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.

All electromagnetic scattering bodies are matrix-valued oscillators.

Scattering theory is the basis of all linear optical and photonic devices, whose spectral response underpins wide-ranging applications from sensing to energy conversion. Unlike the Shannon theory for communication channels, or the Fano theory for electric circuits, understanding the limits of spectral wave scattering remains a notoriously challenging open problem. We introduce a mathematical scattering representation that inherently embeds fundamental principles of causality and passivity into its elemental degrees of freedom. We use this representation to reveal strong constraints in the mathematical structure of scattered fields, and to develop a general theory of the maximum radiative heat transfer in the near field, resolving a long-standing open question. Our approach can be seamlessly applied to high-interest applications across nanophotonics, and appears extensible to general classical and quantum scattering theory.

Probing the Limits to Near-Field Heat Transfer Enhancements in Phonon-Polaritonic Materials.

Near-field radiative heat transfer (NFRHT) arises between objects separated by nanoscale gaps and leads to dramatic enhancements in heat transfer rates compared to the far-field. Recent experiments have provided first insights into these enhancements, especially using silicon dioxide (SiO2) surfaces, which support surface phonon polaritons (SPhP). Yet, theoretical analysis suggests that SPhPs in SiO2 occur at frequencies far higher than optimal. Here, we first show theoretically that SPhP-mediated NFRHT, at room temperature, can be 5-fold larger than that of SiO2, for materials that support SPhPs closer to an optimal frequency of 67 meV. Next, we experimentally demonstrate that MgF2 and Al2O3 closely approach this limit. Specifically, we demonstrate that near-field thermal conductance between MgF2 plates separated by 50 nm approaches within nearly 50% of the global SPhP bound. These findings lay the foundation for exploring the limits to radiative heat transfer rates at the nanoscale.

Conservation-Law-Based Global Bounds to Quantum Optimal Control.

Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related inequalities, but such bounds utilize only coarse system information and loosen significantly in the presence of constraints and complex interaction dynamics. We show that an integral-equation-based formulation of conservation laws in quantum dynamics leads to a systematic framework for identifying fundamental limits to any quantum control scenario. We demonstrate the utility of our bounds in three scenarios-three-level driving, decoherence suppression, and maximum-fidelity gate implementations-and show that in each case our bounds are tight or nearly so. Global bounds complement local-optimization-based designs, illuminating performance levels that may be possible, as well as those that cannot be surpassed.

Fundamental Limits to the Refractive Index of Transparent Optical Materials.

Increasing the refractive index available for optical and nanophotonic systems opens new vistas for design, for applications ranging from broadband metalenses to ultrathin photovoltaics to high-quality-factor resonators. In this work, fundamental limits to the refractive index of any material are derived, given only the underlying electron density and either the maximum allowable dispersion or the minimum bandwidth of interest. In the realm of small to modest dispersion, the bounds are closely approached and not surpassed by a wide range of natural materials, showing that nature has already nearly reached a Pareto frontier for refractive index and dispersion. Conversely, for narrow-bandwidth applications, nature does not provide the highly dispersive, high-index materials that the bounds suggest should be possible. The theory of composites to identify metal-based metamaterials that can exhibit small losses and sizeable increases in refractive index over the current best materials is used. Moreover, if the "elusive lossless metal" can be synthesized, it is shown that it would enable arbitrarily high refractive index in the high-dispersion regime, nearly achieving the bounds even at refractive indices of 100 and beyond at optical frequencies.

Approaching the upper limits of the local density of states via optimized metallic cavities.

By computational optimization of air-void cavities in metallic substrates, we show that the local density of states (LDOS) can reach within a factor of ≈10 of recent theoretical upper limits and within a factor ≈4 for the single-polarization LDOS, demonstrating that the theoretical limits are nearly attainable. Optimizing the total LDOS results in a spontaneous symmetry breaking where it is preferable to couple to a specific polarization. Moreover, simple shapes such as optimized cylinders attain nearly the performance of complicated many-parameter optima, suggesting that only one or two key parameters matter in order to approach the theoretical LDOS bounds for metallic resonators.

Limits to surface-enhanced Raman scattering near arbitrary-shape scatterers: erratum.

In this erratum, we correct two minor algebraic errors from our previous published manuscript [Opt. Express 27, 35189 (2019)], which do not affect the main results or conclusions, and make a corresponding small change to one figure.

High-NA achromatic metalenses by inverse design.

We use inverse design to discover metalens structures that exhibit broadband, achromatic focusing across low, moderate, and high numerical apertures. We show that standard unit-cell approaches cannot achieve high-efficiency high-NA focusing, even at a single frequency, due to the incompleteness of the unit-cell basis, and we provide computational upper bounds on their maximum efficiencies. At low NA, our devices exhibit the highest theoretical efficiencies to date. At high NA-of 0.9 with translation-invariant films and of 0.99 with "freeform" structures-our designs are the first to exhibit achromatic high-NA focusing.

Computational Bounds to Light-Matter Interactions via Local Conservation Laws.

