Photonic flatband resonances for free-electron radiation.

Flatbands have become a cornerstone of contemporary condensed-matter physics and photonics. In electronics, flatbands entail comparable energy bandwidth and Coulomb interaction, leading to correlated phenomena such as the fractional quantum Hall effect and recently those in magic-angle systems. In photonics, they enable properties including slow light1 and lasing2. Notably, flatbands support supercollimation-diffractionless wavepacket propagation-in both systems3,4. Despite these intense parallel efforts, flatbands have never been shown to affect the core interaction between free electrons and photons. Their interaction, pivotal for free-electron lasers5, microscopy and spectroscopy6,7, and particle accelerators8,9, is, in fact, limited by a dimensionality mismatch between localized electrons and extended photons. Here we reveal theoretically that photonic flatbands can overcome this mismatch and thus remarkably boost their interaction. We design flatband resonances in a silicon-on-insulator photonic crystal slab to control and enhance the associated free-electron radiation by tuning their trajectory and velocity. We observe signatures of flatband enhancement, recording a two-order increase from the conventional diffraction-enabled Smith-Purcell radiation. The enhancement enables polarization shaping of free-electron radiation and characterization of photonic bands through electron-beam measurements. Our results support the use of flatbands as test beds for strong light-electron interaction, particularly relevant for efficient and compact free-electron light sources and accelerators.

Observation of topologically enabled unidirectional guided resonances.

Unidirectional radiation is important for various optoelectronic applications, such as lasers, grating couplers and optical antennas. However, almost all existing unidirectional emitters rely on the use of materials or structures that forbid outgoing waves-that is, mirrors, which are often bulky, lossy and difficult to fabricate. Here we theoretically propose and experimentally demonstrate a class of resonances in photonic crystal slabs that radiate only towards one side of the slab, with no mirror placed on the other side. These resonances, which we name 'unidirectional guided resonances', are found to be topological in nature: they emerge when a pair of half-integer topological charges1-3 in the polarization field bounce into each other in momentum space. We experimentally demonstrate unidirectional guided resonances in the telecommunication regime by achieving single-side radiative quality factors as high as 1.6 × 105. We further demonstrate their topological nature through far-field polarimetry measurements. Our work represents a characteristic example of applying topological principles4,5 to control optical fields and could lead to energy-efficient grating couplers and antennas for light detection and ranging.

Inference in artificial intelligence with deep optics and photonics.

Artificial intelligence tasks across numerous applications require accelerators for fast and low-power execution. Optical computing systems may be able to meet these domain-specific needs but, despite half a century of research, general-purpose optical computing systems have yet to mature into a practical technology. Artificial intelligence inference, however, especially for visual computing applications, may offer opportunities for inference based on optical and photonic systems. In this Perspective, we review recent work on optical computing for artificial intelligence applications and discuss its promise and challenges.

Creating large Fock states and massively squeezed states in optics using systems with nonlinear bound states in the continuum.

The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of an effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The effect, which we call an n-photon bound state in the continuum, is one in which a photonic resonance (such as a cavity mode) becomes lossless when a precise number of photons n is inside the resonance. Based on analytical theory and numerical simulations, we show that these bound states enable a remarkable phenomenon in which a coherent state of light, when injected into a system supporting this bound state, can spontaneously evolve into a Fock state of a controllable photon number. This effect is also directly applicable for creating (highly) squeezed states of light, whose photon number fluctuations are (far) below the value expected from classical physics (i.e., shot noise). We suggest several examples of systems to experimentally realize the effects predicted here in nonlinear nanophotonic systems, showing examples of generating both optical Fock states with large n (n >  10), as well as more macroscopic photonic states with very large squeezing, with over 90% less noise (10 dB) than the classical value associated with shot noise.

Topologically enabled ultrahigh-Q guided resonances robust to out-of-plane scattering.

Because of their ability to confine light, optical resonators1-3 are of great importance to science and technology, but their performance is often limited by out-of-plane-scattering losses caused by inevitable fabrication imperfections4,5. Here we theoretically propose and experimentally demonstrate a class of guided resonances in photonic crystal slabs, in which out-of-plane-scattering losses are strongly suppressed by their topological nature. These resonances arise when multiple bound states in the continuum-each carrying a topological charge6-merge in momentum space and enhance the quality factors Q of all nearby resonances in the same band. Using such resonances in the telecommunication regime, we experimentally achieve quality factors as high as 4.9 × 105-12 times higher than those obtained with standard designs-and this enhancement remains robust for all of our samples. Our work paves the way for future explorations of topological photonics in systems with open boundary conditions and for their application to the improvement of optoelectronic devices in photonic integrated circuits.

