Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure

Nanometer-Scale Cavities for Mid-Infrared Radiation via Image Phonon Polariton Resonators

Surface polaritons play a pivotal role in strong light-matter interactions at the nanoscale due to their ability to confine light to deep-subwavelength dimensions. A promising class of materials exhibiting such a polaritonic response is polar dielectrics, which support surface phonon polaritons (SPhPs). While SPhPs offer significantly lower losses compared to other polaritons, their potential has been underutilized due to their limited ability to reach large confinement factors. Here, we demonstrate a system composed of silver nanocubes deposited on a SiC polar dielectric, which experimentally realizes the antisymmetric-image-phonon-polariton mode, a hybridized SPhP mode that can confine mid-infrared radiation to extremely small mode volumes, almost a billion times smaller than their free-space volume, with quality factors an order-of-magnitude greater than those of surface plasmons or graphene plasmons, surpassing values of 180. Our method is general, scalable, and applicable to any polar dielectric, opening the path for controlling and manipulating strong light-matter interactions at the nanoscale in the long-wavelength range.

Topological Band Engineering in q-BICs and EPs Derived from Visible Range Plasmons

Topological photonics, owing to its band topology, has substantial potential in applications such as quantum computation and photonic chips. However, attaining flexible control over band topology for effective light-matter interactions at the subwavelength scale remains elusive. In this study, we present a metal-insulator-metal (MIM) dimerized grating structure based on the one-dimensional (1D) Su-Schrieffer-Heeger model (SSH). This structure is designed for tuning optical band topology with a relatively high quality factor and small mode volume. Specifically, by variation of the grating thickness, topological band inversion with plasmonic quasi-bound states in the continuum (q-BICs) can be achieved. Moreover, through the modulation of gain-loss and coupling strength, the corresponding exceptional points (EPs) can emerge near the Brillouin zone center (Γ point). Consequently, this MIM dimerized grating structure offers a novel approach for the design of advanced topological devices.

Role of complex energy and momentum in open cavity resonances

Complex power, also known as alternating current (AC) power, is a well-established concept in an electric circuit composed of resistive and reactive elements. On the other hand, the role of complex power in optics has been elusive. In this work, we reveal that the complex energy and momentum determine the resonance frequency and the decay rate of open cavity resonance, the so-called quasinormal modes (QNMs), respectively. We also demonstrate the role of the complex energy and momentum in typical open cavities analytically and numerically: the Fabry-Perot cavity, the surface plasmon polaritons (SPPs), the plasmonic nanorod, the nanosphere, and the dielectric supercavity.

Non-Hermitian singularities in scattering spectra of Mie resonators

Non-Hermitian systems are known to have unique singularities, notably exceptional points. Mie resonators demonstrate fruitful electromagnetic multipole interference effects in scattering behavior. The research of these non-Hermitian singularities is typically conducted independently with the analysis of scattering interference. Here, we demonstrate fundamental relationships between non-Hermitian singularities and observe their manifestation in the scattering spectra. We reveal that exceptional points always exist in the anapole regime, and diabolic points are associated with superscattering. We confirm our theoretical findings in the microwave experiment by measuring the extinction spectra of subwavelength Mie-resonant ceramic rings. Our study underpins the generic behavior of non-Hermitian singularities in the scattering spectra of subwavelength Mie resonators, uncovering their special applications in non-Hermitian nonlinear optics and topological photonics.

Accurate characterization of complex Bloch modes in optical chain waveguides using real-valued computations

This research presents a highly accurate and easy-to-implement method to characterize the complex Bloch modes propagating along optical chain waveguides with three-dimensional (3D) layered geometries and dispersive negative-epsilon material compositions. The technique combines commercial EM solver results with analytical post-processing to avoid iterative complex root estimation on the complex plane. The proposed methodology is based on the real-valued computations that yield the complex Bloch wavevector with superior accuracy even when both radiation and material losses are present. In addition, we introduce a single unit-cell technique to provide the possibility of dense meshing of 3D geometries when available computational resources are limited. To verify our results, two different plasmonic and dielectric case studies are discussed. The obtained results agree well with numerical and experimental results from the literature. Due to its generality, robustness, and high accuracy, the method is beneficial for studying a large variety of waveguide-based nanophotonic components.

