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We conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C2v symmetry. We analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator. Optical properties are examined using the FDTD method. It is demonstrated that all three shapes exhibit two prominent plasmon bands associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model where the electron pressure term is explicitly accounted for. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. For CW pumping, we explore properties of the SHG. Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. For pulsed excitations, we discuss the phenomenon of broadband THz generation induced by the DFG. It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose a simple analytical theory that agrees very well with the numerical experiments. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C2v symmetry.

With the help of a theoretical model and finite-difference-time-domain simulations based on the hydrodynamic-Maxwell model, we examine the effect of difference frequency generation in an array of L-shaped metal nano-particles characterized by intrinsic plasmonic nonlinearity. The outcomes of the calculations reveal the spectral interplay of the gain and loss in the vicinity of the fundamental frequency of the localized surface-plasmon resonances. Subsequently, we identify different array depths and pumping regimes facilitating parametric amplification and parametric down-conversion. Our results suggest that the parametric amplification regime becomes feasible on a scale of hundreds of nanometers and parametric downconversion on the scale of tens of nanometers, opening up new exciting opportunities for developing building blocks of photonic metasurfaces., Comment: 5 pages, 3 figures, journal article

Fabry-Perot microcavities can strongly enhance interactions between light and molecules, leading to the formation of hybrid light-matter states known as polaritons. Polaritons possess much smaller effective masses and much larger group velocities when the molecules are resonant with cavity modes that have finite (non-zero) in-plane wavevectors, giving rise to the possibilities of long-range and ultrafast ballistic transport. In this paper, we present results of numerical simulations of the ultrafast ballistic transport phenomenon in real space and time during and after initialization with a short, spatially localized pulse. We find that the transport of the molecular excitons as induced by the external light field is synchronized with the evolution of the enhanced and localized electromagnetic field inside the cavity. Moreover, the synchronized transport rate is in good agreement with the group velocities predicted from a calculated dispersion relation across a wide range of frequencies. These simulations provide an intuitive tool for understanding the collective motion of light and excitons and helps to better understand how experimental observations of polaritons should be interpreted., Comment: 22 Pages, 6 figures

We investigate the effect of a cavity on nonlinear two-photon transitions of a molecular system and how such an effect depends on the cavity quality factor, the field enhancement and the possibility of dephasing. We find that the molecular response to strong light fields in a cavity with variable quality factor can be understood as arising from a balance between (i) the ability of the cavity to enhance the field of an external probe and promote multiphoton transitions more easily and (ii) the fact that the strict selection rules on multiphoton transitions in a cavity support only one resonant frequency within the excitation range. Although our simulations use a classical-level description of the radiation field (i.e. we solve Maxwell-Bloch or Maxwell-Liouville equations within the Ehrenfest approximation for the field-molecule interaction), based on experience with this level of approximation in past studies of plasmonic and polaritonic systems, we believe that our results are valid over a wide range of external probing., Comment: 19 pages, 6 figures

The rigorous quantum mechanical description of the collective interaction of many molecules with the radiation field is usually considered numerically intractable, and approximation schemes must be employed. Standard spectroscopy usually contains some levels of perturbation theory, but under strong coupling conditions, other approximations are used. A common approximation is the 1-exciton model in which processes involving weak excitations are described using a basis comprising of the ground state and singly excited states of the molecule cavity-mode system. In another frequently used approximation in numerical investigations, the electromagnetic field is described classically, and the quantum molecular subsystem is treated in the mean-field Hartree approximation with its wavefunction assumed to be a product of single molecules' wavefunctions. The former disregards states that take long time to populate, and is therefore essentially a short time approximation. The latter is not limited in this way, but by its nature, disregards some intermolecular and molecule-field correlations. In this work, we directly compare results obtained from these approximations when applied to several prototype problems involving the optical response of molecule-in-optical cavities systems. In particular, we show that our recent model investigation (J. Chem. Phys. 157, 114108 (2022)) of the interplay between the electronic strong coupling and molecular nuclear dynamics using the truncated 1-exciton approximation agrees very well with the semiclassical mean-field calculation.

