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.

Metasurface Light-Emitting Diodes with Directional and Focused Emission.

Phased-array metasurfaces enable the imprinting of complex beam structures onto coherent incident light. Recent demonstrations of photoluminescent phased-array metasurfaces highlight possibilities for achieving similar control in electroluminescent light-emitting diodes (LEDs). However, phased-array metasurface LEDs have not yet been demonstrated owing to the complexities of integrating device stacks and electrodes within nanopatterned metasurfaces. Here, we demonstrate metasurface LEDs that emit directional or focused light. We first design nanoribbon elements that achieve the requisite phase control within typical LED device constraints. Subsequently, we demonstrate unidirectional emission that can be engineered at will via phased-array concepts. This control is further exhibited in metasurface LEDs that directly emit focused beams. Finally, we show that these metasurface LEDs exhibit external quantum efficiencies (EQEs) superior to those of unpatterned LEDs. These results demonstrate metasurface designs that are compatible with high-EQE metal-free LED devices and portend opportunities for new classes of metasurface LEDs that directly produce complex beam structures.

Designing Highly Directional Luminescent Phased-Array Metasurfaces with Reciprocity-Based Simulations.

Phased-array metasurfaces grant the ability to arbitrarily shape the wavefront of light. As such, they have been used as various optical elements including waveplates, lenses, and beam deflectors. Luminescent metasurfaces, on the other hand, have largely comprised uniform arrays and are therefore unable to provide the same control over the wavefront of emitted light. Recently, phased-array control of the wavefront of spontaneous emission has been experimentally demonstrated in luminescent phased-array metalenses and beam deflectors. However, current luminescent metasurface beam deflectors exhibit unidirectional emission for only p-polarized light. In this paper, we use a reciprocal simulation strategy to explain the polarization disparity and improve the directionality of incoherent emission from current quantum-well emitting phased-array metasurfaces. We also design complementary metasurfaces to direct emission from systems where emission originates from alternate quantum mechanical processes.

Optical-Frequency Magnetic Polarizability in a Layered Semiconductor.

The optical response of crystals is most commonly attributed to electric dipole interactions between light and matter. Although metamaterials support "artificial" magnetic resonances supported by mesoscale structuring, there are no naturally occurring materials known to exhibit a nonzero optical-frequency magnetic polarizability. Here, we experimentally demonstrate and quantify a naturally occurring nonzero magnetic polarizability in a layered semiconductor system: two-dimensional (Ruddlesden-Popper phase) hybrid organic-inorganic perovskites. These results demonstrate the only known material with an optical-frequency permeability that differs appreciably from vacuum, informing future efforts to find, synthesize, or exploit atomic-scale optical magnetism for novel optical phenomena such as negative index of refraction and electromagnetic cloaking.

Light-emitting metalenses and meta-axicons for focusing and beaming of spontaneous emission.

Phased-array metasurfaces have been extensively used for wavefront shaping of coherent incident light. Due to the incoherent nature of spontaneous emission, the ability to similarly tailor photoluminescence remains largely unexplored. Recently, unidirectional photoluminescence from InGaN/GaN quantum-well metasurfaces incorporating one-dimensional phase profiles has been shown. However, the possibility of generating arbitrary two-dimensional waveforms-such as focused beams-is not yet realized. Here, we demonstrate two-dimensional metasurface axicons and lenses that emit collimated and focused beams, respectively. First, we develop off-axis meta-axicon/metalens equations designed to redirect surface-guided waves that dominate the natural emission pattern of quantum wells. Next, we show that photoluminescence properties are well predicted by passive transmission results using suitably engineered incident light sources. Finally, we compare collimating and focusing performances across a variety of different light-emitting metasurface axicons and lenses. These generated two-dimensional phased-array photoluminescence waveforms facilitate future development of light sources with arbitrary functionalities.

Even-Parity Self-Trapped Excitons Lead to Magnetic Dipole Radiation in Two-Dimensional Lead Halide Perovskites.