A general theoretical and experimental framework for nanoscale electromagnetism.

The macroscopic electromagnetic boundary conditions, which have been established for over a century1, are essential for the understanding of photonics at macroscopic length scales. Even state-of-the-art nanoplasmonic studies2-4, exemplars of extremely interface-localized fields, rely on their validity. This classical description, however, neglects the intrinsic electronic length scales (of the order of ångström) associated with interfaces, leading to considerable discrepancies between classical predictions and experimental observations in systems with deeply nanoscale feature sizes, which are typically evident below about 10 to 20 nanometres5-10. The onset of these discrepancies has a mesoscopic character: it lies between the granular microscopic (electronic-scale) and continuous macroscopic (wavelength-scale) domains. Existing top-down phenomenological approaches deal only with individual aspects of these omissions, such as nonlocality11-13 and local-response spill-out14,15. Alternatively, bottom-up first-principles approaches-for example, time-dependent density functional theory16,17-are severely constrained by computational demands and thus become impractical for multiscale problems. Consequently, a general and unified framework for nanoscale electromagnetism remains absent. Here we introduce and experimentally demonstrate such a framework-amenable to both analytics and numerics, and applicable to multiscale problems-that reintroduces the electronic length scale via surface-response functions known as Feibelman d parameters18,19. We establish an experimental procedure to measure these complex dispersive surface-response functions, using quasi-normal-mode perturbation theory and observations of pronounced nonclassical effects. We observe nonclassical spectral shifts in excess of 30 per cent and the breakdown of Kreibig-like broadening in a quintessential multiscale architecture: film-coupled nanoresonators, with feature sizes comparable to both the wavelength and the electronic length scale. Our results provide a general framework for modelling and understanding nanoscale (that is, all relevant length scales above about 1 nanometre) electromagnetic phenomena.

Topogivity: A Machine-Learned Chemical Rule for Discovering Topological Materials.

Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered using methods that involve symmetry-based analysis of the quantum wave function. Here we use machine learning to develop a simple-to-use heuristic chemical rule that diagnoses with a high accuracy whether a material is topological using only its chemical formula. This heuristic rule is based on a notion that we term topogivity, a machine-learned numerical value for each element that loosely captures its tendency to form topological materials. We next implement a high-throughput procedure for discovering topological materials based on the heuristic topogivity-rule prediction followed by ab initio validation. This way, we discover new topological materials that are not diagnosable using symmetry indicators, including several that may be promising for experimental observation.

Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics.

Traditional optical elements and conventional metasurfaces obey shift-invariance in the paraxial regime. For imaging systems obeying paraxial shift-invariance, a small shift in input angle causes a corresponding shift in the sensor image. Shift-invariance has deep implications for the design and functionality of optical devices, such as the necessity of free space between components (as in compound objectives made of several curved surfaces). We present a method for nanophotonic inverse design of compact imaging systems whose resolution is not constrained by paraxial shift-invariance. Our method is end-to-end, in that it integrates density-based full-Maxwell topology optimization with a fully iterative elastic-net reconstruction algorithm. By the design of nanophotonic structures that scatter light in a non-shift-invariant manner, our optimized nanophotonic imaging system overcomes the limitations of paraxial shift-invariance, achieving accurate, noise-robust image reconstruction beyond shift-invariant resolution.

Intense Squeezed Light from Lasers with Sharply Nonlinear Gain at Optical Frequencies.

Nonclassical states of light, such as number-squeezed light, with fluctuations below the classical shot noise level, have important uses in metrology, communication, quantum information processing, and quantum simulation. However, generating these nonclassical states of light, especially with high intensity and a high degree of squeezing, is challenging. To address this problem, we introduce a new concept which uses gain to generate intense sub-Poissonian light at optical frequencies. It exploits a strongly nonlinear gain for photons which arises from a combination of frequency-dependent gain and Kerr nonlinearity. In this laser architecture, the interaction between the gain medium and Kerr nonlinearity suppresses the spontaneous emission at high photon number states, leading to a strong "negative feedback" that suppresses photon-number fluctuations. We discuss realistic implementations of this concept based on the use of solid-state gain media in laser cavities with Kerr nonlinear materials, showing how 90% squeezing of photon number fluctuations below the shot noise level can be realized.

End-to-end metasurface inverse design for single-shot multi-channel imaging.

