Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators

Quantum engineering of the radiative properties of a nanoscale mesoscopic system

Despite the recent advances in quantum technology, the problem of controlling the light emission properties of quantum emitters used in numerous applications remains: a large spectral width, low intensity, blinking, photodegradation, biocompatibility, etc. In this work, we present the theoretical and experimental investigation of quantum light sources - mesoscopic systems consisting of fluorescent molecules in a thin polydopamine layer coupled with metallic or dielectric nanoparticles. Polydopamines possess many attractive adhesive and optical properties that promise their use as host media for dye molecules. However, numerous attempts to incorporate fluorescent molecules into polydopamines have failed, as polydopamine has been shown to be a very efficient fluorescence quencher through Förster resonance energy transfer and/or photoinduced electron transfer. Using the system as an example, we demonstrate new insights into the interactions between molecules and electromagnetic fields by carefully shaping its energy levels through strong matter-wave coupling of molecules to metallic nanoparticles. We show that the strong coupling effectively suppresses the quenching of fluorescent molecules in polydopamine, opening new possibilities for imaging.

Influence of molecular structure on the coupling strength to a plasmonic nanoparticle and hot carrier generation

Strong coupling between metal nanoparticles and molecules mixes their excitations, creating new eigenstates with modified properties such as altered chemical reactivity, different relaxation pathways or modified phase transitions. Here, we explore excited state plasmon-molecule coupling and discuss how strong coupling together with a changed orientation and number of an asymmetric molecule affects the generation of hot carriers in the system. We used a promising plasmonic material, magnesium, for the nanoparticle and coupled it with CPDT molecules, which are used in organic optoelectronic materials for organic electronic applications due to their facile modification, electron-rich structure, low band gap, high electrical conductivity and good charge transport properties. By employing computational quantum electronic tools we demonstrate the existence of a strong coupling mediated charge transfer plasmon whose direction, magnitude, and spectral position can be tuned. We find that the orientation of CPDT changes the nanoparticle-molecule gap for which maximum charge separation occurs, while larger gaps result in trapping hot carriers within the moieties due to weaker interactions. This research highlights the potential for tuning hot carrier generation in strongly coupled plasmon-molecule systems for enhanced energy generation or excited state chemistry.

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.

Spectroscopy in Nanoscopic Cavities: Models and Recent Experiments

The ability of nanophotonic cavities to confine and store light to nanoscale dimensions has important implications for enhancing molecular, excitonic, phononic, and plasmonic optical responses. Spectroscopic signatures of processes that are ordinarily exceedingly weak such as pure absorption and Raman scattering have been brought to the single-particle limit of detection, while new emergent polaritonic states of optical matter have been realized through coupling material and photonic cavity degrees of freedom across a wide range of experimentally accessible interaction strengths. In this review, we discuss both optical and electron beam spectroscopies of cavity-coupled material systems in weak, strong, and ultrastrong coupling regimes, providing a theoretical basis for understanding the physics inherent to each while highlighting recent experimental advances and exciting future directions.

Relations between near-field enhancements and Purcell factors in hybrid nanostructures of plasmonic antennas and dielectric cavities

Strong near-field enhancements (NFEs) of nanophotonic structures are believed to be closely related to high Purcell factors (FP). Here, we theoretically show that the correlation is partially correct; the extinction cross section (σ) response is also critical in determining FP. The divergence between NFE and FP is especially pronounced in plasmonic-dielectric hybrid systems, where the plasmonic antenna supports dipolar plasmon modes and the dielectric cavity hosts Mie-like resonances. The cavity's enhanced-field environment can boost the antenna's NFEs, but the FP is not increased concurrently due to the larger effective σ that is intrinsic to the FP calculations. Interestingly, the peak FP for the coupled system can be predicted by using the NFE and σ responses. Furthermore, the limits for FP of coupled systems are considered; they are determined by the sum of the FP of a redshifted (or modified, if applicable) antenna and an individual cavity. This contrasts starkly with the behavior of NFE which is closely associated with the multiplicative effects of the NFEs provided by the antenna and the dielectric cavity. The differing behaviors of NFE and FP in hybrid cavities have varied impacts on relevant nanophotonic applications such as fluorescence, Raman scattering and enhanced light-matter interactions.

Efficient method for modeling large-scale arrays of optical nanoresonators based on the coupling theory of quasinormal mode

We propose an efficient method for calculating the electromagnetic field of a large-scale array of optical nanoresonators based on the coupling theory of quasinormal mode (QNM). In this method, two approaches of the scattered-field reconstruction and stationary-phase-principle calculated plane-wave expansion are developed to obtain the regularized QNM (RQNM) in different regions. This accurate and efficient calculation of RQNM resolves the far-field divergence issue of QNMs in the QNM-coupling theory, thus enabling a rapid computation of the electromagnetic field of a large-scale array of optical nanoresonators, which is a challenging task for full-wave numerical methods. Using this method, we consider the numerical example of the radiation problem of a single point source in a large-scale periodic array of optical nanoantennas. In comparison to full-wave numerical methods, this method significantly reduces the computation time by 1∼2 orders of magnitude while maintaining accuracy. The high computational efficiency and physical intuitiveness of the method enables to clarify the impact of array size (exceeding 50 × 50 wavelengths), period and field-coupling range (far beyond the tight-binding approximation) on the optical response. The proposed method and results can provide an efficient tool and guidance for the design of large-scale arrays of optical nanoresonators.

