Graphene multilayers for coherent perfect absorption: effects of interlayer separation.

We present a model study to estimate the sensitivity of the optical absorption of multilayered graphene structure to the subnanometer interlayer separation. Starting from a transfer-matrix formalism we derive semi-analytical expressions for the far-field observables. Neglecting the interlayer separation, results in upper bounds to the absorption of 50% for real-valued sheet conductivities, exactly the value needed for coherent perfect absorption (CPA), while for complex-valued conductivities we identify upper bounds that are always lower. For pristine graphene the number of layers required to attain this maximum is found to be fixed by the fine structure constant. For finite interlayer separations we find that this upper bound of absorption only exists until a particular value of interlayer separation (Dlim) which is less than the realistic interlayer separation in graphene multilayers. Beyond this value, we find a strong dependence of absorption with the interlayer separation. For an infinite number of graphene layers a closed-form analytical expression for the absorption is derived, based on a continued-fraction analysis that also leads to a simple expression for Dlim. Our comparison with experiments illustrates that multilayer Van der Waals crystals suitable for CPA can be more accurately modelled as electronically independent layers and more reliable predictions of their optical properties can be obtained if their subnanometer interlayer separations are carefully accounted for.

Quantitative near-field characterization of surface plasmon polaritons on monocrystalline gold platelets.

Near-field microscopy allows for visualization of both the amplitude and phase of surface plasmon polaritons (SPPs). However, their quantitative characterization in a reflection configuration is challenging due to complex wave patterns arising from the interference between several excitation channels. Here, we present near-field measurements of SPPs on large monocrystalline gold platelets in the visible. We study systematically the influence of the incident angle of the exciting light on the SPPs launched by an atomic force microscope tip. We find that the amplitude and phase signals of these SPPs are best disentangled from other signals at grazing incident angle relative to the edge of the gold platelet. Furthermore, we introduce a simple model to extract the wavelength and in particular the propagation length of the tip-launched plasmons. Our experimental results are in excellent agreement with our theoretical model. The presented method allows the quantitative analysis of polaritons occurring in different materials at visible wavelengths.

Efficient stochastic simulation of rate equations and photon statistics of nanolasers.

Based on a rate equation model for single-mode two-level lasers, two algorithms for stochastically simulating the dynamics and steady-state behaviour of micro- and nanolasers are described in detail. Both methods lead to steady-state photon numbers and statistics characteristic of lasers, but one of the algorithms is shown to be significantly more efficient. This algorithm, known as Gillespie's first reaction method (FRM), gives up to a thousandfold reduction in computation time compared to earlier algorithms, while also circumventing numerical issues regarding time-increment size and ordering of events. The FRM is used to examine intra-cavity photon distributions, and it is found that the numerical results follow the analytics exactly. Finally, the FRM is applied to a set of slightly altered rate equations, and it is shown that both the analytical and numerical results exhibit features that are typically associated with the presence of strong inter-emitter correlations in nanolasers.

Magnetoplasmons in monolayer black phosphorus structures.

Two-dimensional materials supporting deep-subwavelength plasmonic modes can also exhibit strong magneto-optical responses. Here, we theoretically investigate magnetoplasmons (MPs) in monolayer black phosphorus (BP) structures under moderate static magnetic fields. We consider three different structures, namely, a continuous BP monolayer, an edge formed by a semi-infinite sheet, and finally, a triangular wedge configuration. Each of these structures shows strongly anisotropic magneto-optical responses induced both by the external magnetic field and by the intrinsic anisotropy of the BP lattice. Starting from the magneto-optical conductivity of a single layer of BP, we derive the dispersion relation of the MPs in the considered geometries, using a combination of analytical, semi-analytical, and numerical methods. We fully characterize the MP dispersions and the properties of the corresponding field distributions, and we show that these structures sustain strongly anisotropic subwavelength modes that are highly tunable. Our results demonstrate that MPs in monolayer BP, with its inherent lattice anisotropy as well as magnetically induced anisotropy, hold potential for tunable anisotropic materials operating below the diffraction limit, thereby paving the way for tailored nanophotonic devices at the nanoscale.

