Vacuum Rabi splitting and strong-coupling dynamics for surface-plasmon polaritons and rhodamine 6G molecules

Strong coupling in molecular systems: a simple predictor employing routine optical measurements

We provide a simple method that enables readily acquired experimental data to be used to predict whether or not a candidate molecular material may exhibit strong coupling. Specifically, we explore the relationship between the hybrid molecular/photonic (polaritonic) states and the bulk optical response of the molecular material. For a given material, this approach enables a prediction of the maximum extent of strong coupling (vacuum Rabi splitting), irrespective of the nature of the confined light field. We provide formulae for the upper limit of the splitting in terms of the molar absorption coefficient, the attenuation coefficient, the extinction coefficient (imaginary part of the refractive index) and the absorbance. To illustrate this approach, we provide a number of examples, and we also discuss some of the limitations of our approach.

Large-Area Near-Infrared Emission Enhancement on Single Upconversion Nanoparticles by Metal Nanohole Array

Single lanthanide (Ln) ion doped upconversion nanoparticles (UCNPs) exhibit great potential for biomolecule sensing and counting. Plasmonic structures can improve the emission efficiency of single UCNPs by modulating the energy transferring process. Yet, achieving robust and large-area single UCNP emission modulation remains a challenge, which obstructs investigation and application of single UCNPs. Here, we present a strategy using metal nanohole arrays (NHAs) to achieve energy-transfer modulation on single UCNPs simultaneously within large-area plasmonic structures. By coupling surface plasmon polaritons (SPPs) with higher-intermediate state (1D2 → 3F3, 1D2 → 3H4) transitions, we achieved a remarkable up to 10-fold enhancement in 800 nm emission, surpassing the conventional approach of coupling SPPs with an intermediate ground state (3H4 → 3H6). We numerically simulate the electrical field distribution and reveal that luminescent enhancement is robust and insensitive to the exact location of particles. It is anticipated that the strategy provides a platform for widely exploring applications in single-particle quantitative biosensing.

Theoretical formulation of chemical equilibrium under vibrational strong coupling

Experiments have suggested that strong interactions between molecular ensembles and infrared microcavities can be employed to control chemical equilibria. Nevertheless, the primary mechanism and key features of the effect remain largely unexplored. In this work, we develop a theory of chemical equilibrium in optical microcavities, which allows us to relate the equilibrium composition of a mixture in different electromagnetic environments. Our theory shows that in planar microcavities under strong coupling with polyatomic molecules, hybrid modes formed between all dipole-active vibrations and cavity resonances contribute to polariton-assisted chemical equilibrium shifts. To illustrate key aspects of our formalism, we explore a model SN2 reaction within a single-mode infrared resonator. Our findings reveal that chemical equilibria can be shifted towards either direction of a chemical reaction, depending on the oscillator strength and frequencies of reactant and product normal modes. Polariton-induced zero-point energy changes provide the dominant contributions, though the effects in idealized single-mode cavities tend to diminish quickly as the temperature and number of molecules increase. Our approach is valid in generic electromagnetic environments and paves the way for understanding and controlling chemical equilibria with microcavities.

Anomalous Dispersion in Reflection and Emission of Dye Molecules Strongly Coupled to Surface Plasmon Polaritons

We have studied dispersion of surface plasmon polaritons (SPPs) in the Kretschmann geometry (prism/Ag/dye-doped polymer) in weak, intermediate, and ultra-strong exciton-plasmon coupling regimes. The dispersion curves obtained in the reflection experiment were in good agreement with the simple model predictions at small concentrations of dye (Rhodamine 590, Rh590) in the polymer (Poly(methyl methacrylate), PMMA). At the same time, highly unusual multi-segment "staircase-like" dispersion curves were observed at extra-large dye concentrations, also in agreement with the simple theoretical model predicting large, small, and negative group velocities featured by different polariton branches. In a separate experiment, we measured angular dependent emission of Rh590 dye and obtained the dispersion curves consisting of two branches, one nearly resembling the SPP dispersion found in reflection and the second one almost horizontal. The results of our study pave the road to unparalleled fundamental science and future applications of weak and strong light-matter interactions.

Modeling the near-field effect on molecular excited states using the discrete interaction model/quantum mechanical method

Strong light-matter interactions significantly modify the optical properties of molecules in the vicinity of plasmonic metal nanoparticles. Since the dimension of the plasmonic cavity approaches that of the molecules, it is critical to explicitly describe the nanoparticle junctions. In this work, we use the discrete interaction model/quantum mechanical (DIM/QM) method to model the coupling between the plasmonic near-field and molecular excited states. DIM/QM is a combined electrodynamics/quantum mechanical model that uses an atomistic description of the nanoparticle. We extend the DIM/QM method to include the local field effects in the sum-over-state formalism of time-dependent density functional theory. As a test of the method, we study the interactions between small organic chromophores and metal nanoparticles. In particular, we examine how the inclusion of multiple electronic transitions and intermolecular interactions modify the coupling between molecules and nanoparticles. Using the sum-over-state formalism of DIM/QM, we show that two-state models break down when the plasmon excitation is detuned from the molecular excitations. To gain further insight, we compare the simple coupled-dipole model (CDM) with the DIM/QM model. We find that CDM works well for simple systems but fails when going beyond the single molecule or single nanoparticle cases. We also find that the coupling depends strongly on the site of the nanoparticle in which the chromophore couples to. Our work suggests the importance of explicitly describing the cavity to capture the atomistic level local field environment in which the molecule strongly couples to.

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.

