The local electromagnetic field distribution over the dielectric (SiC) surface illuminated by mid-IR light of frequency close to the lattice resonance was directly mapped with an apertureless scattering near-field optical microscope. Half of the sample surface was covered with a metal layer, in which some small $(0.2-10 μm)$ holes were formed. It was found, that due to the eliminating of collective surface polarization effects, the amplitude of the electromagnetic field becomes several times higher over such holes than over infinitely open surface of the same dielectric.
The optical nonlocality in symmetric metal-dielectric multilayer metamaterials is theoretically and experimentally investigated with respect to transverse-magnetic-polarized incident light. A nonlocal effective medium theory is derived from the transfer-matrix method to determine the nonlocal effective permittivity depending on both the frequency and wave vector in a symmetric metal-dielectric multilayer stack. In contrast to the local effective medium theory, our proposed nonlocal effective medium theory can accurately predict measured incident angle-dependent reflection spectra from a fabric…
We have constructed a complete quantum theory for an optical process of excitons with nonlocal susceptibility originating from their center-of-mass motion. This theory provides a practical calculation method for arbitrary-structured nano-to-macro scale dielectrics where excitons are weakly confined. We obtain good correspondences with underlying theories, semiclassical microscopic nonlocal theory, and QED theories for dispersive and absorptive materials with local susceptibility.
We provide theoretical and numerical tools to quantitatively study the impact of nonlocality arising from free electrons in metals on the optical properties of metallo-dielectric multilayers. Though effects due to nonlocality are in general quite small, they nevertheless can be important for very thin (typically below 10 nm) metallic layers - as are used in structures characterized by relatively flat dispersion curves. Such structures include those with negative refractive index; hyperbolic metamaterials; and materials with index near zero. We find in all cases that the inclusion of nonlocal e…
The giant optical nonlocality near the Dirac point in lossless metal-dielectric multilayer metamaterials is revealed and investigated through the analysis of the band structure of the multilayer stack in the three-dimensional omega-k space, according to the transfer-matrix method with the optical nonlocal effect. The position of the Dirac point is analytically located in the omega-k space. It is revealed that the emergence of the Dirac point is due to the degeneracy of the symmetric and the asymmetric eigenmodes of the coupled surface plasmon polaritons. The optical nonlocality induced epsilon…
Mie-resonant high-index dielectric particles are at the core of modern all-dielectric photonics. In many situations, their response to the external fields is well-captured by the dipole model which neglects the excitation of higher-order multipoles. In that case, it is commonly assumed that the dipole moments induced by the external fields are given by the product of particle polarizability tensor and the field in the particle center. Here, we demonstrate that the dipole response of non-spherical subwavelength dielectric particles is significantly more complex since the dipole moments are defi…
Evanescent waves in a metal thin film with nonlocality are found to propagate in normal direction to film surface with quenched (to zero) energy dissipation associated with intra-band electron transitions when wave numbers satisfy a resonant condition. It is shown that resonant quenching of energy dissipation (RQED) effect occurs in metal films with thicknesses of less or larger than, but still on the order of, the nonlocality scale length. RQED ceases to exist in metal films whose thickness exceeds a cutoff length or in metal films with local dielectric permittivity. Resonant quenching of ene…
We analyze the impact of nonlocality on the waveguide modes of metallo-dielectric multilayers and optical patch antennas, the latter formed from metal strips closely spaced above a metallic plane. We model both the nonlocal effects associated with the conduction electrons of the metal, as well as the previously overlooked response of bound electrons. We show that the fundamental mode of a metal-dielectric-metal waveguide, sometimes called the gap-plasmon, is very sensitive to nonlocality when the insulating, dielectric layers are thinner than 5 nm. We suggest that optical patch antennas, which…
Sub-wavelength confinement of mid-infrared light can be achieved exploiting the metal-like optical response of polar dielectric crystals in their Reststrahlen spectral region, where they support evanescent modes termed surface phonon polaritons. In the past few years the investigation of phonon polaritons localised in nanoresonators and layered heterostructures has enjoyed remarkable success, highlighting them as a promising platform for mid-infrared nanophotonic applications. Here we prove that the standard local dielectric description of phonon polaritons in nanometric objects fails due to t…
We analyze dispersion properties of metal-dielectric nanostructured metamaterials. We demonstrate that, in a sharp contrast to the results for the corresponding effective medium, the structure demonstrates strong optical nonlocality due to excitation of surface plasmon polaritons that can be engineered by changing a ratio between the thicknesses of metal and dielectric layers. In particular, this nonlocality allows the existence of an additional extraordinary wave that manifests itself in the splitting of the TM-polarized beam scattered at an air-metamaterial interface.
