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.

Enhanced Light-Matter Interaction in Metallic Nanoparticles: A Generic Strategy of Smart Void Filling.

The intrinsic properties of materials play a substantial role in light-matter interactions, impacting both bulk metals and nanostructures. While plasmonic nanostructures exhibit strong interactions with photons via plasmon resonances, achieving efficient light absorption/scattering in other transition metals remains a challenge, impeding various applications related to optoelectronics, chemistry, and energy harvesting. Here, we propose a universal strategy to enhance light-matter interaction, through introducing voids onto the surface of metallic nanoparticles. This strategy spans nine metals including those traditionally considered optically inactive. The absorption cross section of void-filled nanoparticles surpasses the value of plasmonic (Ag/Au) counterparts with tunable resonance peaks across a broad spectral range. Notably, this enhancement is achieved under arbitrary polarizations and varied particle sizes and in the presence of geometric disorder, highlighting the universal adaptability. Our strategy holds promise for inspiring emerging devices in photocatalysis, bioimaging, optical sensing, and beyond, particularly when metals other than gold or silver are preferred.

Exact Maxwell evolution equation of resonator dynamics: temporal coupled-mode theory revisited.

Despite its widespread significance, the temporal coupled-mode theory (CMT) lacks a foundational validation based on electromagnetic principles and stands as a phenomenological theory relying on fitted coupling coefficients. We employ an ab initio Maxwellian approach using quasinormal-mode theory to derive an "exact" Maxwell evolution (EME) equation for resonator dynamics. While the resulting differential equation bears resemblance to the classical one, it introduces novel terms embodying distinct physics, suggesting that the CMT predictions could be faulted by dedicated experiments, for instance carried out with short and off-resonance pulses, or with resonators of sizes comparable to or greater than the wavelength. Nonetheless, our examination indicates that, despite its inherent lack of strictness, the CMT enables precise predictions for numerous experiments due to the flexibility provided by the fitted coupling coefficients. The new EME equation is anticipated to be applicable to all electromagnetic resonator geometries, and the theoretical approach we have taken can be extended to other wave physics.

The visual appearances of disordered optical metasurfaces.

Nanostructured materials have recently emerged as a promising approach for material appearance design. Research has mainly focused on creating structural colours by wave interference, leaving aside other important aspects that constitute the visual appearance of an object, such as the respective weight of specular and diffuse reflectances, object macroscopic shape, illumination and viewing conditions. Here we report the potential of disordered optical metasurfaces to harness visual appearance. We develop a multiscale modelling platform for the predictive rendering of macroscopic objects covered by metasurfaces in realistic settings, and show how nanoscale resonances and mesoscale interferences can be used to spectrally and angularly shape reflected light and thus create unusual visual effects at the macroscale. We validate this property with realistic synthetic images of macroscopic objects and centimetre-scale samples observable with the naked eye. This framework opens new perspectives in many branches of fine and applied visual arts.

Dispersive perfectly matched layers and high-order absorbing boundary conditions for electromagnetic quasinormal modes.

Resonances, also known as quasinormal modes (QNMs) in the non-Hermitian case, play a ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum mechanics, acoustics, electrodynamics, and quantum theory. The non-Hermiticity arises from the system losses, whether they are material (Joule losses in electromagnetism) or linked to the openness of the problem (radiation losses). In this paper, we focus on the latter delicate matter when considering bounded computational domains mandatory when using, e.g., finite elements. We address the important question of whether dispersive perfectly matched layer (PML) and high-order absorbing boundary conditions offer advantages in QNM computation and modal expansion of the optical responses compared with nondispersive PMLs.

Normalization, orthogonality, and completeness of quasinormal modes of open systems: the case of electromagnetism [Invited].