Like a free particle, the initial growth of a broad (relative to lattice spacing) wavepacket placed on an ordered lattice is slow (zero initial slope) and becomes linear in $t$ at long time. On a disordered lattice, the growth is inhibited at long time (Anderson localization). We consider site disorder with nearest-neighbor hopping on 1- and 2-dimensional systems, and show via numerical simulations supported by the analytical study that the short time growth of the particle distribution is faster on the disordered lattice than on the ordered one. Such faster spread takes place on time and length scale that may be relevant to the exciton motion in disordered systems.

We consider an ensemble of diatomic molecules resonantly coupled to an optical cavity under strong coupling conditions at normal incidence. Photodissociation dynamics is examined via direct numerical integration of the coupled Maxwell-Schrodinger equations with molecular ro-vibrational degrees of freedom explicitly taken into account. It is shown that the dissociation is significantly affected (slowed down) when the system is driven at its polaritonic frequencies. The observed effect is demonstrated to be of transient nature and has no classical analog. An intuitive explanation of the dissociation slowdown at polaritonic frequencies is proposed.

An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into three-dimensional domain decomposition methodology implemented for numerical integration of the Maxwell equations. The approach employed enables directly accessing dynamics of collective effects as the number of molecules in simulations can be drastically increased. Numerical experiments measuring speedup factors demonstrate the efficiency of the proposed methodology. As an example, we consider dynamics of nearly 700,000 diatomic molecules with ro-vibrational degrees of freedom explicitly accounted for coupled to electromagnetic radiation crafted by periodic arrays of split-ring resonators and triangular nanoholes. As an application of the approach, dissociation dynamics under strong coupling conditions is scrutinized. It is demonstrated that the dissociation rates are significantly affected near polaritonic frequencies., Comment: J. Comp. Phys. (accepted)

We study the effect of degenerate parametric down-conversion (DPDC) in an ensemble of two-level quantum emitters (QEs) coupled via near-field interactions to a single surface plasmon (SP) mode of a nonlinear plasmonic cavity. For this purpose, we develop a quantum driven-dissipative model capturing non-equilibrium dynamics of the system in which incoherently pumped QEs have transition frequency tuned near the second-harmonic response of the SPs. Considering the strong coupling regime, i.e., the SP-QE interaction rate exceeds system dissipation rates, we find a critical SP-QE coupling attributed to the phase transition between normal and lasing steady states. Examining fluctuations above the system's steady states, we predict new elementary excitations, namely, the exciton-plasmon polaritons formed by the two-SP quanta and single-exciton states of QEs. The contribution of two-SP quanta results in the linear scaling of the SP-QE interaction rate with the number of QEs, ${\cal N}_o$, as opposed to the $\sqrt{{\cal N}_o}$-scaling known for the Dicke and Tavis-Cummings models. We further examine how SP-QE interaction scaling affects the polariton dispersions and power spectra in the vicinity of the critical coupling. For this purpose, we compare the calculation results assuming a finite ensemble of QEs and the model thermodynamic limit. The calculated power spectra predict an interplay of coherent photon emission by QEs near the second-harmonic frequency and correlated photon-pair emission at the fundamental frequency by the SPs (i.e., the photonic DPDC effect)., Comment: 8 pages, 3 figures

We investigate the process of the second harmonic generation by plasmonic nano-antennas that exhibit Fano-like resonances. A rigorous fully vectorial Maxwell-hydrodynamics approach is employed to directly calculate the second order susceptibilities as function of the pump frequency, considering a periodic array of nanodolmens comprised of three Au nanorods. The results of the numerical simulations demonstrate noticeable enhancement of the second harmonic efficiency by the antisymmetric mode. Additionally, a simple analytical model based on two coupled nonlinear oscillators is proposed. It is shown that the second order optical response can be significantly enhanced at the frequency of the antisymmetric normal mode thus supporting our numerical results.

The interplay between static and dynamic disorder and collective optical response in molecular ensembles is an important characteristic of nanoplasmonic and nanophotonic molecular systems. Here we investigate the cooperative superradiant response of a molecular ensemble of quantum emitters under the influence of environmental disorder, including inhomogeneous broadening (as induced by static random distribution of the molecular transition frequencies) and motional narrowing (as induced by stochastic modulation of these excitation energies). The effect of inhomogeneous broadening is to destroy the coherence of the collective molecular excitation and suppress superradiant emission. However, fast stochastic modulation of the molecular excitation energy can effectively restore the coherence of the quantum emitters and lead to a recovery of superradiant emission, which is an unexpected manifestation of motional narrowing. For a light scattering process as induced by an off-resonant incident pulse, stochastic modulation leads to inelastic fluorescence emission at the average excitation energy at long times and suggests that dynamic disorder effects can actually lead to collective excitation of the molecular ensemble.

