Nonlocal Optical Response Research Articles

Homogenization of wire media with a general purpose nonlocal constitutive relation

The wire medium is an important example for a complex artificial electromagnetic material, consisting of metallic nanowires embedded in a non-dispersive, dielectric host medium. It has been explored for various applications, but it is also a prototypical metamaterial that supports a nonlocal optical response. With that, it can be considered as a main research theme for studies revolving around the homogenization of metamaterials. In the past, specific analytical models were derived for the effective properties of the wire medium that were equipped with phenomenologically introduced additional interface conditions. However, the phenomenological approach questions the uniqueness of the effective medium description, as other effective medium theories could capture the optical response equally well. To highlight such issues, we apply here a general purpose nonlocal homogenization theory equipped with rigorously derived additional interface conditions to homogenize a wire medium and compare it to a homogenization theory specifically derived for the wire medium. While the bulk properties can be mapped from one effective medium theory to the other, the interface conditions are different, which renders the models different as well. We discuss the implications of both models in situations where the unit cells are (a) much smaller or (b) only smaller than the operational wavelength.

Nonlocal effect on resonant radiation force exerted on semiconductor coupled quantum well nanostructures**Project supported by the Natural Science Foundation of Guangdong Province, China (Grant Nos. 2016A030313439 and 2018A030313480), GDUPS (2017), the Key Program of the Natural Science Foundation of Guangdong Province, China (Grant No. 2017B030311003), and the Science and Technology Program of Guangzhou City, China (Grant No. 201707010403).

Based on the microscopic nonlocal optical response theory, the resonant radiation force exerted on a semiconductor-coupled quantum well nanostructure (CQWN), induced by the nonlocal interaction between lasers and electrons in conduction bands, is investigated for two different polarized states. The numerical results show that the spatial nonlocality of optical response can cause a radiation shift (blue-shift) for the spectrum of the resonant radiation force, which is dependent on the CQWN width ratio, the barrier height, and polarized states sensitively. It is also confirmed that the resonant radiation force is steerable by the incident and polarized directions of incident light. This work may provide an advantageous method for detecting internal quantum properties of nanostructures, and open novel and raising possibilities for optical manipulation of nano-objects using laser-induced radiation force.

Analysis of the Influence of the Nonlocality Effect on the Characteristics of Plasmon Nanolaser Resonators via the Discrete Sources Method

The problem of the influence of the nonlocality effect on the optical characteristics of plasmon nanolaser resonators is considered. This was performed within the framework of the generalized nonlocal optical response model; we took the nonlocality into account. Based on an extension of the discrete sources method, we performed a comparative analysis of the frequency characteristics of the field intensity in both the far and near zones, depending on the geometry of the resonator. The shapes of layered nonspherical resonators were considered. We established that, taking the nonlocality effect into account, one obtains a decrease of the intensity of plasmon resonance by up to 2.5 times.

Dispersion relation of surface plasmon polaritons in non-local materials.

Here, I report on a highly nonlocal metamaterial formed by means of a plasmonic nanorod composite. An analytical characterization of the nonlocal optical response of plasmonic nanowire metamaterials is presented. The former enables negative refraction, subwavelength light guiding, and emission lifetime engineering. I analyze the dispersion of optical waves propagating in nanowire composite. Moreover, the nonlocal effective medium approximation for this dispersion is derived. Two cases, i.e., hexagon and rectangular metamaterial unit cells, are considered.

Numerical Analysis of Nonlocal Optical Response of Metallic Nanoshells

Nonlocal and quantum effects play an important role in accurately modeling the optical response of nanometer-sized metallic nanoparticles. These effects cannot be described by conventional classical theories, as they neglect essential microscopic details. Quantum hydrodynamic theory (QHT) has emerged as an excellent tool to correctly predict the nonlocal and quantum effects by taking into account the spatial dependence of the charge density. In this article, we used a QHT to investigate the impact of nonlocality and electron spill-out on the plasmonic behavior of spherical Na and Au nanoshells. We adopted a self-consistent way to compute the equilibrium charge density. The results predicted by QHT were compared with those obtained with the local response approximation (LRA) and the Thomas–Fermi hydrodynamic theory (TFHT). We found that nonlocal effects have a strong impact on both the near- and far-field optical properties of nanoshells, in particular, for the antibonding resonant mode. We also investigated the optical response of these systems for different thicknesses of the shell, both for Na and Au metals.

The numerical scheme of the discrete sources method to analyze 3D plasmonic nanostructures accounting for the non-local effect

We present an extension of the discrete sources method for solving the time-harmonic Maxwell equations accounting for the non-local effect. The developed numerical scheme coupling the non-local hydrodynamic Drude model and the generalized non-local optical response model is described in detail. Numerical results computed for a single non-spherical particle and a linear dimer are presented. Our results demonstrate that the discrete sources method can be efficiently used to model the non-local effect in a wide range of 3D scattering problems.