The scattering of electromagnetic waves by resonant systems is determined by the excitation of the quasinormal modes (QNMs), i.e. the eigenmodes, of the system. This Review addresses three fundamental concepts in relation to the representation of the scattered field as a superposition of the excited QNMs: normalization, orthogonality, and completeness. Orthogonality and normalization enable a straightforward assessment of the QNM excitation strength for any incident wave. Completeness guarantees that the scattered field can be faithfully expanded into the complete QNM basis. These concepts are not trivial for non-conservative (non-Hermitian) systems and have driven many theoretical developments since initial studies in the 70's. Yet, they are not easy to grasp from the extensive and scattered literature, especially for newcomers in the field. After recalling fundamental results obtained in initial studies on the completeness of the QNM basis for simple resonant systems, we review recent achievements and the debate on the normalization, clarify under which circumstances the QNM basis is complete, and highlight the concept of QNM regularization with complex coordinate transforms.

MetaNet: a new paradigm for data sharing in photonics research.

Optimization methods are playing an increasingly important role in all facets of photonics engineering, from integrated photonics to free space diffractive optics. However, efforts in the photonics community to develop optimization algorithms remain uncoordinated, which has hindered proper benchmarking of design approaches and access to device designs based on optimization. We introduce MetaNet, an online database of photonic devices and design codes intended to promote coordination and collaboration within the photonics community. Using metagratings as a model system, we have uploaded over one hundred thousand device layouts to the database, as well as source code for implementations of local and global topology optimization methods. Further analyses of these large datasets allow the distribution of optimized devices to be visualized for a given optimization method. We expect that the coordinated research efforts enabled by MetaNet will expedite algorithm development for photonics design.

Shape Deformation of Nanoresonator: A Quasinormal-Mode Perturbation Theory.

When material parameters are fixed, optical responses of nanoresonators are dictated by their shapes and dimensions. Therefore, both designing nanoresonators and understanding their underlying physics would benefit from a theory that predicts the evolutions of resonance modes of open systems-the so-called quasinormal modes (QNMs)-as the nanoresonator shape changes. QNM perturbation theories (PTs) are one ideal choice. However, existing theories developed for tiny material changes are unable to provide accurate perturbation corrections for shape deformations. By introducing a novel extrapolation technique, we develop a rigorous QNM PT that faithfully represents the electromagnetic fields in perturbed domain. Numerical tests performed on the eigenfrequencies, eigenmodes, and optical responses of deformed nanoresonators evidence the predictive force of the present PT, even for large deformations. This opens new avenues for inverse design, as we exemplify by designing super-cavity modes and exceptional points with remarkable ease and physical insight.

Non-Lorentzian Local Density of States in Coupled Photonic Crystal Cavities Probed by Near- and Far-Field Emission.

Recent theories proposed a deep revision of the well-known expression for the Purcell factor, with counterintuitive effects, such as complex modal volumes and non-Lorentzian local density of states. We experimentally demonstrate these predictions in tailored coupled cavities on photonic crystal slabs with relatively low optical losses. Near-field hyperspectral imaging of quantum dot photoluminescence is proved to be a direct tool for measuring the line shape of the local density of states. The experimental results clearly evidence non-Lorentzian character, in perfect agreement with numerical and theoretical predictions. Spatial maps with deep subwavelength resolution of the real and imaginary parts of the complex mode volumes are presented. The generality of these results is confirmed by an additional set of far-field and time-resolved experiments in cavities with larger modal volume and higher quality factors.

Global polarizability matrix method for efficient modeling of light scattering by dense ensembles of non-spherical particles in stratified media.

We introduce a numerical method that enables efficient modeling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each other, to planar interfaces, and/or to localized light sources. The method consists of finding a small set of fictitious polarizable elements-or numerical dipoles-that quantitatively reproduces the field scattered by an individual particle for any excitation and at an arbitrary distance from the particle surface. The set of numerical dipoles is described by a global polarizability matrix that is determined numerically by solving an inverse problem relying on fullwave simulations. The latter are classical and may be performed with any Maxwell's equations solver. Spatial non-locality is an important feature of the numerical dipoles set, providing additional degrees of freedom compared to classical coupled dipoles to reconstruct complex scattered fields. Once the polarizability matrix describing scattering by an individual particle is determined, the multiple scattering problem by ensembles of such particles in stratified media can be solved using a Green tensor formalism and only a few numerical dipoles, thereby with a low physical memory usage, even for dense systems in close vicinity to interfaces. The performance of the method is studied with the example of large high-aspect-ratio high-index dielectric cylinders. The method is easy to implement and may offer new possibilities for the study of complex nanostructured surfaces, which are becoming widespread in emerging photonic technologies.