The interaction between excited states of a molecule and excited states of metal nanostructure (e.g. plasmons) leads to hybrid states with modified optical properties. When plasmon resonance is swept through molecular transition frequency an avoided crossing may be observed, which is often regarded as a signature of strong coupling between plasmons and molecules. Such strong coupling is expected to be realized when $2|U|/{\hbar\Gamma}>1$, where $U$ and ${\Gamma}$ are the molecule-plasmon coupling and the spectral width of the optical transition respectively. Because both $U$ and ${\Gamma}$ strongly increase with decreasing distance between a molecule and a plasmonic structure it is not obvious that this condition can be satisfied for any molecule-metal surface distance. In this work we investigate the behavior of $U$ and ${\Gamma}$ for several geometries. Surprisingly, we find that if the only contributions to ${\Gamma}$ are lifetime broadenings associated with the radiative and nonradiative relaxation of a single molecular vibronic transition, including effects on molecular radiative and nonradiative lifetimes induced by the metal, the criterion $2|U|/{\hbar\Gamma}>1$ is easily satisfied by many configurations irrespective of the metal-molecule distance. This implies that the Rabi splitting can be observed in such structures if other sources of broadening are suppressed. Additionally, when the molecule-metal surface distance is varied keeping all other molecular and metal parameters constant, this behavior is mitigated due to the spectral shift associated with the same molecule-plasmon interaction, making the observation of Rabi splitting more challenging.

We demonstrate strong coupling between a single J-aggregate and an inverse bowtie plasmonic structure, when the J-aggregate is located at a specific axial distance from the metallic surface. Three hybrid modes are clearly observed, witnessing a strong interaction, with a Rabi splitting of up to 290 meV, the precise value of which significantly depends on the orientation of the J-aggregate with respect to the symmetry axis of the plasmonic structure. We repeated our experiments with a set of triangular hole arrays, showing consistent formation of three or more hybrid modes, in good agreement with numerical simulations., Comment: Main paper and then supporting infromation, one after the other, in the same pdf file. All in all - 26 pages 11 figures

We investigate second harmonic generation (SHG) from hexagonal periodic arrays of triangular nano-holes of aluminum using a self-consistent methodology based on the hydrodynamics-Maxwell-Bloch approach. It is shown that angular polarization patterns of the far-field second harmonic response abide to three-fold symmetry constraints on tensors. When a molecular layer is added to the system and its parameters are adjusted to achieve the strong coupling regime between a localized plasmon mode and molecular excitons, Rabi splitting is observed from occurrence of both single- and two-photon transition peaks within the SHG power spectrum. It is argued that the splitting observed for both transitions results from direct transitions between lower and upper polaritonic states of the strongly coupled system. This interpretation can be accounted by a tailored three-level quantum model, with results in agreement with the unbiased numerical approach. Our results suggest the hybrid states formed in strongly coupled systems directly contribute to the nonlinear dynamics. This opens new directions in designing THz sources and nonlinear frequency converters., Comment: submitted to JCP

We report on theoretical study of second-harmonic generation (SHG) in plasmonic nanostructures interacting with two-level quantum emitters (QE) under incoherent energy pump. We generalize driven-dissipative Tavis-Cummings model by introducing anharmonic surface plasmon-polariton (SPP) mode coupled to QEs and examine physical properties of corresponding SPP-QE polariton states. Our calculations of the SHG efficiency for strong QE-SPP coupling demonstrate orders of magnitude enhancement facilitated by the polariton gain. We further discuss time-domain numerical simulations of SHG in a square lattice comprised of Ag nanopillars coupled to QEs utilizing fully vectorial nonperturbative nonlinear hydrodynamic model for conduction electrons coupled to Maxwell-Bloch equations for QEs. The simulations support the idea of gain enhanced SHG and show orders of magnitude increase in the SHG efficiency as the QEs are tuned in resonance with the lattice plasmon mode and brought above the population inversion threshold by incoherent pump. By varying pump frequency and tuning QEs to a localized plasmon mode, we demonstrate further enhancement of the SHG efficiency facilitated by strong local electric fields. The incident light polarization dependence of the SHG is examined and related to the symmetries of participating plasmon modes., Comment: 10 pages, 6 figures