Significance of the nonlocal optical response of metal nanoparticles in describing the operation of plasmonic lasers

A metal nanoparticle (MNP) coupled to a quantum emitter (QE) is a versatile composite nanostructure with unique chemical and physical properties which has been studied intensively, owing to its vast range of promising applications in nanoscience and nanotechnology. When pumped into a higher gain level, an MNP-QE composite nanostructure functions as a nanoplasmonic counterpart of a conventional laser, which is capable of operating at subwavelengths. The theory of plasmonic lasers is hitherto developed on the local optical response of the MNP, disregarding the nanoscale effects of its free electrons. In this paper, we perform a comprehensive quantum mechanical analysis of a complex MNP-QE composite nanostructure, capturing the size-dependent nonclassical effects through the nonlocal optical response of the MNP. Our study reveals that the nonlocal correction introduces significant deviations to the plasmon statistics of the hybrid particle suggested by the local calculations, becoming more prominent when the number of QEs coupled to the MNP increases. Furthermore, for the typical material parameter values used in the literature, we observed the initiation of quenching effects at lower pumping rates than suggested by the local response formalism. In essence, nonlocally assessed plasmon statistics of MNP-QE composite nanostructures demand the concerted coupling of an even higher number of QEs to compensate the deterioration in coherence and to sustain lasing.

Nonlocal optical response of a layered high-temperature superconductor slab

We theoretically study the effect of the spatial dispersion on the optical response of a layered high-temperature superconductor slab. The nonlocality of the inherently-anisotropic layered superconductor comes from the wave vector dependence of its average permittivity tensor, and leads to the generation of additional electromagnetic modes just above the characteristic Josephson plasma frequency, that is in the terahertz range. We calculate p-polarization optical spectra for a Bi2Sr2CaCu2O8+δ (Bi2212) superconductor slab, which show very narrow resonances associated with the quantization of the wave vectors of both long-wavelength electromagnetic modes, having negative dispersion, and short-wavelength additional (nonlocal) modes of positive dispersion. The dependence of the frequency position and shape of the resonances on the nonlocality parameter, the slab thickness, and the components of the quasiparticle conductivity is analyzed. We have found that the quantized long-wavelength modes of negative dispersion, which can only be observed at relatively-large slab thicknesses, give rise to prominent resonances in the p-polarization reflectivity spectrum. On the other hand, the resonances associated with quantized additional short-wavelength electromagnetic modes are weak, but they can be clearly observed when the superconductor slab thickness is smaller than the smallest magnetic-field penetration depth.

Circular Dichroism in Nanoparticle Helices as a Template for Assessing Quantum-Informed Models in Plasmonics

As characteristic lengths in plasmonics rapidly approach the sub-nm regime, quantum-informed models that can capture those aspects of the quantum nature of the electron gas that are not accessible by the standard approximations of classical electrodynamics, or even go beyond the free-electron description, become increasingly more important. Here we propose a template for comparing and validating the predictions of such models, through the circular dichroism signal of a metallic nanoparticle helix. For illustration purposes, we compare three widely used models, each dominant at different nanoparticle separations and governed by its own physical mechanism, namely the hydrodynamic Drude model, the generalised nonlocal optical response theory, and the quantum-corrected model for tunnelling. Our calculations show that indeed, each case is characterised by a fundamentally distinctive response, always dissimilar to the predictions of the local optical response approximation of classical electrodynamics, dominated by a model-sensitive absorptive double-peak feature. In circular dichroism spectra, the striking differences between models manifest themselves as easily traceable sign changes rather than neighbouring absorption peaks, thus overcoming experimental resolution limitations and enabling efficient evaluation of the relevance, validity, and range of applicability of quantum-informed theories for extreme-nanoscale plasmonics.

Superradiance-to-Polariton Crossover of Wannier Excitons with Multiple Resonances.

We demonstrated the superradiance-to-polariton crossover of the blue excitons in Cu_{2}O by varying the sample thicknesses instead of controlling the cavity quality factor. The crossover behavior was compared with unprecedented calculations based on the nonlocal optical response theory with the inclusion of three exciton resonances. The crossover thickness, found to be 177±2 nm, was smaller than the predicted value for a single resonance by a factor of 5. The fact that there was much larger longitudinal-transverse splitting (40±5 meV) than in the bulk implies a surprisingly fast radiative recombination even without a cavity structure.