Multi-faceted plasmonic nanocavities

Plasmonic nanocavities form very robust sub-nanometer gaps between nanometallic structures and confine light within deep subwavelength volumes to enable unprecedented control of light-matter interactions. However, spherical nanoparticles acquire various polyhedral shapes during their synthesis, which has a significant impact in controlling many light-matter interactions, such as photocatalytic reactions. Here, we focus on nanoparticle-on-mirror nanocavities built from three polyhedral nanoparticles (cuboctahedron, rhombicuboctahedron, decahedron) that commonly occur during the synthesis. Their photonic modes have a very intricate and rich optical behaviour, both in the near- and far-field. Through a recombination technique, we obtain the total far-field produced by a molecule placed within these nanocavities, to reveal how energy couples in and out of the system. This work paves the way towards understanding and controlling light-matter interactions, such as photocatalytic reactions and non-linear vibrational pumping, in such extreme environments.

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.

Quantitative Insights into a Plasmonic Ruler Equation from the Perspective of Enhanced Near Field

The plasmonic shift of resonance wavelength induced by near-field coupling enables one to measure nanoscale distances optically. Empirically, the well-known ruler equation correlating plasmon shift with interparticle spacing was proposed. Though it has been widely used in analyzing simulation and experimental outcomes, little is known about the underlying physical mechanism of the characteristic exponential form of the plasmon ruler equation and the universal decay constant therein. In this work, we attempt to decrypt these from the perspective of plasmon near-field enhancement. Based on an analytical quasi-normal mode formula for plasmon shifts, we proved that the exponential decaying electric field is the critical reason that results in the exponential form of the plasmon ruler equation and quantitatively, we found that the universal decay constant in the plasmon ruler equation actually reflects the range of the enhanced near field. This work hopefully helps to deepen the understanding of the mechanism of light-matter interaction in corresponding plasmonic processes.

Generalizing the exact multipole expansion: density of multipole modes in complex photonic nanostructures

The multipole expansion of a nano-photonic structure's electromagnetic response is a versatile tool to interpret optical effects in nano-optics, but it only gives access to the modes that are excited by a specific illumination. In particular the study of various illuminations requires multiple, costly numerical simulations. Here we present a formalism we call "generalized polarizabilities", in which we combine the recently developed exact multipole decomposition [Alaee et al., Opt. Comms. 407, 17-21 (2018)] with the concept of a generalized field propagator. After an initial computation step, our approach allows to instantaneously obtain the exact multipole decomposition for any illumination. Most importantly, since all possible illuminations are included in the generalized polarizabilities, our formalism allows to calculate the total density of multipole modes, regardless of a specific illumination, which is not possible with the conventional multipole expansion. Finally, our approach directly provides the optimum illumination field distributions that maximally couple to specific multipole modes. The formalism will be very useful for various applications in nano-optics like illumination-field engineering, or meta-atom design e.g. for Huygens metasurfaces. We provide a numerical open source implementation compatible with the pyGDM python package.

Can Weak Chirality Induce Strong Coupling between Resonant States?

Strong coupling between resonant states is usually achieved by modulating intrinsic parameters of optical systems, e.g., the refractive index of constituent materials or structural geometries. Externally introduced chiral enantiomers may couple resonances, but the extremely weak chirality of natural enantiomers largely prevents the system from reaching strong coupling regimes. Whether weak chirality could induce strong coupling between resonant states remains an open question. Here, we realize strong coupling between quasibound states in the continuum of a high-Q metasurface, assisted with externally introduced enantiomers of weak chirality. We establish a chirality-involved Hamiltonian to quantitatively describe the correlation between the coupling strength and the chirality of such systems, which provides an insightful recipe for enhancing the coupling of resonant states further in the presence of quite weak chirality. Consequently, high-sensitivity chiral sensing is demonstrated, in which the circular dichroism signal is enhanced 3 orders higher than the case without strong coupling. Our findings present a distinct strategy for manipulating optical coupling between resonances, revealing opportunities in chiral sensing, topological photonics, and quantum optics.