We introduce end-to-end inverse design for multi-channel imaging, in which a nanophotonic frontend is optimized in conjunction with an image-processing backend to extract depth, spectral and polarization channels from a single monochrome image. Unlike diffractive optics, we show that subwavelength-scale "metasurface" designs can easily distinguish similar wavelength and polarization inputs. The proposed technique integrates a single-layer metasurface frontend with an efficient Tikhonov reconstruction backend, without any additional optics except a grayscale sensor. Our method yields multi-channel imaging by spontaneous demultiplexing: the metaoptics front-end separates different channels into distinct spatial domains whose locations on the sensor are optimally discovered by the inverse-design algorithm. We present large-area metasurface designs, compatible with standard lithography, for multi-spectral imaging, depth-spectral imaging, and "all-in-one" spectro-polarimetric-depth imaging with robust reconstruction performance (≲ 10% error with 1% detector noise). In contrast to neural networks, our framework is physically interpretable and does not require large training sets. It can be used to reconstruct arbitrary three-dimensional scenes with full multi-wavelength spectra and polarization textures.

Enhancing Plasmonic Spectral Tunability with Anomalous Material Dispersion.

The field confinement of plasmonic systems enables spectral tunability under structural variations or environmental perturbations, which is the principle for various applications including nanorulers, sensors, and color displays. Here, we propose and demonstrate that materials with anomalous dispersion, such as Ge in the visible, improve spectral tunability. We introduce our proposal with a semianalytical guided mode picture. Using Ge-based film (Ag/Au)-coupled gap plasmon resonators, we implement two architectures and demonstrate the improved tunability with single-particle dark-field scattering, ensemble reflection, and color generation. We observe three-fold enhancement of tunability with Ge nanodisks compared with that of Si, a normal-dispersion material in the visible. The structural color generation of large array systems, made of inversely fabricated Ge-Ag resonators, exhibits a wide gamut. Our results introduce anomalous material dispersion as an extra degree of freedom to engineer the spectral tunability of plasmonic systems, especially relevant for actively tunable plasmonics and metasurfaces.

Casimir Light in Dispersive Nanophotonics.

Time-varying optical media, whose dielectric properties are actively modulated in time, introduce a host of novel effects in the classical propagation of light, and are of intense current interest. In the quantum domain, time-dependent media can be used to convert vacuum fluctuations (virtual photons) into pairs of real photons. We refer to these processes broadly as "dynamical vacuum effects" (DVEs). Despite interest for their potential applications as sources of quantum light, DVEs are generally very weak, presenting many opportunities for enhancement through modern techniques in nanophotonics, such as using media which support excitations such as plasmon and phonon polaritons. Here, we present a theory of weakly modulated DVEs in arbitrary nanostructured, dispersive, and dissipative systems. A key element of our framework is the simultaneous incorporation of time-modulation and "dispersion" through time-translation-breaking linear response theory. As an example, we use our approach to propose a highly efficient scheme for generating entangled surface polaritons based on time-modulation of the optical phonon frequency of a polar insulator.

Spawning rings of exceptional points out of Dirac cones.

The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure--two conical bands touching at a single point--has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity-time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an 'exceptional ring' in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.

A high-efficiency regime for gas-phase terahertz lasers.

We present both an innovative theoretical model and an experimental validation of a molecular gas optically pumped far-infrared (OPFIR) laser at 0.25 THz that exhibits 10× greater efficiency (39% of the Manley-Rowe limit) and 1,000× smaller volume than comparable commercial lasers. Unlike previous OPFIR-laser models involving only a few energy levels that failed even qualitatively to match experiments at high pressures, our ab initio theory matches experiments quantitatively, within experimental uncertainties with no free parameters, by accurately capturing the interplay of millions of degrees of freedom in the laser. We show that previous OPFIR lasers were inefficient simply by being too large and that high powers favor high pressures and small cavities. We believe that these results will revive interest in OPFIR laser as a powerful and compact source of terahertz radiation.

Fullwave Maxwell inverse design of axisymmetric, tunable, and multi-scale multi-wavelength metalenses.

We demonstrate new axisymmetric inverse-design techniques that can solve problems radically different from traditional lenses, including reconfigurable lenses (that shift a multi-frequency focal spot in response to refractive-index changes) and widely separated multi-wavelength lenses (λ = 1 µm and 10 µm). We also present experimental validation for an axisymmetric inverse-designed monochrome lens in the near-infrared fabricated via two-photon polymerization. Axisymmetry allows fullwave Maxwell solvers to be scaled up to structures hundreds or even thousands of wavelengths in diameter before requiring domain-decomposition approximations, while multilayer topology optimization with ∼105 degrees of freedom can tackle challenging design problems even when restricted to axisymmetric structures.

Making two-photon processes dominate one-photon processes using mid-IR phonon polaritons.