Monolayer transition metal dichalcogenides, coupled to metal plasmonic nanocavities, have recently emerged as new platforms for strong light-matter interactions. These systems are expected to have nonlinear optical properties that will enable them to be used as entangled photon sources, compact wave-mixing devices, and other elements for classical and quantum photonic technologies. Here we report the first experimental investigation of the nonlinear properties of these strongly coupled systems, by observing second harmonic generation from a WSe2 monolayer strongly coupled to a single gold nanorod. The pump frequency dependence of the second harmonic signal displays a pronounced splitting that can be explained by a coupled oscillator model with second-order nonlinearities. Rigorous numerical simulations utilizing a nonperturbative nonlinear hydrodynamic model of conduction electrons support this interpretation and reproduce experimental results. Our study thus lays the groundwork for understanding the nonlinear properties of strongly coupled nanoscale systems.

In the developing field of nonlinear plasmonics, it is important to understand the fundamental relationship between properties of the localized surface plasmon resonance (LSPR) of metallic nanostructures and their nonlinear optical responses. A detailed understanding of nonlinear responses from nanostructures with well characterized LSPRs is an essential prerequisite for the future design of sophisticated plasmonic systems with advanced functions to control light. In this article, we investigate the second order harmonic (SH) responses from gold nanocrescent (Au NC) antennas which have wavelength and polarization sensitive LSPRs in the visible and near-infrared wavelength range. The wavelength dependence of the SH intensity exhibits spectral profiles different from dipole LSPR bands in absorbance spectra. The incident polarization angle dependence was found to vary significantly when the excitation wavelength was tuned over the dipole band. Finite-difference time-domain calculations coupled with a nonlinear hydrodynamic model were carried out for Au NC arrays to investigate the local field enhancement of the incoming fundamental and emitting SH light. The experimental and theoretical results indicate that the effects of higher order LSPRs, such as quadrupole and multipole resonances, occurring at SH wavelengths are important in governing the SH generation process. Also, it is shown that the incident polarization angle dependence of SH signals is very strongly sensitive to nanoscale variations in the NC shape.

Optical properties of periodic arrays of nanoholes of a triangular shape with experimentally realizable parameters are examined in both linear and nonlinear regimes. Utilizing fully vectorial three-dimensional approach based on the nonlinear hydrodynamic Drude model describing metal coupled to Maxwells equations and Bloch equations for molecular emitters we analyze linear transmission, reflection, and nonlinear power spectra. Rigorous numerical calculations demonstrating second and third harmonic generation by the triangular hole arrays are performed. It is shown that both the Coulomb interaction of conduction electrons and the convective term contribute on equal footing to the nonlinear response of metal. It is demonstrated that the energy conversion efficiency in the second harmonic process is the highest when the system is pumped at the localized surface plasmon resonance. When molecular emitters are placed on a surface of the hole array lineshapes of the second harmonic signal exhibits three peaks corresponding to second harmonics of the localized surface plasmon mode and upper and lower polaritonic states., Comment: accepted for publication at Journal of Chemical Physics, manuscript includes Supplementary Materials

Have you ever wondered why we have never heard of psychics and palm readers winning millions of dollars in state or local lotteries or becoming Wall Street wolfs? Neither have I. Yet we are constantly bombarded by tabloid news on how vaccines cause autism (hint: they do not), or some unknown firm building a mega-drive that defies the laws of physics (nope, that drive does not work either). And the list continues on and on and on. Sometimes it looks quite legit as, say, various natural vitamin supplements that supposedly increase something that cannot be increased, or enhance something else that is most likely impossible to enhance by simply swallowing a few pills. Or constantly evolving diets that sure work giving a false relieve to those who really need to stop eating too much and actually pay frequent visits to a local gym. It is however understandable that most of us fall for such products and news just because we cannot be experts in everything, and we tend to trust various mass-media sources without even a glimpse of skepticism. So how can we distinguish between baloney statements and real exciting scientific discoveries and breakthroughs? In what follows I will try to do my best to provide a simple how-to user guide to debunking pseudoscientific claims.