Ultrastrong Coupling of a Single Molecule to a Plasmonic Nanocavity: A First-Principles Study

Ultrastrong coupling (USC) is a distinct regime of light-matter interaction in which the coupling strength is comparable to the resonance energy of the cavity or emitter. In the USC regime, common approximations to quantum optical Hamiltonians, such as the rotating wave approximation, break down as the ground state of the coupled system gains photonic character due to admixing of vacuum states with higher excited states, leading to ground-state energy changes. USC is usually achieved by collective coherent coupling of many quantum emitters to a single mode cavity, whereas USC with a single molecule remains challenging. Here, we show by time-dependent density functional theory (TDDFT) calculations that a single organic molecule can reach USC with a plasmonic dimer, consisting of a few hundred atoms. In this context, we discuss the capacity of TDDFT to represent strong coupling and its connection to the quantum optical Hamiltonian. We find that USC leads to appreciable ground-state energy modifications accounting for a non-negligible part of the total interaction energy, comparable to k _B T at room temperature.

SARS-CoV-2 Detection using Colorimetric Plasmonic Sensors: A Proof-of-Concept Computational Study

Traditional molecular techniques for SARS-CoV-2 viral detection are time-consuming and can exhibit a high probability of false negatives. In this work, we present a computational study of SARS-CoV-2 detection using plasmonic gold nanoparticles. The resonance wavelength of a SARS-CoV-2 virus was recently estimated to be in the near-infrared region. By engineering gold nanospheres to specifically bind with the outer surface of the SARS-CoV-2 virus, the resonance frequency can be shifted to the visible range (380 nm - 700 nm). Moreover, we show that broadband absorption will emerge in the visible spectrum when the virus is partially covered with gold nanoparticles at a specific coverage percentage. This broadband absorption can be used to guide the development of an efficient and accurate colorimetric plasmon sensor for COVID-19 detection. Our observation also suggests that this technique is unaffected by the number of protein spikes present on the virus outer surface, hence can pave a potential path for a label-free COVID-19 diagnostic tool independent of the number of protein spikes.

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.

Strong and weak polarization-dependent interactions in connected and disconnected plasmonic nanostructures

We explore numerically and experimentally the formation of hybridized modes between a bright mode displayed by a gold nanodisc and either dark or bright modes of a nanorod - both elements being either separated by a nanometer-size gap (disconnected system) or relied on a metal junction (connected system). In terms of modeling, we compare the scattering or absorption spectra and field distributions obtained under oblique-incidence plane wave illumination with quasi-normal mode computation and an analytical model based on a coupled oscillator model. Both connected and disconnected systems have very different plasmon properties in longitudinal polarization. The disconnected system can be consistently understood in terms of the nature of hybridized modes and coupling strength using either QNMs or coupled oscillator model; however the connected configuration presents intriguing peculiarities based on the strong redistribution of charges implied by the presence of the metal connection. In practice, the fabrication of disconnected or connected configurations depends on the mitigation of lithographic proximity effects inherent to top-down lithography methods, which can lead to the formation of small metal junctions, while careful lithographic dosing allows one to fabricate disconnected systems with a gap as low as 20 nm. We obtained a very good agreement between experimentally measured scattering spectra and numerical predictions. The methods and analyses presented in this work can be applied to a wide range of systems, for potential applications in light-matter interactions, biosensing or strain monitoring.

Anapole enhanced on-chip routing of spin-valley photons in 2D materials for silicon integrated optical communication

Controlling the propagation direction of polarized light is crucial for optical communications and functional optical components. However, all-dielectric on-chip technology exploiting valley photon emission in transition metal dichalcogenides with enhanced emission has yet to be fully explored. Here, we report a design for enhancing valley emission and manipulating valley photon propagation based on degenerate non-radiating anapole states. By placing circularly polarized dipoles on top of a C₄ symmetric cross-slotted silicon disk, the rotating anapole state is excited with a Purcell factor up to two orders. In addition, the photon coupled to the preferred direction of the waveguide are about 2 times larger than that to the opposite direction. Our design could pave the way for realizing on-chip valley-dependent optical communication.