Strong coupling in plasmonic metal nanoparticles

The study of strong coupling between light and matter has gained significant attention in recent years due to its potential applications in diverse fields, including artificial light harvesting, ultraefficient polariton lasing, and quantum information processing. Plasmonic cavities are a compelling alternative of conventional photonic resonators, enabling ultracompact polaritonic systems to operate at room temperature. This review focuses on colloidal metal nanoparticles, highlighting their advantages as plasmonic cavities in terms of their facile synthesis, tunable plasmonic properties, and easy integration with excitonic materials. We explore recent examples of strong coupling in single nanoparticles, dimers, nanoparticle-on-a-mirror configurations, and other types of nanoparticle-based resonators. These systems are coupled with an array of excitonic materials, including atomic emitters, semiconductor quantum dots, two-dimensional materials, and perovskites. In the concluding section, we offer perspectives on the future of strong coupling research in nanoparticle systems, emphasizing the challenges and potentials that lie ahead. By offering a thorough understanding of the current state of research in this field, we aim to inspire further investigations and advances in the study of strongly coupled nanoparticle systems, ultimately unlocking new avenues in nanophotonic applications.

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%.

Plasmon-induced coherence, exciton-induced transparency, and Fano interference for hybrid plasmonic systems in strong coupling regime

We present an analytical model describing the transition to a strong coupling regime for an ensemble of emitters resonantly coupled to a localized surface plasmon in a metal-dielectric structure. The response of a hybrid system to an external field is determined by two distinct mechanisms involving collective states of emitters interacting with the plasmon mode. The first mechanism is the near-field coupling between the bright collective state and the plasmon mode, which underpins the energy exchange between the system components and gives rise to exciton-induced transparency minimum in scattering spectra in the weak coupling regime and to emergence of polaritonic bands as the system transitions to the strong coupling regime. The second mechanism is the Fano interference between the plasmon dipole moment and the plasmon-induced dipole moment of the bright collective state as the hybrid system interacts with the radiation field. The latter mechanism is greatly facilitated by plasmon-induced coherence in a system with the characteristic size below the diffraction limit as the individual emitters comprising the collective state are driven by the same alternating plasmon near field and, therefore, all oscillate in phase. This cooperative effect leads to scaling of the Fano asymmetry parameter and of the Fano function amplitude with the ensemble size, and therefore, it strongly affects the shape of scattering spectra for large ensembles. Specifically, with increasing emitter numbers, the Fano interference leads to a spectral weight shift toward the lower energy polaritonic band.

Exploiting a strong coupling regime of organic pentamer surface plasmon resonance based on the Otto configuration for creatinine detection

The sandwiched material-analyte layer in the surface plasmon resonance (SPR)-Otto configuration emulates an optical cavity and, coupled with large optical nonlinearity material, the rate of light escaping from the system is reduced, allowing the formation of a strong coupling regime. Here, we report an organic pentamer SPR sensor using the Otto configuration to induce a strong coupling regime for creatinine detection. Prior to that, the SPR sensor chip was modified with an organic pentamer, 1,4-bis[2-(5-thiophene-2-yl)-1-benzothiopene]-2,5-dioctyloxybenzene (BOBzBT₂). To improve the experimental calibration curve, a normalisation approach based on the strong coupling-induced second dip was also developed. By using this procedure, the performance of the sensor improved to 0.11 mg/dL and 0.36 mg/dL for the detection and quantification limits, respectively.

Principle and Applications of Multimode Strong Coupling Based on Surface Plasmons

In the past decade, strong coupling between light and matter has transitioned from a theoretical idea to an experimental reality. This represents a new field of quantum light–matter interaction, which makes the coupling strength comparable to the transition frequencies in the system. In addition, the achievement of multimode strong coupling has led to such applications as quantum information processing, lasers, and quantum sensors. This paper introduces the theoretical principle of multimode strong coupling based on surface plasmons and reviews the research related to the multimode interactions between light and matter. Perspectives on the future development of plasmonic multimode coupling are also discussed.

Active control of strong plasmon-exciton coupling in biomimetic pigment-polymer antenna complexes grown by surface-initiated polymerisation from gold nanostructures

Plexcitonic antenna complexes, inspired by photosynthetic light-harvesting complexes, are formed by attachment of chlorophylls (Chl) to poly(cysteine methacrylate) (PCysMA) scaffolds grown by atom-transfer radical polymerisation from gold nanostructure arrays. In these pigment–polymer antenna complexes, localised surface plasmon resonances on gold nanostructures are strongly coupled to Chl excitons, yielding hybrid light–matter states (plexcitons) that are manifested in splitting of the plasmon band. Modelling of the extinction spectra of these systems using a simple coupled oscillator model indicates that their coupling energies are up to twice as large as those measured for LHCs from plants and bacteria. Coupling energies are correlated with the exciton density in the grafted polymer layer, consistent with the collective nature of strong plasmon–exciton coupling. Steric hindrance in fully-dense PCysMA brushes limits binding of bulky chlorophylls, but the chlorophyll concentration can be increased to ∼2 M, exceeding that in biological light-harvesting complexes, by controlling the grafting density and polymerisation time. Moreover, synthetic plexcitonic antenna complexes display pH- and temperature-responsiveness, facilitating active control of plasmon–exciton coupling. Because of the wide range of compatible polymer chemistries and the mild reaction conditions, plexcitonic antenna complexes may offer a versatile route to programmable molecular photonic materials.

Excitons in pigment–polymer antenna complexes formed by attachment of chlorophyll to surface grafted polymers are coupled strongly to plasmon modes, with coupling energies twice those for biological light-harvesting complexes and active control of plasmon–exciton coupling.