Deep ultraviolet AlGaN-multiple quantum wells with photoluminescence enhanced by topological corner state

The AlGaN-based deep ultraviolet light-emitting diode (DUV LED) has advantages of environmentally friendly materials, tunable emission wavelength, and easy miniaturization. However, an increase in Al composition leads to a decline in the lattice quality, thereby reducing the internal quantum efficiency (IQE). In addition, the light extraction efficiency (LEE) is limited due to the strong transverse magnetization polarization emission from the multiple quantum wells. Here, we designed the topological corner structure in AlGaN-MQWs, and the high electric field intensity in a tiny space at the corner results in an extremely high local density of optical states (LDOS), which could shorten the luminescence decay time of the emitter and increase the radiative rate by 26 times. Meanwhile, because the excited topological corner state resonance mode is a transverse-electric mode, enhancing only the transverse-electric luminescence without any gain for transverse-magnetic luminescence, thereby significantly improving the light extraction efficiency. Finally, according to theoretical calculations, the IQE could reach 68.75% at room temperature.

Photonic Flatband Resonances in Multiple Light Scattering

We introduce the concept of photonic flatband resonances and demonstrate it for an array of high-index dielectric particles. We employ the multiple Mie scattering theory and demonstrate that both short- and long-range interactions between the resonators are crucial for the emerging collective resonances and their associated photonic flatbands. By examining both near- and far-field characteristics, we uncover how the flatbands emerge due to a fine tuning of resonators' radiation fields, and predict that hybridization of a flatband resonance with an electric hot spot can lead to giant values of the Purcell factor for the electric dipolar emitters.

Hybrid cavity-antenna architecture for strong and tunable sideband-selective molecular Raman scattering enhancement

Plasmon resonances at the surface of metallic antennas allow for extreme enhancement of Raman scattering. Intrinsic to plasmonics, however, is that extreme field confinement lacks precise spectral control, which would hold great promise in shaping the optomechanical interaction between light and molecular vibrations. We demonstrate an experimental platform composed of a plasmonic nanocube-on-mirror antenna coupled to an open, tunable Fabry-Perot microcavity for selective addressing of individual vibrational lines of molecules with strong Raman scattering enhancement. Multiple narrow and intense optical resonances arising from the hybridization of the cavity modes and the plasmonic broad resonance are used to simultaneously enhance the laser pump and the local density of optical states, and are characterized using rigorous modal analysis. The versatile bottom-up fabrication approach permits quantitative comparison with the bare nanocube-on-mirror system, both theoretically and experimentally. This shows that the hybrid system allows for similar SERS enhancement ratios with narrow optical modes, paving the way for dynamical backaction effects in molecular optomechanics.

Manipulating the quasi-normal modes of radially symmetric resonators

The frequency response of a resonator is governed by the locations of its quasi-normal modes in the complex frequency plane. The real part of the quasi-normal mode determines the resonance frequency and the imaginary part determines the width of the resonance. For applications such as energy harvesting and sensing, the ability to manipulate the frequency, linewidth and multipolar nature of resonances is key. Here, we derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the permittivity of the structure to place a resonance at a particular complex frequency. Next, we employ quasi-normal mode perturbation theory to design radially graded structures with resonances at desired frequencies.

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.

The Rise and Current Status of Polaritonic Photochemistry and Photophysics

The interaction between molecular electronic transitions and electromagnetic fields can be enlarged to the point where distinct hybrid light-matter states, polaritons, emerge. The photonic contribution to these states results in increased complexity as well as an opening to modify the photophysics and photochemistry beyond what normally can be seen in organic molecules. It is today evident that polaritons offer opportunities for molecular photochemistry and photophysics, which has caused an ever-rising interest in the field. Focusing on the experimental landmarks, this review takes its reader from the advent of the field of polaritonic chemistry, over the split into polariton chemistry and photochemistry, to present day status within polaritonic photochemistry and photophysics. To introduce the field, the review starts with a general description of light-matter interactions, how to enhance these, and what characterizes the coupling strength. Then the photochemistry and photophysics of strongly coupled systems using Fabry-Perot and plasmonic cavities are described. This is followed by a description of room-temperature Bose-Einstein condensation/polariton lasing in polaritonic systems. The review ends with a discussion on the benefits, limitations, and future developments of strong exciton-photon coupling using organic molecules.