Efficient Bloch mode calculation of periodic systems with arbitrary geometry and open boundary conditions in the complex wavevector domain

We show how existing iterative methods can be used to efficiently and accurately calculate Bloch periodic solutions of Maxwell's equations in arbitrary geometries. This is carried out in the complex-wavevector domain using a commercial frequency-domain finite-element solver that is available to the general user. The method is capable of dealing with leaky Bloch mode solutions, and is extremely efficient even for 3D geometries with non-trivial material distributions. We perform independent finite-difference time-domain simulations of Maxwell's equations to confirm our results. This comparison demonstrates that the iterative mode finder is more accurate, since it provides the true solutions in the complex-wavevector domain and removes the need for additional signal processing and fitting. Due to its efficiency, generality and reliability, this technique is well suited for complex and novel design tasks in integrated photonics, and also for a wider range of photonics problems.

Efficient hybrid method for the modal analysis of optical microcavities and nanoresonators

We propose a novel hybrid method for accurately and efficiently analyzing microcavities and nanoresonators. The method combines the marked spirit of quasinormal mode expansion approaches, e.g., analyticity and physical insight, with the renowned strengths of real-frequency simulations, e.g., accuracy and flexibility. Real- and complex-frequency simulations offer a complementarity between accuracy and computation speed, opening new perspectives for challenging inverse design of nanoresonators.

Bright Optical Eigenmode of 1 nm^{3} Mode Volume

We report on the discovery and rationale to devise bright single optical eigenmodes that feature quantum-optical mode volumes of about 1  nm^{3}. Our findings rely on the development and application of a quasinormal mode theory that self-consistently treats fields and electron nonlocality, spill-out, and Landau damping around atomistic protrusions on a metallic nanoantenna. By outpacing Landau damping with radiation via properly designed antenna modes, the extremely localized modes become bright with radiation efficiencies reaching 30% and could provide up to 4×10^{7} times intensity enhancement.

Quasinormal modes expansions for nanoresonators made of absorbing dielectric materials: study of the role of static modes

The interaction of light with photonic resonators is determined by the eigenmodes of the system. Modal theories based on quasinormal modes provide a natural tool to calculate and understand light scattering by nanoresonators. We show that, in the case of resonators made of absorbing dielectric materials, eigenmodes with zero eigenfrequency (static modes) play a key role in the modal formalism. The excitation of static modes builds a non-resonant contribution to the modal expansion of the scattered field. This non-resonant term plays a crucial physical role since it largely contributes to the off-resonance signal to which resonances are added in amplitude, possibly leading to interference phenomena and Fano resonances. By considering light scattering by a silicon nanosphere, we quantify the impact of static modes. This study shows that the importance of static modes is not just formal. Static modes are of prime importance in an expansion truncated to only a few modes.

Degenerate quasi-normal mode theory for near-field radiation between plasmonic structures

Near-field radiation can exceed the blackbody radiation limit due to the contributions from evanescent waves. One promising approach to further enhance near-field radiation beyond existing bulk materials is to utilize metamaterials or metasurfaces made from subwavelength plasmonic structures. In this work, we investigate the near-field thermal radiation between complex plasmonic structures with higher-order symmetry and degeneracy, which is crucial for understanding the radiative heat exchange between metamaterials or metasurfaces at extremely small gaps. We demonstrate that the introduction of degeneracy can drastically boost near-field thermal radiation between plasmonic structures. The enhancement of near-field thermal radiation originates from the emergence of degenerate resonance modes and the secondary emission of thermal photons due to the nonzero coupling between the degenerate modes. Our study provides new pathways for designing high-intensity near-field thermal emitters and absorbers for thermophotovoltaics, thermal management, and infrared spectroscopy.

On the pole expansion of electromagnetic fields

In several publications, it has been shown how to calculate the near- or far-field properties for a given source or incident field using the resonant states, also known as quasi-normal modes. As previously noted, this pole expansion is not unique, and there exist many equivalent formulations with dispersive expansion coefficients. Here, we approach the pole expansion of the electromagnetic fields using the Mittag-Leffler theorem and obtain another set of formulations with constant weight factors for each pole. We compare the performance and applicability of these formulations using analytical and numerical examples. It turns out that the accuracy of all approaches is rather comparable with a slightly better global convergence of the approach based on a formulation with dispersive expansion coefficients. However, other expansions can be superior locally and are typically faster. Our work will help with selecting appropriate formulations for an efficient description of the electromagnetic response in terms of the resonant states.