Efficient DNA-Driven Nanocavities for Approaching Quasi-Deterministic Strong Coupling to a Few Fluorophores

Strong coupling between light and matter is the foundation of promising quantum photonic devices such as deterministic single photon sources, single atom lasers, and photonic quantum gates, which consist of an atom and a photonic cavity. Unlike atom-based systems, a strong coupling unit based on an emitter-plasmonic nanocavity system has the potential to bring these devices to the microchip scale at ambient conditions. However, efficiently and precisely positioning a single or a few emitters into a plasmonic nanocavity is challenging. In addition, placing a strong coupling unit on a designated substrate location is a demanding task. Here, fluorophore-modified DNA strands are utilized to drive the formation of particle-on-film plasmonic nanocavities and simultaneously integrate the fluorophores into the high field region of the nanocavities. High cavity yield and fluorophore coupling yield are demonstrated. This method is then combined with e-beam lithography to position the strong coupling units on designated locations of a substrate. Furthermore, polariton energy under the detuning of fluorophore embedded nanocavities can fit into a model consisting of three sets of two-level systems, implying vibronic modes may be involved in the strong coupling. Our system makes strong coupling units more practical on the microchip scale and at ambient conditions and provides a stable platform for investigating fluorophore-plasmonic nanocavity interaction.

Surface Plasmonic Sensors: Sensing Mechanism and Recent Applications

Surface plasmonic sensors have been widely used in biology, chemistry, and environment monitoring. These sensors exhibit extraordinary sensitivity based on surface plasmon resonance (SPR) or localized surface plasmon resonance (LSPR) effects, and they have found commercial applications. In this review, we present recent progress in the field of surface plasmonic sensors, mainly in the configurations of planar metastructures and optical-fiber waveguides. In the metastructure platform, the optical sensors based on LSPR, hyperbolic dispersion, Fano resonance, and two-dimensional (2D) materials integration are introduced. The optical-fiber sensors integrated with LSPR/SPR structures and 2D materials are summarized. We also introduce the recent advances in quantum plasmonic sensing beyond the classical shot noise limit. The challenges and opportunities in this field are discussed.

Impact of cavity on interatomic Coulombic decay

The interatomic Coulombic decay (ICD) is an efficient electronic decay process of systems embedded in environment. In ICD, the excess energy of an excited atom A is efficiently utilized to ionize a neighboring atom B. In quantum light, an ensemble of atoms A form polaritonic states which can undergo ICD with B. Here we investigate the impact of quantum light on ICD and show that this process is strongly altered compared to classical ICD. The ICD rate depends sensitively on the atomic distribution and orientation of the ensemble. It is stressed that in contrast to superposition states formed by a laser, forming polaritons by a cavity enables to control the emergence and suppression, as well as the efficiency of ICD.

Effect of molecular Stokes shift on polariton dynamics

When the enhanced electromagnetic field of a confined light mode interacts with photoactive molecules, the system can be driven into the regime of strong coupling, where new hybrid light-matter states, polaritons, are formed. Polaritons, manifested by the Rabi split in the dispersion, have shown potential for controlling the chemistry of the coupled molecules. Here, we show by angle-resolved steady-state experiments accompanied by multi-scale molecular dynamics simulations that the molecular Stokes shift plays a significant role in the relaxation of polaritons formed by organic molecules embedded in a polymer matrix within metallic Fabry-Pérot cavities. Our results suggest that in the case of Rhodamine 6G, a dye with a significant Stokes shift, excitation of the upper polariton leads to a rapid localization of the energy into the fluorescing state of one of the molecules, from where the energy scatters into the lower polariton (radiative pumping), which then emits. In contrast, for excitonic J-aggregates with a negligible Stokes shift, the fluorescing state does not provide an efficient relaxation gateway. Instead, the relaxation is mediated by exchanging energy quanta matching the energy gap between the dark states and lower polariton into vibrational modes (vibrationally assisted scattering). To understand better how the fluorescing state of a molecule that is not strongly coupled to the cavity can transfer its excitation energy to the lower polariton in the radiative pumping mechanism, we performed multi-scale molecular dynamics simulations. The results of these simulations suggest that non-adiabatic couplings between uncoupled molecules and the polaritons are the driving force for this energy transfer process.

Polariton response in the presence of Brownian dissipation from molecular vibrations

We study the elastic response of a stationarily driven system of a cavity field strongly coupled with molecular excitons, taking into account the main dissipation channels due to the finite cavity linewidth and molecular vibrations. We show that the frequently used coupled oscillator model fails in describing this response especially due to the non-Lorentzian dissipation of the molecules to their vibrations. Signatures of this failure are the temperature dependent minimum point of the polariton peak splitting, the uneven polariton peak height at the minimum splitting, and the asymmetric shape of the polariton peaks even at the experimentally accessed "zero-detuning" point. Using a rather generic yet representative model of molecular vibrations, we predict the polariton response in various conditions, depending on the temperature, molecular Stokes shift and vibration frequencies, and the size of the Rabi splitting. Our results can be used as a sanity check of the experiments trying to "prove" results originating from strong coupling, such as vacuum-enhanced chemical reaction rate.

Optically induced crossover from weak to strong coupling regime between surface plasmon polaritons and photochromic molecules

We demonstrate optically induced crossover from a weak to a strong coupling regime in a single photonic system consisting of propagating surface plasmon polaritons (SPPs) on a planar silver film and ultraviolet (UV)-switchable photochromic molecules. A gradual increase is observed in the vacuum Rabi splitting upon increasing UV exposure, along with intriguing behavior, where the reflectivity initially decreases due to increased losses at the weak coupling regime, and then increases due to the emergence of strongly coupled modes and the associated band gap formation at the resonance frequency of the uncoupled states. This work explicitly demonstrates the optical tunability of the degree of hybridization of the SPP and exciton modes, spanning the range from weak to intermediate and finally to the strong coupling regime.