Ultrasmall InGa(As)P Dielectric and Plasmonic Nanolasers

Nanolasers have great potential for both on-chip light sources and optical barcoding particles. We demonstrate ultrasmall InGaP and InGaAsP disk lasers with diameters down to 360 nm (198 nm in height) in the red spectral range. Optically pumped, room-temperature, single-mode lasing was achieved from both disk-on-pillar and isolated particles. When isolated disks were placed on gold, plasmon polariton lasing was obtained with Purcell-enhanced stimulated emission. UV lithography and plasma ashing enabled wafer-scale fabrication of nanodisks with an intended random size variation. Silica-coated nanodisk particles generated stable subnanometer spectra from within biological cells across an 80 nm bandwidth from 635 to 715 nm.

Q-Factor Optimization of Modes in Ordered and Disordered Photonic Systems Using Non-Hermitian Perturbation Theory

The quality factor, Q, of photonic resonators permeates most figures of merit in applications that rely on cavity-enhanced light-matter interaction such as all-optical information processing, high-resolution sensing, or ultralow-threshold lasing. As a consequence, large-scale efforts have been devoted to understanding and efficiently computing and optimizing the Q of optical resonators in the design stage. This has generated large know-how on the relation between physical quantities of the cavity, e.g., Q, and controllable parameters, e.g., hole positions, for engineered cavities in gaped photonic crystals. However, such a correspondence is much less intuitive in the case of modes in disordered photonic media, e.g., Anderson-localized modes. Here, we demonstrate that the theoretical framework of quasinormal modes (QNMs), a non-Hermitian perturbation theory for shifting material boundaries, and a finite-element complex eigensolver provide an ideal toolbox for the automated shape optimization of Q of a single photonic mode in both ordered and disordered environments. We benchmark the non-Hermitian perturbation formula and employ it to optimize the Q-factor of a photonic mode relative to the position of vertically etched holes in a dielectric slab for two different settings: first, for the fundamental mode of L3 cavities with various footprints, demonstrating that the approach simultaneously takes in-plane and out-of-plane losses into account and leads to minor modal structure modifications; and second, for an Anderson-localized mode with an initial Q of 200, which evolves into a completely different mode, displaying a threefold reduction in the mode volume, a different overall spatial location, and, notably, a 3 order of magnitude increase in Q.

Highly Efficient Single-Exciton Strong Coupling with Plasmons by Lowering Critical Interaction Strength at an Exceptional Point

The single-exciton strong coupling with the localized plasmon mode (LPM) at room temperature is highly desirable for exploiting quantum technology. However, its realization has been a very low probability event due to the harsh critical conditions, severely compromising its application. Here, we present a highly efficient approach for achieving such a strong coupling by reducing the critical interaction strength at the exceptional point based upon the damping inhibition and matching of the coupled system, instead of enhancing the coupling strength to overcome the system's large damping. Experimentally, we compress the LPM's damping linewidth from about 45 nm to about 14 nm using a leaky Fabry-Perot cavity, a good match to the excitonic linewidth of about 10 nm. This method dramatically relaxes the harsh requirement in mode volume by more than an order of magnitude and allows a maximum direction angle of the exciton dipole relative to the mode field of up to around 71.9°, significantly improving the success rate of achieving the single-exciton strong coupling with LPMs from about 1% to about 80%.

Bloch-Surface Plasmon Polariton Enhanced Amplified and Directional Spontaneous Emission from Plasmonic Hexagonal Nanohole Array

The light-matter interactions at nanoscale can be enhanced by Bloch-surface plasmon polariton (Bloch-SPP) on the plasmonic lattice. An Ag nanohole array in hexagonal arrangement served as an optical cavity to realize the directional and polarized amplified spontaneous emission (ASE) of R6G. A 100-fold enhanced ASE was observed at 15° emission angle under TM polarization when the pump power density exceeded the threshold of 198 W/cm² based on the degenerated high state density modes. Moreover, a specific polarization dependence of ASE was modulated by the Bloch-SPP modes, and the degree of polarization was enhanced from 1.3 to 2.1 when the pump power density exceeded the threshold of ASE. This work clarifies the interaction between the gain media and plasmonic systems, which lays a foundation for the plasmonic device designing.

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.

Dimers of Plasmonic Nanocubes to Reach Single-Molecule Strong Coupling with High Emission Yields

Reaching reproducible strong coupling between a quantum emitter and a plasmonic resonator at room temperature, while maintaining high emission yields, would make quantum information processing with light possible outside of cryogenic conditions. We theoretically propose to exploit the high local curvatures at the tips of plasmonic nanocubes to reach Purcell factors of >10⁶ at visible frequencies, rendering single-molecule strong coupling more easily accessible than with the faceted spherical nanoparticles used in recent experimental demonstrations. In the case of gold nanocube dimers, we highlight a trade-off between coupling strength and emission yield that depends on the nanocube size. Electrodynamic simulations on silver nanostructures are performed using a realistic dielectric constant, as confirmed by scattering spectroscopy performed on single nanocubes. Dimers of silver nanocubes feature Purcell factors similar to those of gold while allowing emission yields of >60%, thus providing design rules for efficient strongly coupled hybrid nanostructures at room temperature.