Recently, unconventional bright magnetic dipole (MD) radiation was observed from two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs). According to commonly accepted HOIP band structure calculations, such MD light emission from the ground-state exciton should be strictly symmetry forbidden. These results suggest that MD emission arises in conjunction with an as-yet unidentified symmetry-breaking mechanism. In this paper, we show that MD light emission originates from a self-trapped p-like exciton stabilized at energies below the primary electric dipole (ED)-emitting 1s exciton. Using suitable combinations of sample and collection geometries, we isolate the distinct temperature-dependent properties of the ED and MD photoluminescence (PL). We show that the ED emission wavelength is nearly constant with temperature, whereas the MD emission wavelength exhibits substantial red shifts with heating. To explain these results, we derive a microscopic model comprising two distinct parity exciton states coupled to lattice distortions. The model explains many experimental observations, including the thermal red shift, the difference in emission wavelengths, and the relative intensities of the ED and MD emission. Thermodynamic analysis of temperature-dependent PL reveals that the MD emission originates from a locally distorted structure. Finally, we demonstrate unusual hysteresis effects of the MD-emitting state near structural phase transitions. We hypothesize that this is another manifestation of the local distortions, indicating that they are insensitive to phase changes in the equilibrium lattice structure.

Bright magnetic dipole radiation from two-dimensional lead-halide perovskites.

Light-matter interactions in semiconductors are uniformly treated within the electric dipole approximation; multipolar interactions are considered "forbidden." We experimentally demonstrate that this approximation inadequately describes light emission in two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs), solution processable semiconductors with promising optoelectronic properties. By exploiting the highly oriented crystal structure, we use energy-momentum spectroscopies to demonstrate that an exciton-like sideband in 2D HOIPs exhibits a multipolar radiation pattern with highly directed emission. Electromagnetic and quantum-mechanical analyses indicate that this emission originates from an out-of-plane magnetic dipole transition arising from the 2D character of electronic states. Symmetry arguments and temperature-dependent measurements suggest a dynamic symmetry-breaking mechanism that is active over a broad temperature range. These results challenge the paradigm of electric dipole-dominated light-matter interactions in optoelectronic materials, provide new perspectives on the origins of unexpected sideband emission in HOIPs, and tease the possibility of metamaterial-like scattering phenomena at the quantum-mechanical level.

Chemical and Structural Diversity of Hybrid Layered Double Perovskite Halides.

Hybrid halide double perovskites are a class of compounds attracting growing interest because of their richness of structure and property. Two-dimensional (2D) derivatives of hybrid double perovskites are formed by the incorporation of organic spacer cations into three-dimensional (3D) double perovskites. Here, we report a series of seven new layered double perovskite halides with propylammonium (PA), octylammonium (OCA), and 1,4-butyldiammonium (BDA) cations. The general formulas of the compounds are AmMIMIIIX8 (single-layered Ruddlesden-Popper type with m = 4 and A = PA or OCA, and single-layered Dion-Jacobson type with m = 2 and A = BDA, MI = Ag, MIII= In or Bi, X = Cl or Br) and PA2CsMIMIIIBr7 (bilayered, with MI = Ag, MIII = In or Bi). These families of compounds demonstrate great versatility, with tunable layer thickness, the ability to vary the interlayer spacing, and the ability to selectively tune the band gap by varying the MI and MIII cations along with the halide anions. The band gap of the single-layered materials varies from 2.41 eV for PA4AgBiBr8 to 3.96 eV for PA4AgInCl8. Photoluminescent emission spectra of the layered double perovskites at low-temperature (100 K) are reported, and density functional theory electronic structure calculations are presented to understand the nature of the band gap evolution. The development of new structural and compositions in layered double perovskite halides enhances the understanding of structure-property relations in this important family.

Optical Constants and Effective-Medium Origins of Large Optical Anisotropies in Layered Hybrid Organic/Inorganic Perovskites.