Femtosecond laser writing of near-surface waveguides for refractive-index sensing.

Femtosecond laser writing of optical waveguides and components in glasses has been a remarkably growing research field during the last two decades. However, such laser- inscribed optical components were mostly written within the volume of the glass due to the unavoidable ablation that arises when the focal spot is approaching the glass surface. This has generally limited the interaction of light with the surrounding medium thus preventing sensing functionality. In this paper, we present the inscription of surface and near-surface silver based waveguides in a silver containing glass with no need for additional processing as it is the case for standard type I waveguides. In addition, an ultra-sensitive refractive index sensor in a 1 cm glass chip is obtained based on near-surface waveguides interacting with liquid droplets acting as top-layer on the glass surface. Remarkably, the device exhibits a novel double-wing feature that sharpens the response and enhances its sensitivity. Our results highlight the advantages of silver based waveguides paving the way towards further surface based sensors in fibers.

Quasinormal-mode analysis of grating spectra at fixed incidence angles.

Grating spectra exhibit sharp variations of the scattered light, known as grating anomalies. The latter are due to resonances that have fascinated specialists of optics and physics for decades and are today used in many applications. We present a comprehensive theory of grating anomalies and develop a formalism to expand the field scattered by metallic or dielectric gratings into the basis of its natural resonances, thereby enabling the possibility to reconstruct grating spectra measured for fixed illumination angles as a sum over every individual resonance contribution with closed-form expressions. This gives physical insights into the spectral properties and direct access to the resonances to engineer the spectral response of gratings and their sensitivity to tiny perturbations.

Quasi-cylindrical wave contribution in experiments on extraordinary optical transmission.

A metal film perforated by a regular array of subwavelength holes shows unexpectedly large transmission at particular wavelengths, a phenomenon known as the extraordinary optical transmission (EOT) of metal hole arrays. EOT was first attributed to surface plasmon polaritons, stimulating a renewed interest in plasmonics and metallic surfaces with subwavelength features. Experiments soon revealed that the field diffracted at a hole or slit is not a surface plasmon polariton mode alone. Further theoretical analysis predicted that the extra contribution, from quasi-cylindrical waves, also affects EOT. Here we report the experimental demonstration of the relative importance of surface plasmon polaritons and quasi-cylindrical waves in EOT by considering hole arrays of different hole densities. From the measured transmission spectra, we determine microscopic scattering parameters which allow us to show that quasi-cylindrical waves affect EOT only for high densities, when the hole spacing is roughly one wavelength. Apart from providing a deeper understanding of EOT, the determination of microscopic scattering parameters from the measurement of macroscopic optical properties paves the way to novel design strategies.

Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing.

We derive a closed-form expression that accurately predicts the peak frequency shift and broadening induced by tiny perturbations of plasmonic nanoresonators without critically relying on repeated electrodynamic simulations of the spectral response of nanoresonator for various locations, sizes, or shapes of the perturbing objects. In comparison with other approaches of the same kind, the force of the present approach is that the derivation is supported by a mathematical formalism based on a rigorous normalization of the resonance modes of nanoresonators consisting of lossy and dispersive materials. Accordingly, accurate predictions are obtained for a large range of nanoparticle shapes and sizes used in various plasmonic nanosensors even beyond the quasistatic limit. The expression gives quantitative insight and, combined with an open-source code, provides accurate and fast predictions that are ideally suited for preliminary designs or for interpretation of experimental data. It is also valid for photonic resonators with large mode volumes.

Theoretical treatment of the interaction between two-level atoms and periodic waveguides.