A hybrid photonic-plasmonic resonator based on a partially encapsulated 1D photonic crystal waveguide and a plasmonic nanoparticle

In this paper, a hybrid photonic-plasmonic resonator is proposed. The device consists of a partially encapsulated 1D photonic crystal waveguide and a plasmonic nanoparticle to yield high radiation efficiency for integrated photonic platforms, owing to a high Q-factor and a small mode volume. The design of the resonator is accomplished in two consecutive steps: first of all, a partially encapsulated photonic crystal nanobeam with a robust mechanical stability and a high-Q factor is prepared; secondly, a plasmonic nanoparticle is placed on the surface of the nanobeam to interact the optical mode with the localized surface plasmons of the gold nanoparticle which is being present in the vicinity of the radiating dipole. Strongly enhanced electromagnetic field, regenerated through the optical mode field inside the hybrid resonator, enables to reduce the optical mode volume of the device and significantly enhance the Purcell factor.

Quasinormal Mode Expansion Theory for Mesoscale Plasmonic Nanoresonators: An Analytical Treatment of Nonclassical Electromagnetic Boundary Condition

Nonclassical quantum effects will significantly affect the optical response of plasmonic nanoresonators with mesoscale feature sizes between about 2 and 20 nm, and can be fully described by the nonclassical electromagnetic boundary condition (NEBC) expressed with the surface-response Feibelman d parameters. In this Letter, a quasinormal mode (QNM) expansion theory under the NEBC is proposed. By adopting the easily solved classical QNMs under the classical electromagnetic boundary condition as a complete set of basis functions, rigorous expansions of the nonclassical source-free QNMs and source-excited electromagnetic field under the nonperturbative NEBC are provided. With the obtained nonclassical QNMs as basis functions, expansions of the nonclassical source-excited field and Green's function tensor are further obtained. These expansions have a fully analytical dependence on the NEBC and classical QNMs, thus transparently unveiling their impact on the nonclassical QNMs and source-excited electromagnetic field. For instance, a new expression of mode volume is proposed for analyzing the nonclassically corrected Purcell factor. The proposed theory is physically intuitive and computationally efficient which is enabled by the dominance of a small set of classical QNMs, thus providing an efficient tool for understanding and designing mesoscale plasmonic nanoresonators.

One-Step Exfoliation Method for Plasmonic Activation of Large-Area 2D Crystals

Advanced exfoliation techniques are crucial for exploring the intrinsic properties and applications of 2D materials. Though the recently discovered Au-enhanced exfoliation technique provides an effective strategy for the preparation of large-scale 2D crystals, the high cost of gold hinders this method from being widely adopted in industrial applications. In addition, direct Au contact could significantly quench photoluminescence (PL) emission in 2D semiconductors. It is therefore crucial to find alternative metals that can replace gold to achieve efficient exfoliation of 2D materials. Here, the authors present a one-step Ag-assisted method that can efficiently exfoliate many large-area 2D monolayers, where the yield ratio is comparable to Au-enhanced exfoliation method. Differing from Au film, however, the surface roughness of as-prepared Ag films on SiO₂ /Si substrate is much higher, which facilitates the generation of surface plasmons resulting from the nanostructures formed on the rough Ag surface. More interestingly, the strong coupling between 2D semiconductor crystals (e.g., MoS₂ , MoSe₂ ) and Ag film leads to a unique PL enhancement that has not been observed in other mechanical exfoliation techniques, which can be mainly attributed to enhanced light-matter interaction as a result of extended propagation of surface plasmonic polariton (SPP). This work provides a lower-cost and universal Ag-assisted exfoliation method, while at the same time offering enhanced SPP-matter interactions.

Scaling Theory of Wave Confinement in Classical and Quantum Periodic Systems

Functional defects in periodic media confine waves-acoustic, electromagnetic, electronic, spin, etc.-in various dimensions, depending on the structure of the defect. While defects are usually modeled by a superlattice with a typical band-structure representation of energy levels, determining the confinement associated with a given band is highly nontrivial and no analytical method is known to date. Therefore, we propose a rigorous method to classify the dimensionality of wave confinement. Starting from the confinement energy and the mode volume, we use finite-size scaling to find that ratios of these quantities raised to certain powers yield the confinement dimensionality of each band. Our classification has negligible additional computational costs compared to a band structure calculation and is valid for any type of wave, both quantum and classical, and in any dimension. In the quantum regime, we illustrate our method on electronic confinement in 2D hexagonal boron nitride (BN) with a nitrogen vacancy, in agreement with previous results. In the classical case, we study a three-dimensional photonic band gap cavity superlattice, where we identify novel acceptorlike behavior. We briefly discuss the generalization to quasiperiodic lattices.

Metasurface optofluidics for dynamic control of light fields

The ability to manipulate light and liquids on integrated optofluidics chips has spurred a myriad of important developments in biology, medicine, chemistry and display technologies. Here we show how the convergence of optofluidics and metasurface optics can lead to conceptually new platforms for the dynamic control of light fields. We first demonstrate metasurface building blocks that display an extreme sensitivity in their scattering properties to their dielectric environment. These blocks are then used to create metasurface-based flat optics inside microfluidic channels where liquids with different refractive indices can be directed to manipulate their optical behaviour. We demonstrate the intensity and spectral tuning of metasurface colour pixels as well as on-demand optical elements. We finally demonstrate automated control in an integrated meta-optofluidic platform to open up new display functions. Combined with large-scale microfluidic integration, our dynamic-metasurface flat-optics platform could open up the possibility of dynamic display, imaging, holography and sensing applications.