Continuous family of exact Dispersive Quasi-Normal Modal (DQNM) expansions for dispersive photonic structures

In photonics, Dispersive Quasi-Normal Modes (DQNMs) refer to optical resonant modes, solutions of spectral problems associated with Maxwell's equations for open photonic structures involving dispersive media. Since these DQNMs are the constituents determining optical responses, studying DQNM expansion formalisms is the key to model the physical properties of a considered system. In this paper, we emphasize the non-uniqueness of the expansions related to the over-completeness of the set of modes and discuss a family of DQNM expansions depending on continuous parameters that can be freely chosen. These expansions can be applied to dispersive, anisotropic, and even non-reciprocal materials. As an example, we particularly demonstrate the modal analysis on a 2-D scattering model where the permittivity of a silicon object is drawn directly from actual measurement data.

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.

Extreme multiexciton emission from deterministically assembled single-emitter subwavelength plasmonic patch antennas

Coupling nano-emitters to plasmonic antennas is a key milestone for the development of nanoscale quantum light sources. One challenge, however, is the precise nanoscale positioning of the emitter in the structure. Here, we present a laser etching protocol that deterministically positions a single colloidal CdSe/CdS core/shell quantum dot emitter inside a subwavelength plasmonic patch antenna with three-dimensional nanoscale control. By exploiting the properties of metal-insulator-metal structures at the nanoscale, the fabricated single-emitter antenna exhibits a very high-Purcell factor (>72) and a brightness enhancement of a factor of 70. Due to the unprecedented quenching of Auger processes and the strong acceleration of the multiexciton emission, more than 4 photons per pulse can be emitted by a single quantum dot, thus increasing the device yield. Our technology can be applied to a wide range of photonic nanostructures and emitters, paving the way for scalable and reliable fabrication of ultra-compact light sources.

Bound state and non-Markovian dynamics of a quantum emitter around a surface plasmonic nanostructure

A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the excited QE will not relax completely to its ground state and is partially stabilized in its excited state after a long time. We develop some theoretical methods for investigating this problem and show how to form such a bound state and its effect on the non-Markovian decay dynamics. We put forward an efficient numerical approach for calculating the analytical part of the self-energy for frequency below the lower energy threshold. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range. With the above two quantities obtained, we show that the non-Markovian decay dynamics of an initially excited QE can be efficiently obtained by the method based on the Green's function expression for the evolution operator when a bound state exists. A general criterion for identifying the existence of a bound state is presented. The performances of the above methods are numerically demonstrated for a QE located around a metal nanosphere and in a gap plasmonic nanocavity. Numerical results show that these methods work well and the QE becomes partially stabilized in its excited state at a long time for the transition dipole moment beyond its critical value. In addition, it is also found that this critical value is heavily dependent on the distance between the QE and the metal surface, but nearly independent on the size of the nanosphere or the rod. Our methods can be utilized to understand the suppressed decay dynamics for a QE in an open quantum system and provide a general picture on how to form such a bound state.

Antenna surface plasmon emission by inelastic tunneling

Surface plasmons polaritons are mixed electronic and electromagnetic waves. They have become a workhorse of nanophotonics because plasmonic modes can be confined in space at the nanometer scale and in time at the 10 fs scale. However, in practice, plasmonic modes are often excited using diffraction-limited beams. In order to take full advantage of their potential for sensing and information technology, it is necessary to develop a microscale ultrafast electrical source of surface plasmons. Here, we report the design, fabrication and characterization of nanoantennas to emit surface plasmons by inelastic electron tunneling. The antenna controls the emission spectrum, the emission polarization, and enhances the emission efficiency by more than three orders of magnitude. We introduce a theoretical model of the antenna in good agreement with the results.

Channel competition in emitter-plasmon coupling

When an emitter is close to a plasmonic nanoantenna, besides coupling to the dipolar antenna mode, the emitter also considerably couples to a superposition of the high-order modes, referred to as a pseudomode. We comprehensively investigate the differences between the dipolar mode channel and the pseudomode channel in a representative system where a dipole emitter couples to a silver nanorod. The two channels are shown to be distinct in their mechanisms, characteristics (including chromatic dispersion and field distribution), and dependences on system parameters (including emitter-antenna distance, antenna geometry, and material loss). The study provides physical insight and reveals important design rules for controlling the competition between the two channels.