On the applicability of quantum-optical concepts in strong-coupling nanophotonics

Rooted in quantum optics and benefiting from its well-established foundations, strong coupling in nanophotonics has experienced increasing popularity in recent years. With nanophotonics being an experiment-driven field, the absence of appropriate theoretical methods to describe ground-breaking advances has often emerged as an important issue. To address this problem, the temptation to directly transfer and extend concepts already available from quantum optics is strong, even if a rigorous justification is not always available. In this review we discuss situations where, in our view, this strategy has indeed overstepped its bounds. We focus on exciton-plasmon interactions, and particularly on the idea of calculating the number of excitons involved in the coupling. We analyse how, starting from an unfounded interpretation of the term N/V that appears in theoretical descriptions at different levels of complexity, one might be tempted to make independent assumptions for what the number N and the volume V are, and attempt to calculate them separately. Such an approach can lead to different, often contradictory results, depending on the initial assumptions (e.g. through different treatments of V as the-ambiguous in plasmonics-mode volume). We argue that the source of such contradictions is the question itself-How many excitons are coupled?, which disregards the true nature of the coupled components of the system, has no meaning and often not even any practical importance. If one is interested in validating the quantum nature of the system-which appears to be the motivation driving the pursuit of strong coupling with small N-one could instead focus on quantities such as the photon emission rate or the second-order correlation function. While many of the issues discussed here may appear straightforward to specialists, our target audience is predominantly newcomers to the field, either students or scientists specialised in different disciplines. We have thus tried to minimise the occurrence of proofs and overly-technical details, and instead provide a qualitative discussion of analyses that should be avoided, hoping to facilitate further growth of this promising area.

Tuning of the polariton modes induced by longitudinal strong coupling in the graphene hybridized DBR cavity

In this Letter, we construct a graphene hybridized distributed Bragg reflector (DBR) cavity, where spatially longitudinal strong coupling occurs between the Tamm plasmon polaritons (TPPs) existing around the graphene layer and the cavity mode (CM) existing in the DBR cavity. As a result, two hybrid polariton modes emerge, which contain both the TPP and the CM components. In the simulation, we demonstrate that the resonant frequencies and the damping rates of the polariton modes can be actively tuned by the graphene Fermi level and the incident angle of light. Besides, the coupling strength and the damping rates are also passively tuned by the pair number of the layers in the DBR. Theoretically, we analyze the TPP-CM strong coupling by the coupled harmonic oscillator equations, which help to explain the regulation process. The controllable TPP-CM longitudinal strong coupling with two absorption bands may achieve potential applications in developing graphene-based active optoelectronic and polaritonic devices in terahertz waves.

Nanoscale quantum plasmon sensing based on strong photon-exciton coupling

We propose a scheme of quantum plasmon sensing system based on strong photon-exciton coupling in the gap surface plasmon nanostructure. The system's sensitivity is characterized as Rabi splitting, which is sensitive to a slight change in environmental permittivity and determined by the coupling coefficient and detuning between the emitter and plasmon nanocavity. By increasing the dipole moment of the emitter, the sensitivity can exceed that of a traditional plasmon sensing system while only depending on the resonance spectral shift. Quantum plasmon sensing provides a unique mechanism in the application of bio-sensing, opto-chemical sensing, and quantum photonics at the nanoscale.

Principle and Applications of the Coupling of Surface Plasmons and Excitons

Surface plasmons have been attracting increasing attention and have been studied extensively in recent decades because of their half-light and half-material polarized properties. On the one hand, the tightly confined surface plasmonic mode may reduce the size of integrated optical devices beyond the diffraction limit; on the other hand, it provides an approach toward enhancement of the interactions between light and matter. In recent experiments, researchers have realized promising applications for surface plasmons in quantum information processing, ultra-low-power lasers, and micro-nano processing devices by using plasmonic structures, which have demonstrated their superiority over traditional optics structures. In this paper, we introduce the theoretical principle of surface plasmons and review the research work related to the interactions between plasmons and excitons. Some perspectives with regard to the future development of plasmonic coupling are also outlined.

Enhanced Optical Absorption and Slowed Light of Reduced-Dimensional CsPbBr3 Nanowire Crystal by Exciton-Polariton

Metallic halide perovskites are promising for low-cost, low-consumption, flexible optoelectronic devices. However, research is lacking on light propagation and dielectric behaviors as fundamental properties for optoelectronic perovskite applications, particularly the mechanism supporting a strong light-matter interaction and the different properties of low-dimensional structures from their bulk counterparts. We use spatially resolved photoluminescence (SRPL) spectroscopy to explore light propagation and measure the refractive index of CsPbBr₃ nanowires (NWs). Owing to strong exciton-photon interactions, light is guided as an exciton-polariton inside the NWs at room temperature. Remarkable spatial dispersion is confirmed, in which both the real and imaginary parts of the refractive index increase dramatically approaching exciton resonance, thus slowing light and enhancing absorption, respectively. Reducing the NWs dimension increases exciton-photon coupling and the exciton fraction, increasing the light absorption coefficient and group index 5- and 3-fold, respectively, relative to those of bulk films and slowing the light group velocity by ∼74%. Furthermore, dispersive absorption induces an energy redshift to the propagating PL at 4.1-5.5 meV μm^-1 until the bottleneck region. These findings clarify light-matter interaction in confined perovskite structures to improve their optoelectronic device performance.

Double Rabi Splitting in a Strongly Coupled System of Core-Shell Au@Ag Nanorods and J-Aggregates of Multiple Fluorophores

The interaction of several components in the strong coupling regime yielding multiple Rabi splittings opens up remarkable possibilities for studies of multimode hybridization and energy transfer, which is of considerable interest in both fundamental and applied science. Here we demonstrate that three different components, such as core-shell Au@Ag nanorods and J-aggregates of two different dyes, can be integrated into a single hybrid structure, which leads to strong collective exciton-plasmon coupling and double-mode Rabi splitting totaling 338 meV. We demonstrate strong coupling in these multicomponent plexitonic nanostructures by means of magnetic circular dichroism spectroscopy and demonstrate strong magneto-optical activity for the three hybridized states resulting from this coupling. The J-aggregates of two different nonmagnetic dyes interact with metal nanoparticles effectively, achieving magnetic properties due to the hybridization of electronic excitations in the three-component system.