On collective Rabi splitting in nanolasers and nano-LEDs.

We analytically calculate the optical emission spectrum of nanolasers and nano-LEDs based on a model of many incoherently pumped two-level emitters in a cavity. At low pump rates, we find two peaks in the spectrum for large coupling strengths and numbers of emitters. We interpret the double-peaked spectrum as a signature of collective Rabi splitting, and discuss the difference between the splitting of the spectrum and the existence of two eigenmodes. We show that an LED will never exhibit a split spectrum, even though it can have distinct eigenmodes. For systems where the splitting is possible, we show that the two peaks merge into a single one when the pump rate is increased. Finally, we compute the linewidth of the systems, and discuss the influence of inter-emitter correlations on the lineshape.

Nonlocal study of ultimate plasmon hybridization.

Within our recently proposed generalized nonlocal optical response (GNOR) model, where nonlocal response is included by taking into account both convective and diffusive currents of the conduction electrons, we revisit the fundamental problem of an optically excited plasmonic dimer. We consider the transition from separated dimers via touching dimers to finally overlapping dimers. In particular, we focus on the touching case, showing a fundamental limit on the hybridization of the bonding plasmon modes due to nonlocality. Using transformation optics, we determine a simple analytical equation for the resonance energies.

Projected Dipole Model for Quantum Plasmonics.

Quantum effects of plasmonic phenomena have been explored through ab initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer-the only introduced parameter-is mapped from the free-electron distribution near the metal surface as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied in two and three dimensions to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects of nonlocal response and a finite work function with TDDFT-level accuracy. Applying the theory to dimers, we find quantum corrections to the hybridization even in mesoscopic dimers, as long as the gap itself is subnanometric.

Hyperbolic metamaterial lens with hydrodynamic nonlocal response.

We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we propose to measure the near-field distribution of a hyperbolic metamaterial lens.

Blueshift of the surface plasmon resonance in silver nanoparticles: substrate effects.

We study the blueshift of the surface plasmon (SP) resonance energy of isolated Ag nanoparticles with decreasing particle diameter, which we recently measured using electron energy loss spectroscopy (EELS) [1]. As the particle diameter decreases from 26 down to 3.5 nm, a large blueshift of 0.5 eV of the SP resonance energy is observed. In this paper, we base our theoretical interpretation of our experimental findings on the nonlocal hydrodynamic model, and compare the effect of the substrate on the SP resonance energy to the approach of an effective homogeneous background permittivity. We derive the nonlocal polarizability of a small metal sphere embedded in a homogeneous dielectric environment, leading to the nonlocal generalization of the classical Clausius-Mossotti factor. We also present an exact formalism based on multipole expansions and scattering matrices to determine the optical response of a metal sphere on a dielectric substrate of finite thickness, taking into account retardation and nonlocal effects. We find that the substrate-based calculations show a similar-sized blueshift as calculations based on a sphere in a homogeneous environment, and that they both agree qualitatively with the EELS measurements.

Quantum optical effective-medium theory for loss-compensated metamaterials.

A central aim in metamaterial research is to engineer subwavelength unit cells that give rise to desired effective-medium properties and parameters, such as a negative refractive index. Ideally one can disregard the details of the unit cell and employ the effective description instead. A popular strategy to compensate for the inevitable losses in metallic components of metamaterials is to add optical gain material. Here we study the quantum optics of such loss-compensated metamaterials at frequencies for which effective parameters can be unambiguously determined. We demonstrate that the usual effective parameters are insufficient to describe the propagation of quantum states of light. Furthermore, we propose a quantum optical effective-medium theory instead and show that it correctly predicts the properties of the light emerging from loss-compensated metamaterials.

Quantum Optical Effective-Medium Theory for Layered Metamaterials at Any Angle of Incidence.