We develop a computational framework for identifying bounds to light-matter interactions, originating from polarization-current-based formulations of local conservation laws embedded in Maxwell's equations. We propose an iterative method for imposing only the maximally violated constraints, enabling rapid convergence to global bounds. Our framework can identify bounds to the minimum size of any scatterer that encodes a specific linear operator, given only its material properties, as we demonstrate for the optical computation of a discrete Fourier transform. It further resolves bounds on far-field scattering properties over any arbitrary bandwidth, where previous bounds diverge.

Limits to surface-enhanced Raman scattering near arbitrary-shape scatterers.

The low efficiency of Raman spectroscopy can be overcome by placing the active molecules in the vicinity of scatterers, typically rough surfaces or nanostructures with various shapes. This surface-enhanced Raman scattering (SERS) leads to substantial enhancement that depends on the scatterer that is used. In this work, we find fundamental upper bounds on the Raman enhancement for arbitrary-shaped scatterers, depending only on its material constants and the separation distance from the molecule. According to our metric, silver is optimal in visible wavelengths while aluminum is better in the near-UV region. Our general analytical bound scales as the volume of the scatterer and the inverse sixth power of the distance to the active molecule. Numerical computations show that simple geometries fall short of the bounds, suggesting further design opportunities for future improvement. For periodic scatterers, we use two formulations to discover different bounds, and the tighter of the two always must apply. Comparing these bounds suggests an optimal period depending on the volume of the scatterer.

Active Radiative Thermal Switching with Graphene Plasmon Resonators.

We theoretically demonstrate a near-field radiative thermal switch based on thermally excited surface plasmons in graphene resonators. The high tunability of graphene enables substantial modulation of near-field radiative heat transfer, which, when combined with the use of resonant structures, overcomes the intrinsically broadband nature of thermal radiation. In canonical geometries, we use nonlinear optimization to show that stacked graphene sheets offer improved heat conductance contrast between "ON" and "OFF" switching states and that a >10× higher modulation is achieved between isolated graphene resonators than for parallel graphene sheets. In all cases, we find that carrier mobility is a crucial parameter for the performance of a radiative thermal switch. Furthermore, we derive shape-agnostic analytical approximations for the resonant heat transfer that provide general scaling laws and allow for direct comparison between different resonator geometries dominated by a single mode. The presented scheme is relevant for active thermal management and energy harvesting as well as probing excited-state dynamics at the nanoscale.

Limits to the Optical Response of Graphene and Two-Dimensional Materials.

Two-dimensional (2D) materials provide a platform for strong light-matter interactions, creating wide-ranging design opportunities via new-material discoveries and new methods for geometrical structuring. We derive general upper bounds to the strength of such light-matter interactions, given only the optical conductivity of the material, including spatial nonlocality, and otherwise independent of shape and configuration. Our material figure-of-merit shows that highly doped graphene is an optimal material at infrared frequencies, whereas single-atomic-layer silver is optimal in the visible. For quantities ranging from absorption and scattering to near-field spontaneous-emission enhancements and radiative heat transfer, we consider canonical geometrical structures and show that in certain cases the bounds can be approached, while in others there may be significant opportunity for design improvement. The bounds can encourage systematic improvements in the design of ultrathin broadband absorbers, 2D antennas, and near-field energy harvesters.

General theory of spontaneous emission near exceptional points.

We present a general theory of spontaneous emission at exceptional points (EPs)-exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light-matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding 400×) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, which are typically associated with Lorentzian emission curves in systems with low losses, EPs are associated with non-Lorentzian lineshapes, leading to enhancements that scale nonlinearly with the resonance quality factor. Our theory can be applied to dispersive media, with proper normalization of the resonant modes.

Topologically enabled optical nanomotors.

Shaping the topology of light, by way of spin or orbital angular momentum engineering, is a powerful tool to manipulate matter on the nanoscale. Conventionally, such methods focus on shaping the incident beam of light and not the full interaction between the light and the object to be manipulated. We theoretically show that tailoring the topology of the phase space of the light particle interaction is a fundamentally more versatile approach, enabling dynamics that may not be achievable by shaping of the light alone. In this manner, we find that optically asymmetric (Janus) particles can become stable nanoscale motors even in a light field with zero angular momentum. These precessing steady states arise from topologically protected anticrossing behavior of the vortices of the optical torque vector field. Furthermore, by varying the wavelength of the incident light, we can control the number, orientations, and the stability of the spinning states. These results show that the combination of phase-space topology and particle asymmetry can provide a powerful degree of freedom in designing nanoparticles for optimal external manipulation in a range of nano-optomechanical applications.

Low-Loss Plasmonic Dielectric Nanoresonators.