Influence of Fano resonance on SERS enhancement in Fano-plasmonic oligomers

Plasmonic oligomers can provide profound Fano resonance in their scattering responses. The sub-radiant mode of Fano resonance can result in significant near-field enhancement due to its light trapping capability into the so-called hotspots. Appearance of these highly localized hotspots at the excitation and/or Stokes wavelengths of the analytes makes such oligomers promising SERS active substrates. In this work, we numerically and experimentally investigate optical properties of two disk-type gold oligomers, which have different strength and origin of Fano resonance. Raman analysis of rhodamine 6G and adenine with the presence of the fabricated oligomers clearly indicates that an increment in the strength of Fano resonance can improve the Raman enhancement of an oligomer significantly. Therefore, by suitable engineering of Fano lineshape, one can achieve efficient SERS active substrates with spatially localized hotspots.

Strong coupling of emitters to single plasmonic nanoparticles: exciton-induced transparency and Rabi splitting

Strong coupling between plasmons in metal nanoparticles and single excitons in molecules or semiconductor nanomaterials has recently attracted considerable experimental effort for potential applications in quantum-mechanical and classical optical information processing and for fundamental studies of light-matter interaction. Here, we review the theory behind strong plasmon-exciton coupling and provide analytical expressions that can be used for fitting experimental data, particularly the commonly measured scattering spectra. We re-analyze published data using these expressions, providing a uniform method for evaluating and quantifying claims of strong coupling that avoids ambiguities in distinguishing between Rabi splitting and exciton-induced transparency (or Fano-like interference between plasmons and excitons).

Exciton-Plasmon Energy Exchange Drives the Transition to a Strong Coupling Regime

We present a model for exciton-plasmon coupling based on an energy exchange mechanism between quantum emitters (QE) and localized surface plasmons in metal-dielectric structures. Plasmonic correlations between QEs give rise to a collective state exchanging its energy cooperatively with a resonant plasmon mode. By defining carefully the plasmon mode volume for a QE ensemble, we obtain a relation between QE-plasmon coupling and a cooperative energy transfer rate that is expressed in terms of local fields. For a single QE near a sharp metal tip, we find analytically the enhancement factor for QE-plasmon coupling relative to QE coupling to a cavity mode. For QEs distributed in an extended region enclosing a plasmonic structure, we find that the ensemble QE-plasmon coupling saturates to a universal value independent of system size and shape, consistent with the experiment.

Fano resonance and polarization transformation induced by interpolarization coupling of Bloch surface waves

In this work, the resonant coupling behaviors between the transverse-electric (TE) and transverse-magnetic (TM) Bloch surface waves (BSWs) on a dielectric multilayer have been theoretically studied. Due to the different penetration depths in the dielectric multilayer, the TM BSWs and TE BSWs can act as the radiative and dark electromagnetic modes, respectively. By using a rectangular grating on the dielectric multilayer, both Rabi splitting and Fano resonance phenomena based on the coupling of the two BSW modes were demonstrated, through tuning the period of the grating and the azimuthal angle of the incoming wave. Furthermore, by using the temporal coupled-mode theory, we show that the anti-Hermitian coupling between the two BSW modes contributes to the enhanced diffraction and the huge polarization transformation efficiency of incoming waves in the weak coupling regime.

Angular dependent strong coupling between localized waveguide resonance and surface plasmon resonance in complementary metamaterials

We give direct evidence of both surface plasmon resonance (SPR) and localized waveguide resonance (LWR) contribution to the extraordinary optical transmission in complementary metamaterials. Strong coupling between SPR and LWR are also observed with clear evidence of Rabi splitting and anti-crossing phenomena. The splitting introduces sharp phase shift, which in turn enhances group velocity delay by the incident angle without geometric parameter change. The results not only clarify SPR and LWR effects in the extraordinary optical transmission, but also provide a novel route to control light-metamaterial interaction by angular modulation for on-chip slow light devices.

Polariton-assisted splitting of broadband emission spectra of strongly coupled organic dye excitons in tunable optical microcavity

Resonance interaction between a localized electromagnetic field and excited states in molecules paves the way to control fundamental properties of a matter. In this study, we encapsulated organic molecules with relatively low unoriented dipole moments in the polymer matrix, placed them in tunable optical microcavity and realized, for the first time, controllable modification of the broad photoluminescence (PL) emission of these molecules in strong coupling regime at room temperature. Notably, while in most previous studies it was reported that the single mode dominates in the PL signal (radiation of the so-called branch of the lower polariton), here we report on the observation of two distinct PL peaks, evolution of which has been followed as the microcavity mode is detuned from the excitonic resonance. A significant Rabi splitting estimated from the modified PL spectra was as large as 225 meV. The developed approach can be used both in fundamental research of resonant light-mater coupling and its practical applications in sensing and development of coherent spontaneous emission sources using a combination of carefully designed microcavity with a wide variety of organic molecules.

Polaritonic Hybrid-Epsilon-near-Zero Modes: Beating the Plasmonic Confinement vs Propagation-Length Trade-Off with Doped Cadmium Oxide Bilayers

Polaritonic materials that support epsilon-near-zero (ENZ) modes offer the opportunity to design light-matter interactions at the nanoscale through extreme subwavelength light confinement, producing phenomena like resonant perfect absorption. However, the utility of ENZ modes in nanophotonic applications has been limited by a flat spectral dispersion, which leads to small group velocities and extremely short propagation lengths. Here, we overcome this constraint by hybridizing ENZ and surface plasmon polariton (SPP) modes in doped cadmium oxide epitaxial bilayers. This results in strongly coupled hybrid modes that are characterized by an anticrossing in the polariton dispersion and a large spectral splitting on the order of 1/3 of the mode frequency. These hybrid modes simultaneously achieve modal propagation and ENZ mode-like interior field confinement, adding propagation character to ENZ mode properties. We subsequently tune the resonant frequencies, dispersion, and coupling of these polaritonic-hybrid-epsilon-near-zero (PH-ENZ) modes by tailoring the modal oscillator strength and the ENZ-SPP spectral overlap. PH-ENZ modes ultimately leverage the most desirable characteristics of both ENZ and SPP modes, allowing us to overcome the canonical plasmonic trade-off between confinement and propagation length.