Few-mode field quantization for multiple emitters

The control of the interaction between quantum emitters using nanophotonic structures holds great promise for quantum technology applications, while its theoretical description for complex nanostructures is a highly demanding task as the electromagnetic (EM) modes form a high-dimensional continuum. We here introduce an approach that permits a quantized description of the full EM field through a small number of discrete modes. This extends the previous work in ref. (I. Medina, F. J. García-Vidal, A. I. Fernández-Domínguez, and J. Feist, "Few-mode field quantization of arbitrary electromagnetic spectral densities," Phys. Rev. Lett., vol. 126, p. 093601, 2021) to the case of an arbitrary number of emitters, without any restrictions on the emitter level structure or dipole operators. The low computational demand of this method makes it suitable for studying dynamics for a wide range of parameters. We illustrate the power of our approach for a system of three emitters placed within a hybrid metallodielectric photonic structure and show that excitation transfer is highly sensitive to the properties of the hybrid photonic-plasmonic modes.

Mode-dependent energy exchange between near- and far-field through silicon-supported single silver nanorods

Optical antenna effects endow plasmonic nanoparticles with the capability to enhance and control various types of light-matter interaction. Most reported plasmonic systems can be regarded as single-channel nanoantennas, which rely only on a bright dipole plasmon mode for energy exchange between near- and far-field. Herein we demonstrate a dual-channel plasmonic system that can separate the excitation and emission processes into two energy exchange pathways mediated by the different plasmon modes, offering a higher degree of freedom for the manipulation of light-matter interaction. Our system, consisting of high-aspect-ratio Ag nanorods and Si substrates, can support a series of bright and dark plasmon modes with distinct near- and far-field properties and generate relatively intensive local field enhancement in the gap region. As a proof-of-principle, we take plasmon-enhanced fluorescence of dye molecules as an example to reveal the energy exchange mechanism in the dual-channel plasmonic system. Such a system is potentially also useful for manipulating other types of light-matter interaction. Our work represents a step toward the utilization of a broader class of plasmon resonance for the development of optical antennas and various on-chip nanophotonic components.

Purcell effect with extended sources: the role of the cross density of states

We analyze the change in the spontaneous decay rate, or Purcell effect, of an extended quantum emitter in a structured photonic environment. Based on a simple theory, we show that the cross density of states is the central quantity driving interferences in the emission process. Using numerical simulations in realistic photonic cavity geometries, we demonstrate that a structured cross density of states can induce subradiance or superradiance, and change substantially the emission spectrum. Interestingly, the spectral lineshape of the Purcell effect of an extended source cannot be predicted from the sole knowledge of the spectral dependence of the local density of states.

Spontaneous emission enhancement by rotationally-symmetric optical nanoantennas: impact of radially and axially propagating surface plasmon polaritons

The excitation and radiation properties of rotationally-symmetric optical nanoantennas are independent of the azimuth angle, which enables great convenience and superior performances in practical applications. However, for rotationally-symmetric nanoantennas, the physical mechanisms behind their resonance properties remain to be clarified. In this paper, firstly, for a simple single-nanocylinder-on-mirror antenna (S-antenna), we establish a first-principles-based semianalytical model of surface plasmon polariton (SPP) by considering an intuitive multiple-scattering process of the radially-propagating gap surface plasmon (RGSP) in the nanogap and the axially-propagating surface plasmon (ASP) on the nanocylinder. The model can comprehensively reproduce all the radiation properties of the S-antenna such as the total and radiative emission rates, SPP excitation rates, and far-field radiation pattern. The model indicates that when the antenna radius is small (respectively, large), the enhancement of spontaneous emission mainly results from the resonance of ASP (respectively, RGSP). To show the wide applicability of the SPP model along with its unveiled decisive role of the RGSP and ASP in the spontaneous emission enhancement for other rotationally-symmetric nanoantennas of cylindrical shapes, we extend the SPP model to a more complex ring-nanocylinder-on-mirror antenna (R-antenna) that supports two ASPs. Moreover, to provide an explicit explanation of the resonance properties of the R-antenna, we further establish a semianalytical model for the resonant modes (called quasinormal modes, QNMs) supported by the R-antenna based on the SPP model, which quantitatively reveals the role of the RGSP and ASP in forming the antenna resonant modes and the resultant enhancement of spontaneous emission.