Computing resonant modes of circular cylindrical resonators by vertical mode expansions

Open subwavelength cylindrical resonators of finite height are widely used in various photonics applications. Circular cylindrical resonators are particularly important in nanophotonics, since they are relatively easy to fabricate and can be designed to exhibit different resonance effects. In this paper, an efficient and robust numerical method is developed for computing resonant modes of circular cylinders which may have a few layers and may be embedded in a layered background. The resonant modes are complex-frequency outgoing solutions of the Maxwell's equations with no sources or incident waves. The method uses field expansions in one-dimensional (1D) "vertical" modes to reduce the original three-dimensional eigenvalue problem to 1D problems and uses Chebyshev pseudospectral method to compute the 1D modes and set up the discretized eigenvalue problem. In addition, a new iterative scheme is developed so that the 1D nonlinear eigenvalue problems can be reliably solved. For metallic cylinders, the resonant modes are calculated based on analytic models for the dielectric functions of metals. The method is validated by comparisons with existing numerical results, and it is also used to explore subwavelength dielectric cylinders with high-Q resonances and analyze gold nanocylinders.

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.

Quantization of Quasinormal Modes for Open Cavities and Plasmonic Cavity Quantum Electrodynamics

We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multiplasmon or multiphoton Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off-diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission. To illustrate the practical application of the theory, we show examples using a gold nanorod dimer and a hybrid dielectric-metal cavity structure.

Quasi-confined ENZ mode in an anisotropic uniaxial thin slab

In this paper, we present a numerical modal study of a simple slab, made of an uniaxial anisotropic material having an "epsilon-near-zero" (ENZ) dielectric function, surrounded by vacuum. We use two Drude models with a different plasma frequency for the direction parallel and perpendicular to the slab surface as toy models to study the effect of uniaxial anisotropy of type I (∊_‖ > 0, ∊_⊥ < 0) and type II (∊_‖ < 0, ∊_⊥ > 0) on the different electromagnetic modes of the system. In addition to the so-called ENZ mode, studied in detail by Campione et. al [ Phys. Rev. B91, 121408(R) (2015)], the slab can support quasi-confined (QC) mode in the type I and type II anisotropy frequency ranges. We show that those modes exhibit a strong electric field enhancement, caused by the ENZ character of the dielectric function. In strong contrast with the ENZ mode, QC modes can have a strong electric field enhancement for thick slabs, with a Fabry-Perot-like electromagnetic field distribution spanning over the whole slab thickness. This opens the way for large electric field enhancement in thick slabs with QC ENZ modes. Thick slabs also allow metamaterial designs, giving the possibility to engineer the anisotropy of the effective dielectric function, opening interesting perspectives for the control of field enhancement of the ENZ QC modes and their integration in operating devices, such as detectors, sources, or modulators.

Quasinormal mode solvers for resonators with dispersive materials

Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This raises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM solvers for computing and normalizing the QNMs of micro- and nanoresonators made of highly dispersive materials. We benchmark several methods for three geometries, a two-dimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, with the perspective to elaborate standards for the computation of resonance modes.

Novel Modal Approximation Scheme for Plasmonic Transmission Problems

The concept of resonances and modes for the description of particle plasmons has recently received great interest, both in the context of efficient simulations as well as for an intuitive interpretation in physical terms. While resonance modes have been successfully employed for geometries whose optical response is governed by a few modes only, the resonance mode description exhibits considerable difficulties for larger nanoparticles with their richer mode spectra. We analyze the problem using a boundary element method approach together with a Mie solution for spherical particles, and identify the fixed link between the electric and magnetic components of the resonance modes as the main source for this shortcoming. We suggest a novel modal approximation scheme that allows us in principle to overcome this problem.

Photonics in highly dispersive media: the exact modal expansion

We present exact modal expansions for photonic systems including highly dispersive media. The formulas, based on a simple version of the Keldyš theorem, are very general since both permeability and permittivity can be dispersive, anisotropic, and even possibly nonreciprocal. A simple dispersive test case where both plasmonic and geometrical resonances strongly interact exemplifies the numerical efficiency of our approach.