The physics of collective optical response of molecular assemblies, pioneered by Dicke in 1954, has long been at the center of theoretical and experimental scrutiny. The influence of the environment on such phenomena is also of great interest due to various important applications in e.g. energy conversion devices. In this manuscript we demonstrate both experimentally and theoretically the spatial modulations of the collective decay rates of molecules placed in proximity to a metal interface. We show in a very simple framework how the cooperative optical response can be analyzed in terms of intermolecular correlations causing interference between the response of different molecules and the polarization induced on a nearby metallic boundary and predict similar collective interference phenomena in excitation energy transfer between molecular aggregates.

Rigorous electrodynamical simulations based on the nonlinear Drude model are performed to investigate the influence of strong coupling on high harmonic generation by periodic metal gratings. It is shown that a thin dispersive material with a third order nonlinearity strongly coupled to surface plasmon-polaritons significantly affects even harmonics generated solely by the metal. The physical nature of this effect is explained using a simple analytical model and further supported by numerical simulations. Furthermore, the behavior of the second and third harmonics is investigated as a function of various physical parameters of the model material system, revealing highly complex dynamics. The nonlinear optical response of 2D few-layer WS2 with both second and third order susceptibilities coupled to a periodic plasmonic grating is shown to have a significant effect on the second harmonic generation of the metal., Comment: submitted to Journal of Physical Chemistry A

In a previous paper, we introduced Ehrenfest+R dynamics for a two-level system and showed how spontaneous emission can be heuristically included such that, after averaging over an ensemble of Ehrenfest+R trajectories, one can recover both coherent and incoherent electromagnetic fields. In the present paper, we now show that Ehrenfest+R dynamics can also correctly describe Raman scattering, whose features are completely absent from standard Ehrenfest dynamics. Ehrenfest+R dynamics appear to be quantitatively accurate both for resonant and off-resonant Raman signals, as compared with Kramers-Heisenberg-Dirac (KHD) theory.

The dynamics of an electronic system interacting with an electromagnetic field is investigated within mixed quantum-classical theory. Beyond the classical path approximation (where we ignore all feedback from the electronic system on the photon field), we consider all electron-photon interactions explicitly according to Ehrenfest (i.e. mean-field) dynamics and a set of coupled Maxwell-Liouville equations. Because Ehrenfest dynamics cannot capture certain quantum features of the photon field correctly, we propose a new Ehrenfest+R method that can recover (by construction) spontaneous emission while also distinguishing between electromagnetic fluctuations and coherent emission.

We investigate two key representative semiclassical approaches for propagating resonant energy transfer between a pair of electronic two-level systems (donor and acceptor) with coupled Maxwell-Liouville equations. On the one hand, when the electromagnetic (EM) field is treated classically and Coulomb interactions are treated quantum-mechanically, we find that a quantum-classical mismatch leads to a violation of causality, i.e., the acceptor can be excited before the retarded EM field arrives. On the other hand, if we invoke a classical intermolecular Coulomb operator, we find that the energy transfer in the near field loses quantitative accuracy compared with F\"orster theory, even though causality is strictly obeyed. Thus, our work raises a fundamental paradox when choosing a semiclassical electrodynamics algorithm. Namely, which is more important: Accurate short range interactions or long range causality? Apparently, one cannot have one's cake and eat it too., Comment: 2 figures, 21 pages

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one and three dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. We consider three flavors of mixed quantum-classical dynamics: the classical path approximation (CPA), Ehrenfest dynamics, and symmetrical quantum-classical (SQC) dynamics. The CPA fails to recover a consistent description of spontaneous emission. A consistent "spontaneous" emission can be obtained from Ehrenfest dynamics--provided that one starts in an electronic superposition state. Spontaneous emission is always obtained using SQC dynamics. Using the SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by W. Miller [J. Chem. Phys. 69, 2188-2195, 1978] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights new possibilities for studying light-matter interactions with semiclassical mechanics., Comment: 15 figures