Hybrid organic/inorganic perovskites (HOIPs) are of great interest for optoelectronic applications due to their quality electronic and optical properties and the exceptional ease of room-temperature synthesis. Layered HOIP structures, e.g., Ruddlesden-Popper phases, offer additional synthetic means to define self-assembling multiple quantum well structures. Measurements of Ruddlesden-Popper HOIP optical constants are currently lacking, but are critical for both a fundamental understanding as well as optoelectronic device design. Here, we use momentum-resolved optical techniques to measure error-constrained complex uniaxial optical constants of layered lead-iodide perovskites incorporating a variety of organic spacer molecules. We demonstrate how large optical anisotropies measured in these materials arise primarily from classical dielectric inhomogeneities rather than the two-dimensional nature of the electronic states. We subsequently show how variations among these materials can be understood within a classical effective-medium model that accounts for dielectric inhomogeneity. We find agreement between experimentally inferred dielectric properties and quantum-mechanical calculations only after accounting for these purely classical effects. This work provides a library of optical constants for this class of materials and clarifies the origins of large absorption and photoluminescence anisotropies witnessed in these and other layered nanomaterials.

Phase Stability and Diffusion in Lateral Heterostructures of Methyl Ammonium Lead Halide Perovskites.

Mixed halide hybrid organic-inorganic perovskites have band gaps that span the visible spectrum making them candidates for optoelectronic devices. Transport of the halide atoms in methyl ammonium lead iodide (MAPbI3) and its alloys with bromine has been observed in both dark and under illumination. While halide transport upon application of electric fields has received much attention, less is known regarding bromide and iodide interdiffusion down concentration gradients. This work provides an upper bound on the bromide-iodide interdiffusion coefficient Di in thin films of MAPb(BrxI1-x)3 using a diffusion couples of lateral heterostructures. The upper bound of Di was extracted from changes in the interface profiles of the heterostructures upon exposure to heat. The stability of thoroughly heated interfacial profiles suggests that the miscibility gap extends to higher temperatures and to a higher fractional composition of bromine than predicted by theory. The results of this work provide guidance for compositions of thermally stable heterostructures of hybrid halide perovskites.

Ultrawide thermal free-carrier tuning of dielectric antennas coupled to epsilon-near-zero substrates.

The principal challenge for achieving reconfigurable optical antennas and metasurfaces is the need to generate continuous and large tunability of subwavelength, low-Q resonators. We demonstrate continuous and steady-state refractive index tuning at mid-infrared wavelengths using temperature-dependent control over the low-loss plasma frequency in III-V semiconductors. In doped InSb we demonstrate nearly two-fold increase in the electron effective mass leading to a positive refractive index shift (Δn > 1.5) that is an order of magnitude greater than conventional thermo-optic effects. In undoped films we demonstrate more than 10-fold change in the thermal free-carrier concentration producing a near-unity negative refractive index shift. Exploiting both effects within a single resonator system-intrinsic InSb wires on a heavily doped (epsilon-near-zero) InSb substrate-we demonstrate dynamically steady-state tunable Mie resonances. The observed line-width resonance shifts (Δλ > 1.7 µm) suggest new avenues for highly tunable and steady-state mid-infrared semiconductor antennas.Achieving large tunability of subwavelength resonators is a central challenge in nanophotonics. Here the authors demonstrate refractive index tuning at mid-infrared wavelengths using temperature-dependent control over the low loss plasma frequency in III-V semiconductors.

Enhancing Organic Semiconductor-Surface Plasmon Polariton Coupling with Molecular Orientation.