Reconfigurable phase-change meta-absorbers with on-demand quality factor control

Perfect absorber type devices are well-suited to many applications, such as solar cells, spatial light modulators, bio-sensors, and highly-sensitive photo-detectors. In such applications, a method for the design and fabrication of devices in a simple and efficient way, while at the same time maintaining design control over the key performance characteristics of resonant frequency, reflection coefficient at resonance and quality factor, would be particularly advantageous. In this work we develop such a method, based on eigenmode analysis and critical coupling theory, and apply it to the design of reconfigurable phase-change metasurface absorber devices. To validate the method, the design and fabrication of a family of absorbers was carried out with a range of 'on-demand' quality factors, all operating at the same resonant frequency and able to be fabricated simply and simultaneously on the same chip. Furthermore, by switching the phase-change layer between its amorphous and crystalline states, we show that our devices can provide an active or reconfigurable functionality.

Highly Sensitive Refractive Index Sensors with Plasmonic Nanoantennas-Utilization of Optimal Spectral Detuning of Fano Resonances

We analyze and optimize the performance of coupled plasmonic nanoantennas for refractive index sensing. The investigated structure supports a sub- and super-radiant mode that originates from the weak coupling of a dipolar and quadrupolar mode, resulting in a Fano-type spectral line shape. In our study, we vary the near-field coupling of the two modes and particularly examine the influence of the spectral detuning between them on the sensing performance. Surprisingly, the case of matched resonance frequencies does not provide the best sensor. Instead, we find that the right amount of coupling strength and spectral detuning allows for achieving the ideal combination of narrow line width and sufficient excitation strength of the subradiant mode, and therefore results in optimized sensor performance. Our findings are confirmed by experimental results and first-order perturbation theory. The latter is based on the resonant state expansion and provides direct access to resonance frequency shifts and line width changes as well as the excitation strength of the modes. Based on these parameters, we define a figure of merit that can be easily calculated for different sensing geometries and agrees well with the numerical and experimental results.

Benchmarking five numerical simulation techniques for computing resonance wavelengths and quality factors in photonic crystal membrane line defect cavities

We present numerical studies of two photonic crystal membrane microcavities, a short line-defect cavity with a relatively low quality (Q) factor and a longer cavity with a high Q. We use five state-of-the-art numerical simulation techniques to compute the cavity Q factor and the resonance wavelength λ for the fundamental cavity mode in both structures. For each method, the relevant computational parameters are systematically varied to estimate the computational uncertainty. We show that some methods are more suitable than others for treating these challenging geometries.

Mode Matching for Optical Antennas

The emission rate of a point dipole can be strongly increased in the presence of a well-designed optical antenna. Yet, optical antenna design is largely based on radio-frequency rules, ignoring, e.g., Ohmic losses and non-negligible field penetration in metals at optical frequencies. Here, we combine reciprocity and Poynting's theorem to derive a set of optical-frequency antenna design rules for benchmarking and optimizing the performance of optical antennas driven by single quantum emitters. Based on these findings a novel plasmonic cavity antenna design is presented exhibiting a considerably improved performance compared to a reference two-wire antenna. Our work will be useful for the design of high-performance optical antennas and nanoresonators for diverse applications ranging from quantum optics to antenna-enhanced single-emitter spectroscopy and sensing.

Use of aperiodic Fourier modal method for calculating complex-frequency eigenmodes of long-period photonic crystal slabs

We present an iterative method for calculating complex-frequency eigenmodes of photonic crystal slabs with 1D periodicity based on the aperiodic Fourier modal method. By comparison with the known methods, we show that the proposed method is efficient for studying resonant properties of long-period photonic crystal slabs and diffraction gratings. We demonstrate that the method can be used to calculate the eigenmodes of the structures with periods up to at least 500λ. We discuss different aspects of the mode calculation, including convergence of the method, mode field and dispersion analysis. Potential applications of the presented method include investigation of periodic structures with defects and of quasiperiodic and random structures within the super-cell approach.

