: the Miller architecture, which requires the singular-value decomposition, and an alternative intuitive direct-complex-matrix (DCM) architecture introduced here, which does not require a priori mathematical decomposition. As examples, we demonstrate, using system-level simulation tools, the solutions of integral and differential equations. We then expand the matrix inverting capabilities of both architectures toward evaluating the generalized Moore-Penrose matrix inversion. Therefore, we provide evidence that metadevices can implement generalized matrix inversions and act as the basis for the gradient descent method for solutions to a wide variety of problems. Finally, a general upper bound of the solution convergence time reveals the rich potential that such metadevices can offer for stationary iterative schemes.

Direct observation of ideal electromagnetic fluids.

Near-zero-index (NZI) media have been theoretically identified as media where electromagnetic radiations behave like ideal electromagnetic fluids. Within NZI media, the electromagnetic power flow obeys equations similar to those of motion for the velocity field in an ideal fluid, so that optical turbulence is intrinsically inhibited. Here, we experimentally observe the electromagnetic power flow distribution of such an ideal electromagnetic fluid propagating within a cutoff waveguide by a semi-analytical reconstruction technique. This technique provides direct proof of the inhibition of electromagnetic vorticity at the NZI frequency, even in the presence of complex obstacles and topological changes in the waveguide. Phase uniformity and spatially-static field distributions, essential characteristics of NZI materials, are also observed. Measurement of the same structure outside the NZI frequency range reveals existence of vortices in the power flow, as expected for conventional optical systems. Therefore, our results provide an important step forward in the development of ideal electromagnetic fluids, and introduce a tool to explore the subwavelength behavior of NZI media including fully vectorial and phase information.

Dispersion coding of ENZ media via multiple photonic dopants.

Epsilon-near-zero (ENZ) media are opening up exciting opportunities to observe exotic wave phenomena. In this work, we demonstrate that the ENZ medium comprising multiple dielectric photonic dopants would yield a comb-like dispersion of the effective permeability, with each magnetic resonance dominated by one specific dopant. Furthermore, at multiple frequencies of interest, the resonant supercouplings appearing or not can be controlled discretely via whether corresponding dopants are assigned or not. Importantly, the multiple dopants in the ENZ host at their magnetic resonances are demonstrated to be independent. Based on this platform, the concept of dispersion coding is proposed, where photonic dopants serve as "bits" to program the spectral response of the whole composite medium. As a proof of concept, a compact multi-doped ENZ cavity is fabricated and experimentally characterized, whose transmission spectrum is manifested as a multi-bit reconfigurable frequency comb. The dispersion coding is demonstrated to fuel a batch of innovative applications including dynamically tunable comb-like dispersion profiled filters, radio-frequency identification tags, etc.

Geometry-independent antenna based on Epsilon-near-zero medium.

It is well known that electromagnetic radiation from radiating elements (e.g., antennas, apertures, etc.) shows dependence on the element's geometry shape in terms of operating frequencies. This basic principle is ubiquitous in the design of radiators in multiple applications spanning from microwave, to optics and plasmonics. The emergence of epsilon-near-zero media exceptionally allows for an infinite wavelength of electromagnetic waves, manifesting exotic spatially-static wave dynamics which is not dependent on geometry. In this work, we analyze theoretically and verify experimentally such geometry-independent features for radiation, thus presenting a novel class of radiating resonators, i.e., antennas, with an operating frequency irrelevant to the geometry shape while only determined by the host material's dispersions. Despite being translated into different shapes and topologies, the designed epsilon-near-zero antenna resonates at a same frequency, while exhibiting very different far-field radiation patterns, with beams varying from wide to narrow, or even from single to multiple. Additionally, the photonic doping technique is employed to facilitate the high-efficiency radiation. The material-determined geometry-independent radiation may lead to numerous applications in flexible design and manufacturing for wireless communications, sensing, and wavefront engineering.

Momentum considerations inside near-zero index materials.