Exciton behavior under the influence of metal nanoparticle near fields: Significance of nonlocal effects

We analytically characterize the influence of a neighboring metal nanoparticle (MNP) on the behavioral trends of a quantum dot (QD) using a generalized nonlocal optical response (GNOR) method based approach, taking the MNP distance dependent modifications to the QD population relaxation and dephasing rates into account. The GNOR model is a recent generalization and an extension of the hydrodynamic Drude model (HDM), which goes beyond HDM by taking into account both the convection current and electron diffusion in the MNPs. It allows unified theoretical explanation of some experimentally observed plasmonic phenomena which otherwise would require ab initio analysis as the conventional local response approximation (LRA) fails to account for them. For example, it has been demonstrated in literature that the GNOR model captures size dependent resonance shifts of small MNPs which are unrevealed by the conventional LRA based methods, and it has proven to yield results displaying better agreement with the experimental observations for plasmonic experiments. Attempts to incorporate MNP nonlocal effects in the analytical characterization of vicinal excitons found in literature utilize the phenomenological hydrodynamic model and assume the absence of MNP interband effects. Moreover, they are only applicable to narrow parameter regions. In this paper we present a complete analytical characterization which overcomes these drawbacks and lends to the perusal of the system over wide continua of various parameters, enabling us to get an elevated view at a much lesser level of complexity compared to the conventional LRA based numerical methods or the conventional ab initio methods of accounting for the nonlocal effects. Our proposed GNOR based model predicts strong modifications to various QD properties such as population difference, absorption, MNP induced shifts to excitonic energy and F\orster enhanced broadening, coherent plasmonic field enhancement, and quantum state purity, compared to the conventional LRA based predictions. Such modifications are prominent with small MNP radii, high QD dipole moments, small detunings (of the coherent external illumination from the bare excitonic resonance), and near parameter regions exhibiting plasmonic meta resonance (PMR)-like behavior. Moreover, our complete analytical characterization enables optimization of the large system parameter space for different applications, a luxury not fully offered by the methods currently available in literature.

Numerical simulation of electron energy loss spectroscopy accounting for nonlocal effect in plasmonic nanoparticles

Interaction between an electron in straight uniform motion and a nearby plasmonic nanoparticle deposited in homogeneous medium is examined numerically in norecoil approximation. To account for the nonlocal effect occurring in the plasmonic medium Generalized Nonlocal Optical Response scattering problem statement is considered. Discrete Source Method is employed to construct the solution. Electron energy loss probability is computed as a function of incident field frequency and obtained surface plasmon resonance energy is compared to local response simulations. It is shown that surface plasmon resonance peak frequency blueshift can be resolved within the proposed approach.

Analysis of the Influence of Longitudinal Fields on the Scattering Properties of Nonspherical Plasmonic Nanoparticle Clusters via the Discrete-Sources Method

We consider the problem of diffraction of a plane electromagnetic wave field at a linear cluster consisting of two plasmonic nanoparticles while accounting for the nonlocal effect. The research is based on the mathematical model of the generalized non-local optical response. On the basis of the modification of the discrete sources method, a comparative numerical analysis of the scattering characteristics in the frequency domain is carried out depending on the geometry of the particles and the distance between them. It has been established that taking longitudinal fields into account has a significant influence on the extinction cross section and even more on the scattering cross section.

Enhancing the nonlinear optical properties of graphene oxide by repairing with palladium nanoparticles

In this paper, enhancement of the nonlinear optical properties of graphene oxide by repairing with palladium nanoparticles is reported. Graphene oxide, palladium nanoparticles, and their nanocomposite are prepared by chemical methods. Structural and optical properties of all the synthesized samples have been investigated. It is shown that palladium nanoparticles repair the graphene oxide sheet by reducing the number of oxygen functional defects and simultaneously increasing the number of sp2 carbon atoms and delocalized π-electrons. Employing the Z-scan technique for measuring the nonlinear optical properties of the samples, it is shown that Pd nanoparticles can considerably enhance the nonlinear refractive index and absorption coefficient of graphene oxide. Enhanced nonlinear optical properties of graphene oxide can open up exciting prospects for its application in different fields. The used nonlocal Z-scan theory for interpreting the nonlinear measurement data indicates that Mie scattering from the spherical nanoparticles dominates their nonlocal optical response.

Discrete sources method for modeling the nonlocal optical response of a nonspherical particle dimer

A modified scheme of the discrete sources method for modeling the nonlocal optical response of a plasmonic dimer consisting of two identical axisymmetric metallic particles has been developed. The optical cross sections have been computed in the frequency domain for prolate spheroids with different aspect ratios and for different gap sizes. The results show that the generalized nonlocal optical response model leads to a blue shift, a plasmon mode damping, and a plasmon mode broadening of the optical cross sections as compared to the local-response approximation. These effects more pronounced when the aspect ratio of the spheroid increases and the gap size decreases. It has been confirmed that the additional boundary condition appears to be the main origin for the blue shift.