We study theoretically optical response of WS2 monolayer located near periodic metal nanostructured arrays in two and three dimensions. The emphasis of simulations is on the strong coupling regime of excitons supported by WS2 and surface plasmon-polaritons supported by various periodic plasmonic interfaces. It is demonstrated that a monolayer of WS2 placed in a close proximity of periodic arrays of either slits or holes results in a Rabi splitting of the corresponding surface plasmon-polariton resonance as revealed in calculated transmission and reflection spectra. The nonlinear regime, at which the monolayer of WS2 exhibits the third harmonic generation is studied in details. It is shown that at the strong coupling regime the third harmonic signal is significantly affected by plasmon-polaritons and the symmetry of hybrid exciton-plasmon modes. It is also shown that the local electromagnetic field induced by plasmons is the major contributor to the enhancement of the third harmonic signal in three dimensions. The local electromagnetic fields resulted from the third harmonic generation are greatly localized and highly sensitive to the environment making it a great tool for nano-probes.

This review provides a brief introduction to the physics of coupled exciton-plasmon systems, the theoretical description and experimental manifestation of such phenomena, followed by an account of the state-of-the-art methodology for the numerical simulations of such phenomena and supplemented by a number of FORTRAN codes, by which the interested reader can introduce himself/herself to the practice of such simulations. Applications to CW light scattering as well as transient response and relaxation are described. Particular attention is given to so-called strong coupling limit, where the hybrid exciton-plasmon nature of the system response is strongly expressed. While traditional descriptions of such phenomena usually rely on analysis of the electromagnetic response of inhomogeneous dielectric environments that individually support plasmon and exciton excitations, here we explore also the consequences of a more detailed description of the molecular environment in terms of its quantum density matrix (applied in a mean field approximation level). Such a description makes it possible to account for characteristics that cannot be described by the dielectric response model: the effects of dephasing on the molecular response on one hand, and nonlinear response on the other. It also highlights the still missing important ingredients in the numerical approach, in particular its limitation to a classical description of the radiation field and its reliance on a mean field description of the many-body molecular system. We end our review with an outlook to the near future, where these limitations will be addressed and new novel applications of the numerical approach will be pursued., Comment: topical review submitted to Journal of Physics: Condensed Matter

We study the strong coupling between the molecular excited state and the plasmonic modes of silver hole arrays with a resonant frequency very close to the asymptotic line of the plasmonic dispersion relation, at the nonlinear regime. We demonstrate that the strong coupling regime can be achieved between the two sub-systems at low molecular densities with negligible damping of the electromagnetic field. Our results are supported by rigorous numerical simulations showing that the strong coupling is observed when the molecular transition lies within the nonlinear regime of the dispersion relation rather than the linear regime., Comment: submitted to PCCP, 7 pages and 3 pages supporting information

We extend the model of exciton-plasmon materials to include a ro-vibrational structure of molecules using wave-packet propagations on electronic potential energy surfaces. The new model replaces conventional two-level emitters with more complex molecules allowing to examine the influence of alignment and vibrational dynamics on strong coupling with surface plasmon-polaritons. We apply the model to a hybrid system comprising a thin layer of molecules placed on top of a periodic array of slits. Rigorous simulations are performed for two types of molecular systems described by vibrational bound-bound and bound-continuum electronic transitions. Calculations reveal new features in transmission, reflection and absorption spectra including the observation of significantly higher values of the Rabi splitting and vibrational patterns clearly seen in the corresponding spectra. We also examine the influence of anisotropic initial conditions on optical properties of hybrid materials demonstrating that the optical response of the system is significantly affected by an initial pre-alignment of the molecules. Our work demonstrates that pre-aligned molecules could serve as an efficient probe for the sub-diffraction characterization of the near-field near metal interfaces., Comment: 14 pages, 4 figures, submitted to PRB

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 a 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 the 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 effective thin metal layer., Comment: submitted to Scientific Reports

We investigate the dynamics of photon echo exhibited by exciton-plasmon systems under strong coupling conditions. Using a self-consistent model based on coupled Maxwell-Bloch equations we investigate femtosecond time dynamics of ensembles of interacting molecules optically coupled to surface plasmon supporting materials. It is shown that observed photon echoes under two pulse pump-probe sequence are highly dependent on various material parameters such as molecular concentration and periodicity. Simulations of photon echoes in exciton-plasmon materials reveal a unique signature of the strong exciton-plasmon coupling, namely a double-peak structure in spectra of recorded echo signals. This phenomenon is shown to be related to hybrid states (upper and lower polaritons) in exciton-plasmon systems under strong coupling conditions. It is also demonstrated that the double-peak echo is highly sensitive to mild deviations of the coupling from resonant conditions making it a great tool for ultrafast probes., Comment: submitted to JCP