Computation of transverse-electric polarized optical eigenstates in dielectric systems based on perfectly matched layer

The optical resonance problem is an eigenproblem with an exponential-growing boundary condition imposed at infinity. This inconvenient boundary condition is caused by the openness of dielectric systems, and it is explained as the effect of retardation. Following our previous work [Jiang and Xiang, Phys. Rev. A 102, 053704 (2020)2469-992610.1103/PhysRevA.102.053704] where a perfectly-matched-layer method is developed for transverse-magnetic modes, we extend the method in this paper to transverse-electric modes and apply it to study mode symmetries. The method is implemented by introducing an extra layer to absorb outgoing waves at the far-field region, based on which we derive a damping eigenequation. A finite-element-based numerical approach is developed to compute the eigenstates of the damping eigenproblem. Our method is validated by application to the circular cavity and comparison with exact analytical solutions of whispering-gallery modes. We apply the method to the elliptic cavity to study the even- and odd-symmetric optical eigenstates. We also apply the method to trace the evolution of a pair of degenerate eigenstates with cavity shapes smoothly deformed from circles to squares.

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.

Plasmonic Nanocavity Induced Coupling and Boost of Dark Excitons in Monolayer WSe2 at Room Temperature

Spin-forbidden excitons in monolayer transition metal dichalcogenides are optically inactive at room temperature. Probing and manipulating these dark excitons are essential for understanding exciton spin relaxation and valley coherence of these 2D materials. Here, we show that the coupling of dark excitons to a metal nanoparticle-on-mirror cavity leads to plasmon-induced resonant emission with the intensity comparable to that of the spin-allowed bright excitons. A three-state quantum model combined with full-wave electrodynamic calculations reveals that the radiative decay rate of the dark excitons can be enhanced by nearly 6 orders of magnitude through the Purcell effect, therefore compensating its intrinsic nature of weak radiation. Our nanocavity approach provides a useful paradigm for understanding the room-temperature dynamics of dark excitons, potentially paving the road for employing dark exciton in quantum computing and nanoscale optoelectronics.

Enhanced light-matter interaction in two-dimensional transition metal dichalcogenides

Two-dimensional (2D) transition metal dichalcogenide (TMDC) materials, such as MoS₂, WS₂, MoSe₂, and WSe₂, have received extensive attention in the past decade due to their extraordinary electronic, optical and thermal properties. They evolve from indirect bandgap semiconductors to direct bandgap semiconductors while their layer number is reduced from a few layers to a monolayer limit. Consequently, there is strong photoluminescence in a monolayer (1L) TMDC due to the large quantum yield. Moreover, such monolayer semiconductors have two other exciting properties: large binding energy of excitons and valley polarization. These properties make them become ideal materials for various electronic, photonic and optoelectronic devices. However, their performance is limited by the relatively weak light-matter interactions due to their atomically thin form factor. Resonant nanophotonic structures provide a viable way to address this issue and enhance light-matter interactions in 2D TMDCs. Here, we provide an overview of this research area, showcasing relevant applications, including exotic light emission, absorption and scattering features. We start by overviewing the concept of excitons in 1L-TMDC and the fundamental theory of cavity-enhanced emission, followed by a discussion on the recent progress of enhanced light emission, strong coupling and valleytronics. The atomically thin nature of 1L-TMDC enables a broad range of ways to tune its electric and optical properties. Thus, we continue by reviewing advances in TMDC-based tunable photonic devices. Next, we survey the recent progress in enhanced light absorption over narrow and broad bandwidths using 1L or few-layer TMDCs, and their applications for photovoltaics and photodetectors. We also review recent efforts of engineering light scattering, e.g., inducing Fano resonances, wavefront engineering in 1L or few-layer TMDCs by either integrating resonant structures, such as plasmonic/Mie resonant metasurfaces, or directly patterning monolayer/few layers TMDCs. We then overview the intriguing physical properties of different van der Waals heterostructures, and their applications in optoelectronic and photonic devices. Finally, we draw our opinion on potential opportunities and challenges in this rapidly developing field of research.

Strong Purcell enhancement at telecom wavelengths afforded by spinel Fe3O4 nanocrystals with size-tunable plasmonic properties

Developments in the field of nanoplasmonics have the potential to advance applications from information processing and telecommunications to light-based sensing. Traditionally, nanoscale noble metals such as gold and silver have been used to achieve the targeted enhancements in light-matter interactions that result from the presence of localized surface plasmons (LSPs). However, interest has recently shifted to intrinsically doped semiconductor nanocrystals (NCs) for their ability to display LSP resonances (LSPRs) over a much broader spectral range, including the infrared (IR). Among semiconducting plasmonic NCs, spinel metal oxides (sp-MOs) are an emerging class of materials with distinct advantages in accessing the telecommunications bands in the IR and affording useful environmental stability. Here, we report the plasmonic properties of Fe₃O₄ sp-MO NCs, known previously only for their magnetic functionality, and demonstrate their ability to modify the light-emission properties of telecom-emitting quantum dots (QDs). We establish the synthetic conditions for tuning sp-MO NC size, composition and doping characteristics, resulting in unprecedented tunability of electronic behavior and plasmonic response over 450 nm. In particular, with diameter-dependent variations in free-electron concentration across the Fe₃O₄ NC series, we introduce a strong NC size dependency onto the optical response. In addition, our observation of plasmonics-enhanced decay rates from telecom-emitting QDs reveals Purcell enhancement factors for simple plasmonic-spacer-emitter sandwich structures up to 51-fold, which are comparable to values achieved previously only for emitters in the visible range coupled with conventional noble metal NCs.