Material losses in metals are a central bottleneck in plasmonics for many applications. Here we propose and theoretically demonstrate that metal losses can be successfully mitigated with dielectric particles on metallic films, giving rise to hybrid dielectric-metal resonances. In the far field, they yield strong and efficient scattering, beyond even the theoretical limits of all-metal and all-dielectric structures. In the near field, they offer high Purcell factor (>5000), high quantum efficiency (>90%), and highly directional emission at visible and infrared wavelengths. Their quality factors can be readily tailored from plasmonic-like (∼10) to dielectric-like (∼103), with wide control over the individual resonant coupling to photon, plasmon, and dissipative channels. Compared with conventional plasmonic nanostructures, such resonances show robustness against detrimental nonlocal effects and provide higher field enhancement at extreme nanoscopic sizes and spacings. These hybrid resonances equip plasmonics with high efficiency, which has been the predominant goal since the field's inception.

Computational inverse design of non-intuitive illumination patterns to maximize optical force or torque.

This paper aims to maximize optical force or torque on arbitrary micro- and nanoscale objects using numerically optimized structured illumination. By developing a numerical framework for computer-automated design of 3d vector-field illumination, we demonstrate a 20-fold enhancement in optical torque per intensity over circularly polarized plane wave on a model plasmonic particle. The nonconvex optimization is efficiently performed by combining a compact cylindrical Bessel basis representation with a fast boundary element method and a standard derivative-free, local optimization algorithm. We analyze the optimization results for 2000 random initial configurations, discuss the tradeoff between robustness and enhancement, and compare the different effects of multipolar plasmon resonances on enhancing force or torque. All results are obtained using open-source computational software available online.

Optically Thin Metallic Films for High-Radiative-Efficiency Plasmonics.

Plasmonics enables deep-subwavelength concentration of light and has become important for fundamental studies as well as real-life applications. Two major existing platforms of plasmonics are metallic nanoparticles and metallic films. Metallic nanoparticles allow efficient coupling to far field radiation, yet their synthesis typically leads to poor material quality. Metallic films offer substantially higher quality materials, but their coupling to radiation is typically jeopardized due to the large momentum mismatch with free space. Here, we propose and theoretically investigate optically thin metallic films as an ideal platform for high-radiative-efficiency plasmonics. For far-field scattering, adding a thin high-quality metallic substrate enables a higher quality factor while maintaining the localization and tunability that the nanoparticle provides. For near-field spontaneous emission, a thin metallic substrate, of high quality or not, greatly improves the field overlap between the emitter environment and propagating surface plasmons, enabling high-Purcell (total enhancement >10(4)), high-quantum-yield (>50%) spontaneous emission, even as the gap size vanishes (3-5 nm). The enhancement has almost spatially independent efficiency and does not suffer from quenching effects that commonly exist in previous structures.

Fundamental limits to optical response in absorptive systems.

At visible and infrared frequencies, metals show tantalizing promise for strong subwavelength resonances, but material loss typically dampens the response. We derive fundamental limits to the optical response of absorptive systems, bounding the largest enhancements possible given intrinsic material losses. Through basic conservation-of-energy principles, we derive geometry-independent limits to per-volume absorption and scattering rates, and to local-density-of-states enhancements that represent the power radiated or expended by a dipole near a material body. We provide examples of structures that approach our absorption and scattering limits at any frequency; by contrast, we find that common "antenna" structures fall far short of our radiative LDOS bounds, suggesting the possibility for significant further improvement. Underlying the limits is a simple metric, |χ|2/Im χ for a material with susceptibility χ, that enables broad technological evaluation of lossy materials across optical frequencies.

Shape-Independent Limits to Near-Field Radiative Heat Transfer.

We derive shape-independent limits to the spectral radiative heat transfer rate between two closely spaced bodies, generalizing the concept of a blackbody to the case of near-field energy transfer. Through conservation of energy and reciprocity, we show that each body of susceptibility χ can emit and absorb radiation at enhanced rates bounded by |χ|(2)/Im χ, optimally mediated by near-field photon transfer proportional to 1/d(2) across a separation distance d. Dipole-dipole and dipole-plate structures approach restricted versions of the limit, but common large-area structures do not exhibit the material enhancement factor and thus fall short of the general limit. By contrast, we find that particle arrays interacting in an idealized Born approximation (i.e., neglecting multiple scattering) exhibit both enhancement factors, suggesting the possibility of orders-of-magnitude improvement beyond previous designs and the potential for radiative heat transfer to be comparable to conductive heat transfer through air at room temperature, and significantly greater at higher temperatures.

Optimization of sharp and viewing-angle-independent structural color.

Structural coloration produces some of the most brilliant colors in nature and has many applications. Motivated by the recently proposed transparent displays that are based on wavelength-selective scattering, here we consider the new problem of transparent structural color, where objects are transparent under omnidirectional broad-band illumination but scatter strongly with a directional narrow-band light source. Transparent structural color requires two competing properties, narrow bandwidth and broad viewing angle, that have not been demonstrated simultaneously previously. Here, we use numerical optimization to discover geometries where a sharp 7% bandwidth in scattering is achieved, yet the peak wavelength varies less than 1%, and the peak height and peak width vary less than 6% over broad viewing angles (0-90°) under a directional illumination. Our model system consists of dipole scatterers arranged into several rings; interference among the scattered waves is optimized to yield the wavelength-selective and angle-insensitive response.