Strong light-matter interactions: a new direction within chemistry

Strong light–matter coupling enables the possibility of changing the properties of molecules, without modifying their chemical structures, thus enabling a completely new way to study chemistry and explore materials.

It is possible to modify the chemical and physical properties of molecules, not only through chemical modifications but also by coupling molecules strongly to light. More intriguingly, strong coupling between molecules and light is possible even without the presence of a photon. The phenomenon that makes this possible is called vacuum fluctuations, which is the finite zero point energy of the quantized electromagnetic field inside an optical cavity. The light–matter coupling, which can be as large as 1 eV (100 kJ mol^–1), leads to the formation of new hybrid states, called polaritons. The formed hybrid states can be viewed as a linear combination of light (vacuum field) and matter (molecules), thus completely changing the energy landscape of the system. Using vacuum fluctuations, strong light–matter interactions have for instance been used to change chemical reactivity, charge conductivity, excited state relaxation pathways and rates of chemical reactions of organic molecules. In this review a brief history of the field is given, followed by a theoretical framework, methods of analysis, and a review of accomplishments. Finally, a personal reflection on the future perspectives and applications within this field is given.

Room-Temperature Strong Coupling of CdSe Nanoplatelets and Plasmonic Hole Arrays

Exciton polaritons are hybrid light-matter quasiparticles that can serve as coherent light sources. Motivated by applications, room-temperature realization of polaritons requires narrow, excitonic transitions with large transition dipoles. Such transitions must then be strongly coupled to an electromagnetic mode confined in a small volume. While much work has explored polaritons in organic materials, semiconductor nanocrystals present an alternative excitonic system with enhanced photostability and spectral tunability. In particular, quasi-two-dimensional nanocrystals known as nanoplatelets (NPLs) exhibit intense, spectrally narrow excitonic transitions useful for polariton formation. Here, we place CdSe NPLs on silver hole arrays to demonstrate exciton-plasmon polaritons at room temperature. Angle-resolved reflection spectra reveal Rabi splittings up to 149 meV for the polariton states. We observe bright, polarized emission arising from the lowest polariton state. Furthermore, we assess the dependence of the Rabi splitting on the hole-array pitch and the number N of NPLs. While the pitch determines the in-plane momentum for which strong coupling is observed, it does not affect the size of the splitting. The Rabi splitting first increases with NPL film thickness before eventually saturating. Instead of the commonly used [Formula: see text] dependence, we develop an analytical expression that includes the transverse confinement of the plasmon modes to describe the measured Rabi splitting as a function of NPL film thickness.

Sensing at terahertz frequency domain using a sapphire whispering gallery mode resonator

In this Letter, we experimentally demonstrate a terahertz (THz) whispering gallery mode (WGM) sensor based on a sapphire WGM resonator. The fundamental mode at 129.49 GHz with a Q-factor of 4.63×10³ is used to study its sensitivity to adsorbed molecules. The efficiency of our sensor to detect rhodamine 6G dye molecules in a polyvinyl alcohol matrix at room temperature has been manifested, and a detection sensitivity of 25 parts per million has been achieved. Also, we report an analytical approach based on coupled-mode theory between the waveguide mode and the spherical resonator mode to evaluate the absorption coefficient of the adsorbed molecule on the resonator. The model is modified to evaluate optical constants of materials. The results obtained have been verified by continuous-wave THz transmission results. The results are of importance in sensing, metrology, and material characterization.

Polarization-dependent strong coupling between silver nanorods and photochromic molecules

Active plasmonics is a key focus for the development of advanced plasmonic applications. By selectively exciting the localized surface plasmon resonance sustained by the short or the long axis of silver nanorods, we demonstrate a polarization-dependent strong coupling between the plasmonic resonance and the excited state of photochromic molecules. By varying the width and the length of the nanorods independently, a clear Rabi splitting appears in the dispersion curves of both resonators.

Strong coupling and induced transparency at room temperature with single quantum dots and gap plasmons

Coherent coupling between plasmons and transition dipole moments in emitters can lead to two distinct spectral effects: vacuum Rabi splitting at strong coupling strengths, and induced transparency (also known as Fano interference) at intermediate coupling strengths. Achieving either strong or intermediate coupling between a single emitter and a localized plasmon resonance has the potential to enable single-photon nonlinearities and other extreme light-matter interactions, at room temperature and on the nanometer scale. Both effects produce two peaks in the spectrum of scattering from the plasmon resonance, and can thus be confused if scattering measurements alone are performed. Here we report measurements of scattering and photoluminescence from individual coupled plasmon-emitter systems that consist of a single colloidal quantum dot in the gap between a gold nanoparticle and a silver film. The measurements unambiguously demonstrate weak coupling (the Purcell effect), intermediate coupling (Fano interference), and strong coupling (Rabi splitting) at room temperature.