Near-zero index (NZI) materials, i.e., materials having a phase refractive index close to zero, are known to enhance or inhibit light-matter interactions. Most theoretical derivations of fundamental radiative processes rely on energetic considerations and detailed balance equations, but not on momentum considerations. Because momentum exchange should also be incorporated into theoretical models, we investigate momentum inside the three categories of NZI materials, i.e., inside epsilon-and-mu-near-zero (EMNZ), epsilon-near-zero (ENZ) and mu-near-zero (MNZ) materials. In the context of Abraham-Minkowski debate in dispersive materials, we show that Minkowski-canonical momentum of light is zero inside all categories of NZI materials while Abraham-kinetic momentum of light is zero in ENZ and MNZ materials but nonzero inside EMNZ materials. We theoretically demonstrate that momentum recoil, transfer momentum from the field to the atom and Doppler shift are inhibited in NZI materials. Fundamental radiative processes inhibition is also explained due to those momentum considerations inside three-dimensional NZI materials. Absence of diffraction pattern in slits experiments is seen as a consequence of zero Minkowski momentum. Lastly, consequence on Heisenberg inequality, microscopy applications and on the canonical momentum as generator of translations are discussed. Those findings are appealing for a better understanding of fundamental light-matter interactions at the nanoscale as well as for lasing applications.

Tunable radiation enhancement and suppression using a pair of photonically doped epsilon-near-zero (ENZ) slabs.

Manipulation of the radiation efficiency and pattern of quantum emitters by engineering the electromagnetic properties of the surrounding medium is crucial for designing various light sources. Here, we theoretically demonstrate the possibility of designing a compact and tunable resonator using a pair of photonically doped epsilon-near-zero (ENZ) slabs that are separated by a deeply subwavelength air gap. Such resonators are shown to be capable of switching between completely transparent and opaque states, for a TM-polarized normally incident plane wave, by slightly changing the permittivity of the dielectric dopants. We exploit this behavior for tunable radiation enhancement and suppression for a quantum emitter placed inside the air gap.

A single inverse-designed photonic structure that performs parallel computing.

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.

Near-zero-index media as electromagnetic ideal fluids.

Near-zero-index (NZI) supercoupling, the transmission of electromagnetic waves inside a waveguide irrespective of its shape, is a counterintuitive wave effect that finds applications in optical interconnects and engineering light-matter interactions. However, there is a limited knowledge on the local properties of the electromagnetic power flow associated with supercoupling phenomena. Here, we theoretically demonstrate that the power flow in two-dimensional (2D) NZI media is fully analogous to that of an ideal fluid. This result opens an interesting connection between NZI electrodynamics and fluid dynamics. This connection is used to explain the robustness of supercoupling against any geometrical deformation, to enable the analysis of the electromagnetic power flow around complex geometries, and to examine the power flow when the medium is doped with dielectric particles. Finally, electromagnetic ideal fluids where the turbulence is intrinsically inhibited might offer interesting technological possibilities, e.g., in the design of optical forces and for optical systems operating under extreme mechanical conditions.

Soft surfaces and enhanced nonlinearity enabled via epsilon-near-zero media doped with zero-area perfect electric conductor inclusions.

Introducing a dielectric inclusion inside an epsilon-near-zero (ENZ) host has been shown to dramatically affect the effective permeability of the host for a TM-polarized incident wave, a concept coined as photonic doping [Science355, 1058 (2017)SCIEAS0036-807510.1126/science.aal2672]. Here, we theoretically study the prospect of doping the ENZ host with infinitesimally thin perfect electric conductor (PEC) inclusions, which we call "zero-area" PEC dopants. First, we theoretically demonstrate that zero-area PEC dopants enable the design of soft surfaces with an arbitrary cross-sectional geometry. Second, we illustrate the possibility of engineering the PEC dopants with the goal of transforming the electric field distribution inside the ENZ while maintaining a spatially invariant magnetic field. We exploit this property to enhance the effective nonlinearity of the ENZ host.

Temporal aiming.

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.

Achieving asymmetry and trapping in diffusion with spatiotemporal metamaterials.

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.

Non-Hermitian doping of epsilon-near-zero media.

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.