Phonon polaritons are guided hybrid modes of photons and optical phonons that can propagate on the surface of a polar dielectric. In this work, we show that the precise combination of confinement and bandwidth offered by phonon polaritons allows for the ability to create highly efficient sources of polariton pairs in the mid-IR/terahertz frequency ranges. Specifically, these polar dielectrics can cause emitters to preferentially decay by the emission of pairs of phonon polaritons, instead of the previously dominant single-photon emission. We show that such two-photon emission processes can occur on nanosecond time scales and can be nearly 2 orders of magnitude faster than competing single-photon transitions, as opposed to being as much as 8-10 orders of magnitude slower in free space. These results are robust to the choice of polar dielectric, allowing potentially versatile implementation in a host of materials such as hexagonal boron nitride, silicon carbide, and others. Our results suggest a design strategy for quantum light sources in the mid-IR/terahertz: ones that prefer to emit a relatively broad spectrum of photon pairs, potentially allowing for new sources of both single and multiple photons.

All-angle negative refraction of highly squeezed plasmon and phonon polaritons in graphene-boron nitride heterostructures.

A fundamental building block for nanophotonics is the ability to achieve negative refraction of polaritons, because this could enable the demonstration of many unique nanoscale applications such as deep-subwavelength imaging, superlens, and novel guiding. However, to achieve negative refraction of highly squeezed polaritons, such as plasmon polaritons in graphene and phonon polaritons in boron nitride (BN) with their wavelengths squeezed by a factor over 100, requires the ability to flip the sign of their group velocity at will, which is challenging. Here we reveal that the strong coupling between plasmon and phonon polaritons in graphene-BN heterostructures can be used to flip the sign of the group velocity of the resulting hybrid (plasmon-phonon-polariton) modes. We predict all-angle negative refraction between plasmon and phonon polaritons and, even more surprisingly, between hybrid graphene plasmons and between hybrid phonon polaritons. Graphene-BN heterostructures thus provide a versatile platform for the design of nanometasurfaces and nanoimaging elements.

Ultrafast Multiharmonic Plasmon Generation by Optically Dressed Electrons.

Interactions between electrons and photons are a source of rich physics from atomic to astronomical scales. Here, we examine a new kind of electron-photon interaction in which an electron, modulated by light, radiates multiple harmonics of plasmons. The emitted plasmons can be femtosecond in duration and nanometer in spatial scale. The extreme subwavelength nature of the plasmons lowers the necessary input light intensity by at least 4 orders of magnitude relative to state-of-the-art strong-field processes involving bound or free electrons. The results presented here reveal a new means of ultrafast (10-1000 fs) interconversion between photonic and plasmonic energy, and a general scheme for generating spatiotemporally shaped ultrashort pulses in optical materials. More generally, our results suggest a route towards realizing analogues of fascinating physical phenomena like nonlinear Compton scattering in plasmonics and nanophotonics with relatively low intensities, slow electrons, and on nanometer length scales.

Gated Orthogonal Recurrent Units: On Learning to Forget.

We present a novel recurrent neural network (RNN)-based model that combines the remembering ability of unitary evolution RNNs with the ability of gated RNNs to effectively forget redundant or irrelevant information in its memory. We achieve this by extending restricted orthogonal evolution RNNs with a gating mechanism similar to gated recurrent unit RNNs with a reset gate and an update gate. Our model is able to outperform long short-term memory, gated recurrent units, and vanilla unitary or orthogonal RNNs on several long-term-dependency benchmark tasks. We empirically show that both orthogonal and unitary RNNs lack the ability to forget. This ability plays an important role in RNNs. We provide competitive results along with an analysis of our model on many natural sequential tasks, including question answering, speech spectrum prediction, character-level language modeling, and synthetic tasks that involve long-term dependencies such as algorithmic, denoising, and copying tasks.

Observation of trapped light within the radiation continuum.

The ability to confine light is important both scientifically and technologically. Many light confinement methods exist, but they all achieve confinement with materials or systems that forbid outgoing waves. These systems can be implemented by metallic mirrors, by photonic band-gap materials, by highly disordered media (Anderson localization) and, for a subset of outgoing waves, by translational symmetry (total internal reflection) or by rotational or reflection symmetry. Exceptions to these examples exist only in theoretical proposals. Here we predict and show experimentally that light can be perfectly confined in a patterned dielectric slab, even though outgoing waves are allowed in the surrounding medium. Technically, this is an observation of an 'embedded eigenvalue'--namely, a bound state in a continuum of radiation modes--that is not due to symmetry incompatibility. Such a bound state can exist stably in a general class of geometries in which all of its radiation amplitudes vanish simultaneously as a result of destructive interference. This method to trap electromagnetic waves is also applicable to electronic and mechanical waves.