Perfect Thermal Emission by Nanoscale Transmission Line Resonators

Thermal radiation with a narrow-band emission spectrum is of great importance in a variety of applications such as infrared sensing, thermophotovoltaics, radiation cooling, and thermal circuits. Although resonant nanophotonic structures such as metamaterials and nanocavities have been demonstrated to achieve the narrow-band thermal emission, maximizing their radiation power toward perfect emission still remains challenging. Here, based on the recently developed quasi-normal mode theory, we prove that thermal emission from a nanoscale transmission line resonator can always be maximized by tuning the waveguiding loss of the resonator or bending the structure. By use of nanoscale transmission line resonators as basic building blocks, we experimentally demonstrate a new type of macroscopic perfect and tunable thermal emitters. Our experimental demonstration in conjunction with the general theoretical framework from the quasi-normal mode theory lays the foundation for designing tunable narrow-band thermal emitters with applications in thermal infrared light sources, thermal management, and infrared sensing and imaging.

Toward Multispectral Imaging with Colloidal Metasurface Pixels

Multispectral colloidal metasurfaces are fabricated that exhibit greater than 85% absorption and ≈100 nm linewidths by patterning film-coupled nanocubes in pixels using a fusion of bottom-up and top-down fabrication techniques over wafer-scale areas. With this technique, the authors realize a multispectral pixel array consisting of six resonances between 580 and 1125 nm and reconstruct an RGB image with 9261 color combinations.

Universal analytical modeling of plasmonic nanoparticles

Analytical expressions are applied to calculate the plasmonic spectra of nanoparticles with arbitrary morphology, in excellent agreement with experimental data.

Eigen-energy effects and non-orthogonality in the quasi-normal mode expansion of Maxwell equations

We derive a quasi-normal mode theory for three-dimensional scatterers, taking care to remove an hypothesis of weakly dispersive materials implicitely used in previous works. In our approach, the normalized modes remain unchanged, but the analytic expansion coefficients onto the set of QNM are modified. In particular, we take into account in a simple way the non-orthogonality of the modes, and we set up a rigourous frame, to treat the case where several QNMs are excited. Eventally, the complex concept of PML integration, previously introduced, becomes unnecessary, even to compute the QNM mode volume. Besides, crossover integrals of QNM fields over the whole space can now be written rigourously, as integrals on the finite volume of the scatterer, without surface terms.

Visible quantum plasmonics from metallic nanodimers

We report theoretical evidence that bulk nonlinear materials weakly interacting with highly localized plasmonic modes in ultra-sub-wavelength metallic nanostructures can lead to nonlinear effects at the single plasmon level in the visible range. In particular, the two-plasmon interaction energy in such systems is numerically estimated to be comparable with the typical plasmon linewidths. Localized surface plasmons are thus predicted to exhibit a purely nonclassical behavior, which can be clearly identified by a sub-Poissonian second-order correlation in the signal scattered from the quantized plasmonic field under coherent electromagnetic excitation. We explicitly show that systems sensitive to single-plasmon scattering can be experimentally realized by combining electromagnetic confinement in the interstitial region of gold nanodimers with local infiltration or deposition of ordinary nonlinear materials. We also propose configurations that could allow to realistically detect such an effect with state-of-the-art technology, overcoming the limitations imposed by the short plasmonic lifetime.

From Dark to Bright: First-Order Perturbation Theory with Analytical Mode Normalization for Plasmonic Nanoantenna Arrays Applied to Refractive Index Sensing

We present a first-order perturbation theory to calculate the frequency shift and linewidth change of photonic resonances in one- and two-dimensional periodic structures under modifications of the surrounding refractive index. Our method is based on the resonant state expansion, for which we extend the analytical mode normalization to periodic structures. We apply this theory to calculate the sensitivity of bright dipolar and much darker quadrupolar plasmonic modes by determining the maximum shift and optimal sensing volume.

Broad working bandwidth and "endlessly" single-mode guidance within hybrid silicon photonics

The successes of nonlinear photonics and hybrid silicon photonics with a growing variety of functional materials entail ever-enlarging bandwidths. It is best exemplified by parametric comb frequency generation. Such operation challenges the dielectric channel waveguide as the basis for guidance, because of the adverse advent of higher order modes at short wavelengths. Surprisingly, the popular mechanism of endlessly single-mode guidance [Opt. Lett.22, 961 (1997).] operating in photonic crystal fibers has not been transposed within silicon photonics yet. We outline here the strategy and potential of this approach within planar and hybrid silicon photonics, whereby in-plane and vertical confinement are shown to be amenable to near-single-mode behavior in the typical silicon band, i.e., λ=1.1  μm to ∼5  μm.

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.