Theory for polariton-assisted remote energy transfer

Strong-coupling between light and matter produces hybridized states (polaritons) whose delocalization and electromagnetic character allow for novel modifications in spectroscopy and chemical reactivity of molecular systems. Recent experiments have demonstrated remarkable distance-independent long-range energy transfer between molecules strongly coupled to optical microcavity modes. To shed light on the mechanism of this phenomenon, we present the first comprehensive theory of polariton-assisted remote energy transfer (PARET) based on strong-coupling of donor and/or acceptor chromophores to surface plasmons. Application of our theory demonstrates that PARET up to a micron is indeed possible. In particular, we report two regimes for PARET: in one case, strong-coupling to a single type of chromophore leads to transfer mediated largely by surface plasmons while in the other case, strong-coupling to both types of chromophores creates energy transfer pathways mediated by vibrational relaxation. Importantly, we highlight conditions under which coherence enhances or deteriorates these processes. For instance, while exclusive strong-coupling to donors can enhance transfer to acceptors, the reverse turns out not to be true. However, strong-coupling to acceptors can shift energy levels in a way that transfer from acceptors to donors can occur, thus yielding a chromophore role-reversal or "carnival effect". This theoretical study demonstrates the potential for confined electromagnetic fields to control and mediate PARET, thus opening doors to the design of remote mesoscale interactions between molecular systems.

A synthetic biological quantum optical system

In strong plasmon-exciton coupling, a surface plasmon mode is coupled to an array of localized emitters to yield new hybrid light-matter states (plexcitons), whose properties may in principle be controlled via modification of the arrangement of emitters. We show that plasmon modes are strongly coupled to synthetic light-harvesting maquette proteins, and that the coupling can be controlled via alteration of the protein structure. For maquettes with a single chlorin binding site, the exciton energy (2.06 ± 0.07 eV) is close to the expected energy of the Qy transition. However, for maquettes containing two chlorin binding sites that are collinear in the field direction, an exciton energy of 2.20 ± 0.01 eV is obtained, intermediate between the energies of the Qx and Qy transitions of the chlorin. This observation is attributed to strong coupling of the LSPR to an H-dimer state not observed under weak coupling.

Light-matter interaction in the strong coupling regime: configurations, conditions, and applications

Resonance interaction between a molecular transition and a confined electromagnetic field can reach the coupling regime where coherent exchange of energy between light and matter becomes reversible. In this case, two new hybrid states separated in energy are formed instead of independent eigenstates, which is known as Rabi splitting. This modification of the energy spectra of the system offers new possibilities for controlled impact on various fundamental properties of coupled matter (such as the rate of chemical reactions and the conductivity of organic semiconductors). To date, the strong coupling regime has been demonstrated in many configurations under different ambient conditions. However, there is still no comprehensive approach to determining parameters for achieving the strong coupling regime for a wide range of practical applications. In this review, a detailed analysis of various systems and corresponding conditions for reaching strong coupling is carried out and their advantages and disadvantages, as well as the prospects for application, are considered. The review also summarizes recent experiments in which the strong coupling regime has led to new interesting results, such as the possibility of collective strong coupling between X-rays and matter excitation in a periodic array of Fe isotopes, which extends the applications of quantum optics; a strong amplification of the Raman scattering signal from a coupled system, which can be used in surface-enhanced and tip-enhanced Raman spectroscopy; and more efficient second-harmonic generation from the low polaritonic state, which is promising for nonlinear optics. The results reviewed demonstrate great potential for further practical applications of strong coupling in the fields of photonics (low-threshold lasers), quantum communications (switches), and biophysics (molecular fingerprinting).

Simple model of saturable localised surface plasmon

Localised surface plasmons (LSPs) are now applied to various fields, such as bio-sensing, solar cell, molecular fluorescence enhancement and quantum-controlled devices at nanometre scale. Recent experiments show that LSPs are optically saturated by high-intensity light. Absorption saturation arises as a result of strong optical nonlinearity and cannot be explained by the conventional boson model of LSPs. Here, we propose a simple model of saturable LSPs using an effective dipole approximation. The strategy is to directly compare the classical linear optical response of an LSP with that obtained from a saturable quantum two-level system in the limit of weak excitation. The second quantization can then be performed by replacing a classical polarizability with a quantum dipole operator. Taking an ellipsoidal nanometal as an example, we analyse in detail the optical response of a single ellipsoidal nanometal to validate our model. Our numerical results show that the plasmon resonance frequency and spectral linewidth decrease as the aspect ratio of the ellipsoid increases, which is similar to the size dependence observed in early experiments.

Signatures of Plexitonic States in Molecular Electroluminescence

We develop a quantum master equation (QME) approach to investigate the electroluminesence (EL) of molecules confined between metallic electrodes and coupled to quantum plasmonic modes. Within our general state-based framework, we describe electronic tunneling, vibrational damping, environmental dephasing, and the quantum coherent dynamics of coupled quantum electromagnetic field modes. As an example, we calculate the STM-induced spontaneous emission of a tetraphenylporphyrin (TPP) molecule coupled to a nanocavity plasmon. In the weak molecular exciton-plasmon coupling regime we find excellent agreement with experiments, including above-threshold hot luminescence, an effect not described by previous semiclassical calculations. In the strong coupling regime, we analyze the spectral features indicative of the formation of plexcitonic states.

Strong Coupling between Self-Assembled Molecules and Surface Plasmon Polaritons

We experimentally demonstrate strong coupling between self-assembled PTCDI-C7 organic molecules and the electromagnetic mode generated by surface plasmon polaritons (SPPs). The system consists of a dense self-assembly of ordered molecules evaporated directly on a thin gold film, which stack perpendicularly to the metal surface to form H-aggregates, without a host matrix. Experimental wavevector-resolved reflectance spectra show the formation of hybrid states that display a clear anticrossing, attesting the strong coupling regime with a Rabi splitting energy of Ω_R ≃ 102 meV at room temperature. We demonstrate that the strength of the observed strong coupling regime derives from the high degree of organization of the dense layers of self-assembled molecules at the nanoscale that results in the concentration of the oscillator strength in a charge-transfer Frenkel exciton, with a dipole moment parallel to the direction of the maximum electric field. We compare our results to numerical simulations of a transfer matrix model and reach good qualitative agreement with the experimental findings. In our nanophotonic system, the use of self-assembled molecules opens interesting prospects in the context of strong coupling regimes with molecular systems.