The quantum optics of metamaterials starts with the question of whether the same effective-medium theories apply as in classical optics. In general, the answer is negative. For active plasmonics but also for some passive metamaterials, we show that an additional effective-medium parameter is indispensable besides the effective index, namely, the effective noise-photon distribution. Only with the extra parameter can one predict how well the quantumness of states of light is preserved in the metamaterial. The fact that the effective index alone is not always sufficient and that one additional effective parameter suffices in the quantum optics of metamaterials is both of fundamental and practical interest. Here, from a Lagrangian description of the quantum electrodynamics of media with both linear gain and loss, we compute the effective noise-photon distribution for quantum light propagation in arbitrary directions in layered metamaterials, thereby detailing and generalizing our previous work. The effective index with its direction and polarization dependence is the same as in classical effective-medium theories. As our main result, we derive both for passive and for active media how the value of the effective noise-photon distribution too depends on the polarization and propagation directions of the light. Interestingly, for s-polarized light incident on passive metamaterials, the noise-photon distribution reduces to a thermal distribution, but for p-polarized light it does not. We illustrate the robustness of our quantum optical effective-medium theory by accurate predictions both for power spectra and for balanced homodyne detection of output quantum states of the metamaterial.

Observation of multiple bulk bound states in the continuum modes in a photonic crystal cavity.

Obtaining bound states in the continuum (BICs) in photonic crystals gives rise to the realization of resonances with high quality factors for lasing and nonlinear applications. For BIC cavities in finite-size photonic crystals, the bulk resonance band turns into discrete modes with different mode profiles and radiation patterns. Here, photonic-crystal BIC cavities encircled by the photonic bandgap of lateral heterostructures are designed. The mirror-like photonic bandgap exhibits strong side leakage suppression to confine the mode profile in the designed cavity. Multiple bulk quantized modes are observed both in simulation and experiment. After exciting the BIC cavity at different positions, different resonance peaks are observed. The physical origin of the dependence between the resonance peak and the illuminating position is explained by analyzing the mode profile distribution and further verified by numerical simulations. Our findings have potential applications regarding the mode selectivity in BIC devices to manipulate the lasing mode in photonic-crystal surface-emitting lasers or the radiation pattern in nonlinear optics.

Combining experiments on luminescent centres in hexagonal boron nitride with the polaron model and ab initio methods towards the identification of their microscopic origin.

The two-dimensional material hexagonal boron nitride (hBN) hosts luminescent centres with emission energies of ∼2 eV which exhibit pronounced phonon sidebands. We investigate the microscopic origin of these luminescent centres by combining ab initio calculations with non-perturbative open quantum system theory to study the emission and absorption properties of 26 defect transitions. Comparing the calculated line shapes with experiments we narrow down the microscopic origin to three carbon-based defects: C2CB, C2CN, and VNCB. The theoretical method developed enables us to calculate so-called photoluminescence excitation (PLE) maps, which show excellent agreement with our experiments. The latter resolves higher-order phonon transitions, thereby confirming both the vibronic structure of the optical transition and the phonon-assisted excitation mechanism with a phonon energy ∼170 meV. We believe that the presented experiments and polaron-based method accurately describe luminescent centres in hBN and will help to identify their microscopic origin.

Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response.

We study the effect of nonlocal optical response on the optical properties of metallic nanowires, by numerically implementing the hydrodynamical Drude model for arbitrary nanowire geometries. We first demonstrate the accuracy of our frequency-domain finite-element implementation by benchmarking it in a wide frequency range against analytical results for the extinction cross section of a cylindrical plasmonic nanowire. Our main results concern more complex geometries, namely cylindrical and bow-tie nanowire dimers that can strongly enhance optical fields. For both types of dimers we find that nonlocal response can strongly affect both the field enhancement in between the dimers and their respective extinction cross sections. In particular, we give examples of blueshifted maximal field enhancements near hybridized plasmonic dimer resonances that are still large but nearly two times smaller than in the usual local-response description. For the same geometry at a fixed frequency, the field enhancement and cross section can also be significantly more enhanced in the nonlocal-response model.

Nanophotonic control of the Förster resonance energy transfer efficiency.