Due to strong electric field enhancements, surface plasmon polaritons (SPPs) are capable of drastically increasing light-molecule coupling in organic optoelectronic devices. The electric field enhancement, however, is anisotropic, offering maximal functional benefits if molecules are oriented perpendicular to the interface. To provide a clear demonstration of this orientation dependence, we study SPP dispersion and SPP-mediated photoluminescence at a model Au/small-molecule interface where identical molecules can be deposited with two very different molecular backbone orientations depending on processing conditions. First, we demonstrate that thin films of p-SIDT(FBTTh2)2 can be deposited with either all "in-plane" (parallel to substrate) or a 50/50 mix of in-plane/"out-of-plane" (perpendicular to substrate) optical transition dipoles by the absence or presence, respectively, of diiodooctane during spin-coating. In contrast to typical orientation control observed in organic thin films, for this particular molecule, this corresponds to films with conjugated backbones purely in-plane, or with a 50/50 mix of in-plane/out-of-plane backbones. Then, using momentum-resolved reflectometry and momentum-resolved photoluminescence, we study and quantify changes in SPP dispersion and photoluminescence intensity arising solely from changes in molecular orientation. We demonstrate increased SPP momentum and a 2-fold enhancement in photoluminescence for systems with out-of-plane oriented transition dipoles. These results agree well with theory and have direct implications for the design and analysis of organic optoelectronic devices.

Ultrawide Thermo-optic Tuning of PbTe Meta-Atoms.

Subwavelength Mie resonators have enabled new classes of optical antenna and nanophotonic devices and can act as the basic meta-atom constituents of low-loss dielectric metasurfaces. In any application, tunable Mie resonances are key to achieving a dynamic and reconfigurable operation. However, the active tuning of these nanoantennas is still limited and usually results in sub-linewidth resonance tuning. Here, we demonstrate the ultrawide dynamic tuning of PbTe Mie resonators fabricated via both laser ablation and a novel solution-processing approach. Taking advantage of the extremely large thermo-optic (TO) coefficient and a high refractive index of PbTe, we demonstrate high-quality factor Mie resonances that are tuned by several linewidths with temperature modulations as small as ΔT ∼ 10 K. We reveal that the origin for this exceptional tunability is due to an increased TO coefficient of PbTe at low temperatures. When combined into metasurface arrays, these effects can be exploited in ultranarrow active notch filers and metasurface phase shifters that require only a few kelvin modulation. These findings demonstrate the enabling potential of PbTe as a versatile, solution-processable, and highly tunable nanophotonic material that suggests new possibilities for meta-atom paints, coatings, and 3D metamaterials fabrication.

Model-blind characterization of thin-film optical constants with momentum-resolved reflectometry.

Determining optical constants of thin material films is important for characterizing their electronic excitations and for the design of optoelectronic devices. Spectroscopic ellipsometry techniques have emerged as the predominant approach for measuring thin-film optical constants. However, ellipsometry methods suffer from complications associated with highly model-dependent, multi-parameter spectral fitting procedures. Here, we present a model-blind, momentum-resolved reflectometry technique that yields accurate and precise optical constants, with quantifiable error estimates, even for film thicknesses less than 50 nm. These capabilities are demonstrated by interrogating an optical absorption resonance in films of the polymer P(NDI2OD-T2). We show that this approach produces exceptional agreement with UV-Vis-NIR absorption measurements, while simultaneously avoiding the need to construct complicated multi-oscillator spectral models. Finally, we use this procedure to resolve subtle differences in the out-of-plane optical properties of different film morphologies that were previously obscured in ellipsometry measurements.

Designing Multipolar Resonances in Dielectric Metamaterials.

Dielectric resonators form the building blocks of nano-scale optical antennas and metamaterials. Due to their multipolar resonant response and low intrinsic losses they offer design flexibility and high-efficiency performance. These resonators are typically described in terms of a spherical harmonic decomposition with Mie theory. In experimental realizations however, a departure from spherical symmetry and the use of high-index substrates leads to new features appearing in the multipolar response. To clarify this behavior, we present a systematic experimental and numerical characterization of Silicon disk resonators. We demonstrate that for disk resonators on low-index quartz substrates, the electric and magnetic dipole modes are easily identifiable across a wide range of aspect-ratios, but that higher order peaks cannot be unambiguously associated with any specific multipolar mode. On high-index Silicon substrates, even the fundamental dipole modes do not have a clear association. When arranged into arrays, resonances are shifted and pronounced preferential forward and backward scattering conditions appear, which are not as apparent in individual resonators and may be associated with interference between multipolar modes. These findings present new opportunities for engineering the multipolar scattering response of dielectric optical antennas and metamaterials, and provide a strategy for designing nano-optical components with unique functionalities.