We introduce an accurate non-Hermitian Schr\"odinger-type approximation of Bloch optical equations for two-level systems. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics in both weak and strong laser fields. In this approach, it is sufficient to propagate the wave function of the quantum system instead of the density matrix, providing that relaxation and dephasing are taken into account via automatically-adjusted time-dependent gain and decay rates. The developed formalism is applied to the problem of scattering and absorption of electromagnetic radiation by a thin layer comprised of interacting two-level emitters.

We study the transfer of electromagnetic energy across a subwavelength gap separating two co-axial metal nanorodes. The absence of spacer in the gap separating the rods the system exhibits the strong coupling between longitudinal plasmons in the two rods. The nature and magnitude of this coupling is studied by varying various geometrical parameters. When the length of one rod is varied this mode spectrum exhibits the familiar anti-crossing behavior that depends on the coupling strength determined by the gap width. As a function of frequency the transmission is dominated by a splitted longitudinal plasmon peak. The two hybrid modes are the dipole-like "bonding" mode characterized by a peak intensity in the gap, and a quadrupole-like "antibonding" mode whose amplitude vanishes at the gap center. When off-resonant $2-$level emitters are placed in the gap, almost no effect on the frequency dependent transmission is observed. In contrast, when the molecular system is resonant with the plasmonic lineshape, the transmission is strongly modified, showing characteristics of strong exciton-plasmon coupling, modifying mostly the transmission near the lower frequency "bonding" plasmon mode. The presence of resonant molecules in the gap affects not only the molecule-field interaction but also the spatial distribution of the field intensity and the electromagnetic energy flux across the junction.

We investigate the optical response of a system consisting of periodic silver V-grooves interacting with quantum emitters. Two surface plasmon-polariton resonances are identified in the reflection spectrum of bare silver grooves, with the intensity of one resonance being localized near the bottom of the groove and that of the other resonance being distributed throughout the entire groove. The linear response of the hybrid silver-emitter system is thoroughly analyzed by considering the coupling between surface plasmon polaritons and emitters as the geometry of the grooves and the spatial distribution of emitters within the grooves are varied. The nonlinear response of the system is also considered by pumping the emitters with a short, high-intensity pulse. By changing the duration or the intensity of the pump, the population of emitters in the ground state at the end of the pump is varied, and it is found (upon probing with a short pulse) that an increase in the fraction of emitters in the ground state corresponds to an increase in Rabi splitting. Spatial variations in the ground state population throughout the emitter region are shown to be a result of field retardation., Comment: 17 pages, 6 figures, submitted to Phys. Rev. B

We consider a hybrid plasmon-exciton system comprised of a resonant molecular subsystem and three Au wires supporting a dipole mode which can be coupled to a dark mode in controllable fashion by variation of a symmetry parameter. The physics of such a system under strong coupling conditions is examined in detail. It is shown that if two wires supporting the dark mode are covered with molecular layers the system exhibits four resonant modes for a strong coupling regime due to asymmetry and lifted degeneracy of the molecular state in this case, while upon having molecular aggregates covering the top wire with dipolar mode, three resonant modes appear. Pump-probe simulations are performed to scrutinize the quantum dynamics and find possible ways to control plasmon-exciton materials. It is demonstrated that one can design hybrid nanomaterials with highly pronounced Fano-type resonances when excited by femtosecond lasers., Comment: 10 pages, 6 figures, submitted to ACS Photonics

A detailed theory describing linear optics of vapors comprised of interacting multi-level quantum emitters is proposed. It is shown both by direct integration of Maxwell-Bloch equations and using a simple analytical model that at large densities narrow transparency windows appear in otherwise completely opaque spectra. The existence of such windows is attributed to overlapping resonances. This effect, first introduced for three-level systems in [R. Puthumpally-Joseph, M. Sukharev, O. Atabek and E. Charron, Phys. Rev. Lett. 113, 163603 (2014)], is due to strongly enhanced dipole-dipole interactions at high emitters' densities. The presented theory extends this effect to the case of multilevel systems. The theory is applied to the D1 transitions of interacting Rb-85 atoms. It is shown that at high atomic densities, Rb-85 atoms can behave as three-level emitters exhibiting all the properties of dipole induced electromagnetic transparency. Applications including slow light and laser pulse shaping are also proposed.