We have studied the influence of the local density of optical states (LDOS) on the rate and efficiency of Förster resonance energy transfer (FRET) from a donor to an acceptor. The donors and acceptors are dye molecules that are separated by a short strand of double-stranded DNA. The LDOS is controlled by carefully positioning the FRET pairs near a mirror. We find that the energy transfer efficiency changes with LDOS, and that, in agreement with theory, the energy transfer rate is independent of the LDOS, which allows one to quantitatively control FRET systems in a new way. Our results imply a change in the characteristic Förster distance, in contrast to common lore that this distance is fixed for a given FRET pair.

Surface plasmon modes of a single silver nanorod: an electron energy loss study.

We present an electron energy loss study using energy filtered TEM of spatially resolved surface plasmon excitations on a silver nanorod of aspect ratio 14.2 resting on a 30 nm thick silicon nitride membrane. Our results show that the excitation is quantized as resonant modes whose intensity maxima vary along the nanorod's length and whose wavelength becomes compressed towards the ends of the nanorod. Theoretical calculations modelling the surface plasmon response of the silver nanorod-silicon nitride system show the importance of including retardation and substrate effects in order to describe accurately the energy dispersion of the resonant modes.

Strongly direction-dependent magnetoplasmons in mixed Faraday-Voigt configurations.

The electrostatic theory of surface magnetoplasmons on a semi-infinite magnetized electron gas is generalized to mixed Faraday-Voigt configurations. We analyze a mixed Faraday-Voigt type of electrostatic surface waves that is strongly direction-dependent, and may be realized on narrow-gap semiconductors in the THz regime. A general expression for the dispersion relation is presented, with its dependence on the magnitude and orientation of the applied magnetic field. Remarkably, the group velocity is always perpendicular to the phase velocity. Both velocity and energy relations of the found magnetoplasmons are discussed in detail. In the appropriate limits the known surface magnetoplasmons in the higher-symmetry Faraday and Voigt configurations are recovered.

Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects.

Molecular spontaneous emission and fluorescence depend strongly on the emitter local environment. Plasmonic nanoparticles provide excellent templates for tailoring fluorophore emission, as they exhibit potential for both fluorescence enhancement and quenching, depending on emitter positioning in the nanoparticle vicinity. Here we explore the influence of hitherto disregarded nonclassical effects on the description of emitter-plasmon hybrids, focusing on the roles of the metal nonlocal response and especially size-dependent plasmon damping. Through extensive modelling of metallic nanospheres and nanoshells coupled to dipole emitters, we show that within a purely classical description a remarkable fluorescence enhancement can be achieved. However, once departing from the local-response approximation, and particularly by implementing the recent generalised nonlocal optical response theory, which provides a more complete physical description combining electron convection and diffusion, we show that not only are fluorescence rates dramatically reduced compared to the predictions of the local description and the common hydrodynamic Drude model, but the optimum emitter-nanoparticle distance is also strongly affected. In this respect, experimental measurements of fluorescence, the theoretical description of which requires a precise concurrent evaluation of far- and near-field properties of the system, constitute a novel, more sensitive probe for assessing the validity of state-of-the-art nonclassical theories.

Robustness of the far-field response of nonlocal plasmonic ensembles.

Contrary to classical predictions, the optical response of few-nm plasmonic particles depends on particle size due to effects such as nonlocality and electron spill-out. Ensembles of such nanoparticles are therefore expected to exhibit a nonclassical inhomogeneous spectral broadening due to size distribution. For a normal distribution of free-electron nanoparticles, and within the simple nonlocal hydrodynamic Drude model, both the nonlocal blueshift and the plasmon linewidth are shown to be considerably affected by ensemble averaging. Size-variance effects tend however to conceal nonlocality to a lesser extent when the homogeneous size-dependent broadening of individual nanoparticles is taken into account, either through a local size-dependent damping model or through the Generalized Nonlocal Optical Response theory. The role of ensemble averaging is further explored in realistic distributions of isolated or weakly-interacting noble-metal nanoparticles, as encountered in experiments, while an analytical expression to evaluate the importance of inhomogeneous broadening through measurable quantities is developed. Our findings are independent of the specific nonclassical theory used, thus providing important insight into a large range of experiments on nanoscale and quantum plasmonics.

Nonlocal optical response in metallic nanostructures.

This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response.