Recent Advances in Two-Dimensional Materials beyond Graphene.

The isolation of graphene in 2004 from graphite was a defining moment for the "birth" of a field: two-dimensional (2D) materials. In recent years, there has been a rapidly increasing number of papers focusing on non-graphene layered materials, including transition-metal dichalcogenides (TMDs), because of the new properties and applications that emerge upon 2D confinement. Here, we review significant recent advances and important new developments in 2D materials "beyond graphene". We provide insight into the theoretical modeling and understanding of the van der Waals (vdW) forces that hold together the 2D layers in bulk solids, as well as their excitonic properties and growth morphologies. Additionally, we highlight recent breakthroughs in TMD synthesis and characterization and discuss the newest families of 2D materials, including monoelement 2D materials (i.e., silicene, phosphorene, etc.) and transition metal carbide- and carbon nitride-based MXenes. We then discuss the doping and functionalization of 2D materials beyond graphene that enable device applications, followed by advances in electronic, optoelectronic, and magnetic devices and theory. Finally, we provide perspectives on the future of 2D materials beyond graphene.

Widely Tunable Infrared Antennas Using Free Carrier Refraction.

We demonstrate tuning of infrared Mie resonances by varying the carrier concentration in doped semiconductor antennas. We fabricate spherical silicon and germanium particles of varying sizes and doping concentrations. Single-particle infrared spectra reveal electric and magnetic dipole, quadrupole, and hexapole resonances. We subsequently demonstrate doping-dependent frequency shifts that follow simple Drude models, culminating in the emergence of plasmonic resonances at high doping levels and long wavelengths. These findings demonstrate the potential for actively tuning infrared Mie resonances by optically or electrically modulating charge carrier densities, thus providing an excellent platform for tunable metamaterials.

Morphology-dependent light trapping in thin-film organic solar cells.

The active layer materials used in organic photovoltaic (OPV) cells often self-assemble into highly ordered morphologies, resulting in significant optical anisotropies. However, the impact of these anisotropies on light trapping in nanophotonic OPV architectures has not been considered. In this paper, we show that optical anisotropies in a canonical OPV material, P3HT, strongly affect absorption enhancements in ultra-thin textured OPV cells. In particular we show that plasmonic and gap-mode solar cell architectures redistribute electromagnetic energy into the out-of-plane field component, independent of the active layer orientation. Using analytical and numerical calculations, we demonstrate how the absorption in these solar cell designs can be significantly increased by reorienting polymer domains such that strongly absorbing axes align with the direction of maximum field enhancement.

Orientation of luminescent excitons in layered nanomaterials.

In nanomaterials, optical anisotropies reveal a fundamental relationship between structural and optical properties. Directional optical properties can be exploited to enhance the performance of optoelectronic devices, optomechanical actuators and metamaterials. In layered materials, optical anisotropies may result from in-plane and out-of-plane dipoles associated with intra- and interlayer excitations, respectively. Here, we resolve the orientation of luminescent excitons and isolate photoluminescence signatures arising from distinct intra- and interlayer optical transitions. Combining analytical calculations with energy- and momentum-resolved spectroscopy, we distinguish between in-plane and out-of-plane oriented excitons in materials with weak or strong interlayer coupling-MoS2 and 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA), respectively. We demonstrate that photoluminescence from MoS2 mono-, bi- and trilayers originates solely from in-plane excitons, whereas PTCDA supports distinct in-plane and out-of-plane exciton species with different spectra, dipole strengths and temporal dynamics. The insights provided by this work are important for understanding fundamental excitonic properties in nanomaterials and designing optical systems that efficiently excite and collect light from exciton species with different orientations.