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.

Nanophotonic Chiral Sensing: How Does It Actually Work?

Nanophotonic chiral sensing has recently attracted a lot of attention. The idea is to exploit the strong light-matter interaction in nanophotonic resonators to determine the concentration of chiral molecules at ultralow thresholds, which is highly attractive for numerous applications in life science and chemistry. However, a thorough understanding of the underlying interactions is still missing. The theoretical description relies on either simple approximations or on purely numerical approaches. We close this gap and present a general theory of chiral light-matter interactions in arbitrary resonators. Our theory describes the chiral interaction as a perturbation of the resonator modes, also known as resonant states or quasi-normal modes. We observe two dominant contributions: A chirality-induced resonance shift and changes in the modes' excitation and emission efficiencies. Our theory brings deep insights for tailoring and enhancing chiral light-matter interactions. Furthermore, it allows us to predict spectra much more efficiently in comparison to conventional approaches. This is particularly true, as chiral interactions are inherently weak and therefore perturbation theory fits extremely well for this problem.

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.

General Framework of Canonical Quasinormal Mode Analysis for Extreme Nano-optics

Optical phenomena associated with an extremely localized field should be understood with considerations of nonlocal and quantum effects, which pose a hurdle to conceptualize the physics with a picture of eigenmodes. Here we first propose a generalized Lorentz model to describe general nonlocal media under linear mean-field approximation and formulate source-free Maxwell's equations as a linear eigenvalue problem to define the quasinormal modes. Then we introduce an orthonormalization scheme for the modes and establish a canonical quasinormal mode framework for general nonlocal media. Explicit formalisms for metals described by a quantum hydrodynamic model and polar dielectrics with nonlocal response are exemplified. The framework enables for the first time a direct modal analysis of mode transition in the quantum tunneling regime and provides physical insights beyond usual far-field spectroscopic analysis. Applied to nonlocal polar dielectrics, the framework also unveils the important roles of longitudinal phonon polaritons in optical response.

Spontaneous Emission Enhancement by a Rectangular-Aperture Optical Nanoantenna: An Intuitive Semi-Analytical Model of Surface Plasmon Polaritons

The spontaneous-emission enhancement effect of a single metallic rectangular-aperture optical nanoantenna on a SiO2 substrate was investigated theoretically. By considering the excitation and multiple scattering of surface plasmon polaritons (SPPs) in the aperture, an intuitive and comprehensive SPP model was established. The model can comprehensively predict the total spontaneous emission rate, the radiative emission rate and the angular distribution of the far-field emission of a point source in the aperture. Two phase-matching conditions are derived from the model for predicting the resonance and show that the spontaneous-emission enhancement by the antenna comes from the Fabry–Perot resonance of the SPP in the aperture. In addition, when scanning the position of the point source and the aperture length, the SPP model does not need to repeatedly solve the Maxwell’s equations, which shows a superior computational efficiency compared to the full-wave numerical method.

Integrated Whispering-Gallery-Mode Resonator for Solid-State Coherent Quantum Photonics

Tailored photonics cavities enhance light-matter interactions, ultimately enabling a fully coherent quantum interface. Here, we report an integrated microdisk cavity containing self-assembled quantum dots to coherently route photons between different access waveguides. We measure a Purcell factor of F_exp = 6.9 ± 0.9 for a cavity quality factor of about 10,000, allowing us to observe clear signatures of coherent scattering of photons by the quantum dots. We show how this integrated system can coherently reroute photons between the drop and bus ports and how this routing is controlled by detuning the quantum dot and resonator or through the strength of the excitation beam, where a critical photon number less than one photon per lifetime is required. We discuss the strengths and limitations of this approach, focusing on how the coherent scattering and single-photon nonlinearity can be used to increase the efficiency of quantum devices such as routers or Bell-state analyzers.

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.

Quantum Optics in Nanostructures

This review is devoted to the study of effects of quantum optics in nanostructures. The mechanisms by which the rates of radiative and nonradiative decay are modified are considered in the model of a two-level quantum emitter (QE) near a plasmonic nanoparticle (NP). The distributions of the intensity and polarization of the near field around an NP are analyzed, which substantially depend on the polarization of the external field and parameters of plasmon resonances of the NP. The effects of quantum optics in the system NP + QE plus external laser field are analyzed-modification of the resonance fluorescence spectrum of a QE in the near field, bunching/antibunching phenomena, quantum statistics of photons in the spectrum, formation of squeezed states of light, and quantum entangled states in these systems.