Shaped ultrafast laser pulses were used to study and control the ionization dynamics of electronically excited pyrazine in a pump and probe experiment. For pump pulses created without feedback from the product signal, the ion growth curve (the parent ion signal as a function of pump/probe delay) was described quantitatively by the classical rate equations for internal conversion of the $S_2$ and $S_1$ states. Very different, non-classical behavior was observed when a genetic algorithm (GA) was used to minimize the ion signal at some pre-determined target time, T. Two qualitatively different control mechanisms were identified for early (T$<1.5$ ps) and late (T$>1.5$ ps) target times. In the former case, the ion signal was largely suppressed for $t1.5$ ps the ion growth curve followed the classical rate equations for $t

We determine the optical response of a thin and dense layer of interacting quantum emitters. We show that in such a dense system, the Lorentz redshift and the associated interaction broadening can be used to control the transmission and reflection spectra. In the presence of overlapping resonances, a Dipole-Induced Electromagnetic Transparency (DIET) regime, similar to Electromagnetically Induced Transparency (EIT), may be achieved. DIET relies on destructive interference between the electromagnetic waves emitted by quantum emitters. Carefully tuning material parameters allows to achieve narrow transmission windows in otherwise completely opaque media. We analyze in details this coherent and collective effect using a generalized Lorentz model and show how it can be controlled. Several potential applications of the phenomenon, such as slow light, are proposed.

The interaction of chirped femtosecond laser pulses with hybrid materials - materials comprised of plasmon sustaining structures and resonant molecules - is scrutinized using a self-consistent model of coupled Maxwell-Bloch equations. The optical properties of such systems are examined with the example of periodic sinusoidal gratings. It is shown that under strong coupling conditions one can control light transmission using chirped pulses in a spatiotemporal manner. The temporal origin of control relies on chirps non-symmetric in time while the space control is achieved via spatial localization of electromagnetic energy due to plasmon resonances., Comment: 7 pages, 5 figures, to be submitted to JCP

The dependence of the radiative emission and the non-radiative (energy transfer to the metal) relaxation rates of a molecule near a small metal particle on the molecule-to-particle distance and on the molecular orientation is calculated using a numerical solution of the Maxwell equations for a model that described the metal as a dispersive dielectric particle and the molecule as an oscillating point dipole. The emission rate is obtained by evaluating the total oscillating dipole in the system, while the non-radiative rate is inferred from the rate of heat production on the particle. For the distance dependence of the non-radiative rate we find, in agreement with experimental observations, marked deviation from the prediction of the standard theory of fluorescence resonance energy transfer (FRET). In departure from previous interpretations, we find that electromagnetic retardation is the main source of this deviation at large molecule-particle separations. The radiative emission rate reflects the total dipole induced in the molecule- particle system, and its behavior as function of distance and orientation stems mostly from the magnitude of the oscillating polarization on the metal particle (which, at resonance, is strongly affected by plasmon excitation), and from the way this polarization combines with the molecular dipole to form the total system dipole., Comment: 20 pages, 6 figures, submitted to J. Phys. Chem. C

The nonlinear optical dynamics of nano-materials comprised of plasmons interacting with quantum emitters is investigated by a self-consistent model based on the coupled Maxwell-Liouville-von Neumann equations. It is shown that ultra-short resonant laser pulses significantly modify the optical properties of such hybrid systems. It is further demonstrated that the energy transfer between interacting molecules and plasmons occurs on a femtosecond time scale and can be controlled with both material and laser parameters., Comment: 15 pages, 9 figures, submitted to ACS Nano

We consider a biased molecular junction subjected to external time-dependent electromagnetic field. We discuss local field formation due to both surface plasmon-polariton excitations in the contacts and the molecular response. Employing realistic parameters we demonstrate that such self-consistent treatment is crucial for proper description of the junction transport characteristics., Comment: 9 pages, 7 figures