Superanomalous Skin Effect for Surface Plasmon Polaritons

It is commonly assumed that surface plasmon-polariton (SPP) excitations on a metal-dielectric interface decay exponentially inside the metallic sample. Here, we show that in a wide spectral interval the SPP field decays much slower, being inversely proportional to the distance to the interface modified by an additional logarithmic factor. This dependence differs from the standard anomalous skin effect and is provisionally referred to as superanomalous. Its origin is the nonlocality and the logarithmic singularity of the dielectric permittivity in metals. This type of decay is pronounced for SPP modes of higher frequencies, but it is suppressed for light waves.

Strongly Asymmetric Spectroscopy in Plasmon-Exciton Hybrid Systems due to Interference-Induced Energy Repartitioning

Recent intense effort has been devoted to exploring different manifestations of resonant excitations of strongly coupled plasmons and excitons, but so far such studies have been limited to situations where the Fano- or Rabi-type spectra are largely symmetric at zero detuning. Using a newly developed full quantum mechanical model, here we reveal the existence of a highly asymmetric spectroscopic regime for both the Rabi splitting and transparency dip. The asymmetric nature is inherently tied to the non-negligible exciton absorbance and is caused by substantial interference-induced energy repartitioning of the resonance peaks. This theoretical framework can be exploited to reveal the quantum behaviors of the two excitation entities with varying mutual coupling strengths in both linear and nonlinear regimes. We also use prototypical systems of rhodamine molecules strongly coupled with AuAg alloyed nanoparticles and well-devised control experiments to demonstrate the validity and tunability of the energy repartitioning and correlated electronic state occupations, as captured by the variations in the asymmetric spectroscopy and corresponding nonlinear absorption coefficient as a function of the Au:Ag ratio. The present study helps to substantially enrich our microscopic understanding of strongly coupled plasmon-exciton systems.

Fano resonance Rabi splitting of surface plasmons

Rabi splitting and Fano resonance are well-known physical phenomena in conventional quantum systems as atoms and quantum dots, arising from strong interaction between two quantum states. In recent years similar features have been observed in various nanophotonic and nanoplasmonic systems. Yet, realization of strong interaction between two or more Fano resonance states has not been accomplished either in quantum or in optical systems. Here we report the observation of Rabi splitting of two strongly coupled surface plasmon Fano resonance states in a three-dimensional plasmonic nanostructure consisting of vertical asymmetric split-ring resonators. The plasmonic system stably supports triple Fano resonance states and double Rabi splittings can occur between lower and upper pairs of the Fano resonance states. The experimental discovery agrees excellently with rigorous numerical simulations, and is well explained by an analytical three-oscillator model. The discovery of Fano resonance Rabi splitting could provide a stimulating insight to explore new fundamental physics in analogous atomic systems and could be used to significantly enhance light-matter interaction for optical sensing and detecting applications.

Polarization-dependent strong coupling between surface plasmon polaritons and excitons in an organic-dye-doped nanostructure

In this work, we demonstrate polarization-dependent strong coupling between surface plasmon polaritons (SPPs) and excitons in the J-aggregates-attached aperture array. It is shown that the excitons strongly couple with the polarization-dependent SPPs, and Rabi splittings are consequently observed. As a result, the polarization-dependent polariton bands are generated in the system. Increasing the incident angle, the polaritons disperse to higher energies under transverse-electric illumination, while the polaritons disperse to lower energies under transverse-magnetic illumination. Therefore, at different polarization incidence, we experimentally achieve distinct polaritons with opposite dispersion directions. In this way, tuning the polarization of the incident light, we can excite different polaritons whose energy propagates to different directions. Furthermore, by retrieving the mixing fractions of the components in these polariton bands, we find that the dispersion properties of the polaritons are inherited from both the SPPs and the excitons. Our investigation may inspire related studies on tunable photon-exciton interactions and achieve some potential applications on active polariton devices.

Plasmonic opals: observation of a collective molecular exciton mode beyond the strong coupling

Achieving and controlling strong light-matter interactions in many-body systems is of paramount importance both for fundamental understanding and potential applications. In this paper we demonstrate both experimentally and theoretically how to manipulate strong coupling between the Bragg-plasmon mode supported by an organo-metallic array and molecular excitons in the form of J-aggregates dispersed on the hybrid structure. We observe experimentally the transition from a conventional strong coupling regime exhibiting the usual upper and lower polaritonic branches to a more complex regime, where a third nondispersive mode is seen, as the concentration of J-aggregates is increased. The numerical simulations confirm the presence of the third resonance. We attribute its physical nature to collective molecule-molecule interactions leading to a collective electromagnetic response. A simple analytical model is proposed to explain the physics of the third mode. The nonlinear dependence on molecular parameters followed from the model are confirmed in a set of rigorous numerical studies. It is shown that at the energy of the collective mode molecules oscillate completely out of phase with the incident radiation acting as an effictive thin metal layer.

Strong Light-Matter Interactions in Single Open Plasmonic Nanocavities at the Quantum Optics Limit

Reaching the quantum optics limit of strong light-matter interactions between a single exciton and a plasmon mode is highly desirable, because it opens up possibilities to explore room-temperature quantum devices operating at the single-photon level. However, two challenges severely hinder the realization of this limit: the integration of single-exciton emitters with plasmonic nanostructures and making the coupling strength at the single-exciton level overcome the large damping of the plasmon mode. Here, we demonstrate that these two hindrances can be overcome by attaching individual J aggregates to single cuboid Au@Ag nanorods. In such hybrid nanosystems, both the ultrasmall mode volume of ∼71  nm^{3} and the ultrashort interaction distance of less than 0.9 nm make the coupling coefficient between a single J-aggregate exciton and the cuboid nanorod as high as ∼41.6  meV, enabling strong light-matter interactions to be achieved at the quantum optics limit in single open plasmonic nanocavities.