Efficient spontaneous emission by metal-dielectric antennas; antenna Purcell factor explained

The rate of spontaneous emission from an optical emitter can be greatly enhanced using a metallic optical antenna at the penalty of efficiency. In this paper we propose a metal-dielectric antenna that eliminates the tradeoff between spontaneous emission enhancement and radiative efficiency by using nanoscopic dielectric structures at the antenna tips. This tradeoff occurs due to Ohmic loss and is further exacerbated by electron surface collisions. We find that our metal-dielectric antenna can enhance spontaneous emission by a factor 5 × 10⁵ with efficiency = 70%, greatly exceeding the radiative efficiency of a purely metallic antenna with similar enhancement. Moreover, the metal-dielectric antenna design strategy is naturally amenable to short-distance optical communications applications. We go on to discuss the Purcell effect within the context of antenna enhancement. Metallic optical antennas are best analyzed with conventional antenna circuit models, but if the Purcell enhancement were to be employed, we provide the effective mode volume, V_eff = (3/4π²)²d²λ(λ/l)⁵, that would be needed.

Intraband hot-electron photoluminescence of a silver nanowire-coupled gold film via high-order gap plasmons

We report a strong one-photon photoluminescence (PL) behavior of a silver nanowire directly coupled gold film. The PL peak position of the silver nanowire-coupled gold film deviates from the intrinsic interband transition of gold materials and is not sensitive to the diameter change of the silver nanowire. We attribute this strong PL behavior to the intraband transition of hot electrons dominated by high-order gap plasmons, which are excited in the ultra-small gap formed by an ultra-thin polyvinyl pyrrolidone (PVP) layer coated on the silver nanowire. The results show that the energy required for the strong PL of the heterogeneous system mainly comes from the gold film, acting as an incident energy absorber enhanced by the high-order gap plasmons, while the silver nanowire acts an efficient incident energy focusing antenna. In situ Raman scattering spectra and time-resolved PL intensity integral curves were used to record the carbonization and disappearance process of PVP. The understanding of the PL behavior of the silver nanowire directly coupled gold film proves the universality of plasmon-modulated PL theory and is also of great significance to improve the generation and utilization efficiency of hot electrons with high-order gap plasmons in the fields of catalysis and incident energy capture.

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.

Efficient method for the calculation of the optical force of a single nanoparticle based on the quasinormal mode expansion

An efficient method for the calculation of the optical force of a single nanoparticle is proposed based on the expansion of quasinormal modes (QNMs), which are eigensolutions of source-free Maxwell's equations with complex eigenfrequencies. In this method, the optical force is calculated by integrating the Maxwell stress tensor (MST) over a closed surface encompassing the nanoparticle. The electromagnetic (EM) field required for evaluating the MST is computed by a rigorous modal analysis, in which the EM field is expanded onto a small set of QNMs. Once the QNMs of the nanoparticle are solved, their excitation coefficients are obtained analytically. This means that additional full-wave computations are not required if the nanoparticle's location and the wavelength or distribution of the excitation field vary. Comparisons with full-wave numerical calculations of optical force evidence the high efficiency and accuracy of our formalism.

Tracking interfacial single-molecule pH and binding dynamics via vibrational spectroscopy

Understanding single-molecule chemical dynamics of surface ligands is of critical importance to reveal their individual pathways and, hence, roles in catalysis, which ensemble measurements cannot see. Here, we use a cascaded nano-optics approach that provides sufficient enhancement to enable direct tracking of chemical trajectories of single surface-bound molecules via vibrational spectroscopy. Atomic protrusions are laser-induced within plasmonic nanojunctions to concentrate light to atomic length scales, optically isolating individual molecules. By stabilizing these atomic sites, we unveil single-molecule deprotonation and binding dynamics under ambient conditions. High-speed field-enhanced spectroscopy allows us to monitor chemical switching of a single carboxylic group between three discrete states. Combining this with theoretical calculation identifies reversible proton transfer dynamics (yielding effective single-molecule pH) and switching between molecule-metal coordination states, where the exact chemical pathway depends on the intitial protonation state. These findings open new domains to explore interfacial single-molecule mechanisms and optical manipulation of their reaction pathways.

Theory of "Hot" Photoluminescence from Drude Metals

We provide a complete quantitative theory for light emission from Drude metals under continuous wave illumination, based on our recently derived steady-state nonequilibrium electron distribution. We show that the electronic contribution to the emission exhibits a dependence on the emission frequency which is very similar to the energy dependence of the nonequilibrium distribution, and characterize different scenarios determining the measurable emission line shape. This enables the identification of experimentally relevant situations, where the emission lineshapes deviate significantly from predictions based on the standard theory (namely, on the photonic density of states), and enables the differentiation between cases where the emission scales with the metal object surface or with its volume. We also provide an analytic description (which is absent from the literature) of the (polynomial) dependence of the metal emission on the electric field, its dependence on the pump laser frequency, and its nontrivial exponential dependence on the electron temperature, both for the Stokes and anti-Stokes regimes. Our results imply that the emission does not originate from either Fermion statistics (due to e-e interactions), and even though one could have expected the emission to follow boson statistics due to involvement of photons (as in Planck's Black Body emission), it turns out that it deviates from that form as well. Finally, we resolve the arguments associated with the effects of electron and lattice temperatures on the emission, and which of them can be extracted from the anti-Stokes emission.