Nonlocal nonlinear optical response of PEGylated superparamagnetic Fe3O4 nanoparticles

PEGylated superparamagnetic Fe3O4 nanoparticles were prepared using co-precipitation method and analyzed by using X-ray diffraction (XRD), UV–Visible spectroscopy, Fourier-transform infrared (FTIR), Transmission electron microscopy (TEM), Dynamic light scattering (DLS), Vibrating sample magnetometer (VSM) and TG analysis. The XRD results showed that an FCC phase of the Fe3O4 structure was formed by an average lattice constant about 8.379 Å. From optical absorbance spectra, the linear absorption coefficient and the band gap of PEGylated Fe3O4 nanoparticles were measured 0.855 cm−1 and 2.27 eV, respectively. The magnetic characteristics indicated that the PEGylated Fe3O4 nanoparticles had the saturation magnetic moments of 61 emug−1. The measurements of nonlinear optical (NLO) properties of PEGylated Fe3O4 nanoparticles have been performed using a nanosecond Nd:YAG pulse laser at 532 nm by the Z-scan technique. Both bare and PEGylated Fe3O4 nanoparticles clearly were exhibited a negative NLO index of refraction at 532 nm. A nonlocality in NLO response of nanoparticles was observed after PEGylation. The NLO absorption of PEGylated Fe3O4 nanoparticles is attributed to 2-photon absorption. A good NLO absorption was observed for both bare and PEG-coated Fe3O4 nanoparticles at 532 nm. Moreover, the nonlinear susceptibility of PEG-coated Fe3O4 nanoparticles was determined by the Z-scan technique of the order of 10−9 esu. The outcomes suggest that PEGylated Fe3O4 nanoparticles may be a promising candidate for the NLO applications.

Probing the ultimate plasmon confinement limits with a van der Waals heterostructure.

The ability to confine light into tiny spatial dimensions is important for applications such as microscopy, sensing, and nanoscale lasers. Although plasmons offer an appealing avenue to confine light, Landau damping in metals imposes a trade-off between optical field confinement and losses. We show that a graphene-insulator-metal heterostructure can overcome that trade-off, and demonstrate plasmon confinement down to the ultimate limit of the length scale of one atom. This is achieved through far-field excitation of plasmon modes squeezed into an atomically thin hexagonal boron nitride dielectric spacer between graphene and metal rods. A theoretical model that takes into account the nonlocal optical response of both graphene and metal is used to describe the results. These ultraconfined plasmonic modes, addressed with far-field light excitation, enable a route to new regimes of ultrastrong light-matter interactions.

Analysis of the scattering properties of 3D non-spherical plasmonic nanoparticles accounting for non-local effects

Based on an extension of the discrete sources method (DSM) our newly developed computer model enables us to analyze polarised light scattering by 3D non-spherical particles accounting for non-local effects (NLE) for plasmonic nanoparticles. Using this theory, computer simulations for spheroid particles of different shape have been conducted. The influence of the NLE both considering the Hydrodynamical Drude model and the generalised non-local optical response on the spectral scattering properties has been analyzed. It has been found that there is a strong influence of particle shape and polarisation of the incident radiation on the scattering properties of a plasmonic particle. Additionally, it has been demonstrated that NLE for non-spherical 3D particles leads to a decrease in intensity of the corresponding localised surface plasmon resonance and provides a blue shift of the plasmon resonance for the non-spherical particles.

Studies on spatial nonlocal optical absorption properties in AlGaAs/GaAs three-step quantum well

To investigate the nonlocal linear intersubband optical absorption properties in AlGaAs/GaAs three-step quantum well (3SQW) nanostructures for a p-polarized states, we deduced the expression of the optical absorption coefficient in the two-level 3SQW system by using Green’s function method and the nonlocal relation between electron and photoelectric field. For the given 3SQW nanostructure, we performed numerical calculations of the optical absorption spectra for different parameters such as angles of incidence, the well width, and the height of the step barrier potential. The numerical results show that spatial nonlocal linear optical response of electrons to light field can induce the radiation shift. It is also demonstrated that the radiation shift and optical absorbance can be controlled by the structure of the 3SQW. These results may bring about a helpful impact in designing nanomaterials with multifarious nonlocality and observing the spatial nonlocal effects in experiment.

Nonlocal optical response in topological phase transitions in the graphene family

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. We also consider the plasmon excitations in the graphene family and find that nonlocality in the optical response can affect the plasmon dispersion spectra of the various phases. The expressions for the conductivity components are valid for the entire graphene family and can be readily used by others.