Light transport in periodic waveguides coupled to two-level atoms is investigated theoretically. By using optical Bloch equations and a photonic modal formalism, we derive a convenient semi-analytical expression for calculating the scattering matrix of single atoms trapped in periodic waveguides. The expression that holds for both photonic and plasmonic waveguides represents a basic building block toward the study of collective effects arising from photon-mediated multi-atom interactions in periodic waveguides.

Wide-angle reflection-mode spatial filtering and splitting with photonic crystal gratings and single-layer rod gratings.

New diffractive optical elements offering a frequency tolerant, very efficient, high-pass and bandpass spatial filtering over a broad range of incidence angles are demonstrated by numerical simulations. The device operates in reflection mode owing to the (nearly) perfect blazing. It relies on two-dimensional square-lattice photonic crystals composed of dielectric rods with simple corrugations at the interface. Similar performance can be obtained with gratings composed of a single rod layer placed in the near field of a metal mirror, indicating a route to geometries that can be easily fabricated with modern nanotechnologies. Also equal splitting between zero and first negative orders can be obtained for incidence-angle variations that are wider than 60°.

Microscopic theory of the extraordinary optical transmission.

The phenomenon of extraordinary light transmission through metallic films perforated by nanohole arrays at optical frequencies was first observed a decade ago and initiated important further experimental and theoretical work. In view of potential applications of such structures--for example, subwavelength optics, optoelectronics devices, and chemical sensing--it is important to understand the underlying physical processes in detail. Here we derive a microscopic theory of the transmission through subwavelength hole arrays, by considering the elementary processes associated with scattering of surface-plasmon-polariton (SPP) modes by individual one-dimensional chains of subwavelength holes. Using a SPP coupled-mode model that coherently gathers these elementary processes, we derive analytical expressions for all the transmission spectrum characteristics--such as the resonance wavelength, the peak transmission and the anti-resonance. Further comparisons of the model predictions with fully vectorial computational results allow us quantitatively to check the model accuracy and to discuss the respective impacts of SPP modes and of other electromagnetic fields on producing the extraordinary transmission of light. The model greatly expands our understanding of the phenomenon and may affect further engineering of nanoplasmonic devices.

Aperiodic-Fourier modal method for analysis of body-of-revolution photonic structures.

Modeling the field produced by a point-like dipole with an arbitrary location in the presence of a rotationally invariant nanostructure is an important issue in the context of designing nanoantennas. This is a challenging problem, as rotational symmetry is broken when introducing a noncentered dipole. Antennas larger than the wavelength are required for directivity, whereas the dipole-antenna distance is highly subwavelength, so there are two different length scales in the problem. In this paper, we introduce an original S-matrix approach based on an aperiodic-Fourier modal method. The potential of the technique is illustrated by considering three examples. We compare our results with a finite element technique.

General properties of the surface charge pattern of one-dimensional metallic gratings.

Under light illumination, metallic gratings present unexpected and fascinating phenomena, which are due to the complex charge patterns generated on the grating surfaces. The moving electrons are due to the launching of surface plasmon polaritons (SPPs), but only in part. We derive analytical expressions quantifying the plasmonic character of the surface charge patterns, i.e. the contribution of SPPs to its formation. The expressions have a general significance, in the sense that they may be applied to a variety of geometries and spectral ranges, irrespective of whether the grating absorbs, transmits, reflects, or how strongly it resonates.

Multi-resonant absorption in ultra-thin silicon solar cells with metallic nanowires.

We propose a design to confine light absorption in flat and ultra-thin amorphous silicon solar cells with a one-dimensional silver grating embedded in the front window of the cell. We show numerically that multi-resonant light trapping is achieved in both TE and TM polarizations. Each resonance is analyzed in detail and modeled by Fabry-Perot resonances or guided modes via grating coupling. This approach is generalized to a complete amorphous silicon solar cell, with the additional degrees of freedom provided by the buffer layers. These results could guide the design of resonant structures for optimized ultra-thin solar cells.