We develop a nonlocal-response generalization to the Green-function surface-integral method (GSIM), also known as the boundary-element method (BEM). This numerically light method can accurately describe the linear hydrodynamic nonlocal response of arbitrarily shaped plasmonic nanowires in arbitrary dielectric backgrounds. All previous general-purpose methods for nonlocal response are bulk methods. We also expand the possible geometries to which the usual local-response GSIM can be applied, by showing how to regularize singularities that occur in the surface integrals when the nanoparticles tou…
Nonlocal (spatial-dispersion) effects in multilayered metamaterials composed of periodic stacks of alternating, deeply subwavelength dielectric layers are known to be negligibly weak. Counterintuitively, under certain critical conditions, weak nonlocality may build up strong boundary effects that are not captured by conventional (local) effective-medium models based on simple mixing formulas. Here, we show that this phenomenon can be fruitfully studied and understood in terms of error propagation in the iterated maps of the trace and anti-trace of the optical transfer matrix of the multilayer.…
We explore in the present work the near-field radiative heat transfer between two semi-infinite parallel nonlocal dielectric planes by means of fluctuational electrodynamics. We use atheory for the nonlocal dielectric permittivityfunction proposed byHalevi and Fuchs. This theory has the advantage to includedifferent models performed in the literature. According to this theory, the nonlocal dielectric function is described by a Lorenz-Drude like single oscillator model, in which the spatial dispersion effects are represented by an additional term depending on the square of the total wavevector …
Most optical systems involve a combination of lenses separated by free-space regions where light acquires the required angle-dependent phase delay for a certain functionality. Very recently, flat-optics structures have been proposed to compress these large free-space volumes and miniaturize the overall optical system. However, these early designs can only replace free-space volumes of limited length, or operate in a very narrow angular range, or require a high-index background. These issues raise questions about the applicability of these devices in practical scenarios. Here, we first derive a…
We study the propagation of surface plasmon polaritons (SPPs) on a metal surface which hosts a thin film of a liquid dielectric. The ohmic losses, that are inherently present due to the coupling of SPPs to conductors' electron plasma, induce temperature gradients and fluid deformation driven by the thermocapillary effect, which lead to a nonlinear and nonlocal change of the effective dielectric constant. The latter extends beyond the regions of highest optical intensity, and constitutes a novel thermally self-induced mechanism that affects the propagation of the SPPs. We derive the nonlinear a…
Singular graphene metasurfaces, conductivity gratings realized by periodically suppressing the local doping level of a graphene sheet, have recently been proposed to efficiently harvest THz light and couple it to surface plasmons over broad absorption bands, achieving remarkably high field enhancement. However, the large momentum wavevectors thus attained are sensitive to the nonlocal behaviour of the underlying electron liquid. Here, we extend the theory of singular graphene metasurfaces to account for the full nonlocal optical response of graphene and discuss the resulting impact on the plas…
Probing topological edge states in multilayer dielectric photonic nanostructures
Research School of Physics, Australian National University（澳大利亚国立大学物理研究学院）；Institute of Photonics and Quantum Sciences, Heriot-Watt University（赫瑞-瓦特大学光子与量子科学研究所）
The coherence length of the thermal electromagnetic field near a planar surface has a minimum value related to the nonlocal dielectric response of the material. We perform two model calculations of the electric energy density and the field's degree of spatial coherence. Above a polar crystal, the lattice constant gives the minimum coherence length. It also gives the upper limit to the near field energy density, cutting off its $1/z^3$ divergence. Near an electron plasma described by the semiclassical Lindhard dielectric function, the corresponding length scale is fixed by plasma screening to t…
Recent studies on fully dielectric multilayered metamaterials have shown that the negligibly small nonlocal effects (spatial dispersion) typically observed in the limit of deeply subwavelength layers may be significantly enhanced by peculiar boundary effects occurring in certain critical parameter regimes. These phenomena, observed so far in periodic and randomly disordered geometries, are manifested as strong differences between the exact optical response of finite-size metamaterial samples and the prediction from conventional effective-theory-medium models based on mixing formulae. Here, wit…
In this paper we analyze the effects of nonlocality on the optical properties of a system consisting of a thin metallic film separated from a graphene sheet by a hexagonal boron nitride (hBN) layer. We show that nonlocal effects in the metal have a strong impact on the spectrum of the surface plasmon-polaritons on graphene. If the graphene sheet is shaped into a grating, we show that the extinction curves can be used to shed light on the importance of nonlocal effects in metals. Therefore, graphene surface plasmons emerge as a tool for probing nonlocal effects in metallic nanostructures, inclu…
Optical phenomena associated with extremely localized field should be understood with considerations of nonlocal and quantum effects, which pose a hurdle to conceptualize the physics with a picture of eigenmodes. Here we first propose a generalized Lorentz model to describe general nonlocal media under linear mean-field approximation and formulate source-free Maxwell's equations as a linear eigenvalue problem to define the quasinormal modes. Then we introduce an orthonormalization scheme for the modes and establish a canonical quasinormal mode framework for general nonlocal media. Explicit for…
The Kirchhoff law of thermal radiation, relating emissivity ε and absorptance α, has been originally formulated for opaque bodies in thermodynamic equilibrium with the environment. However, in many systems of practical importance, both assumptions are often not satisfied. In this work, we revisit the century-old law and examine the limits of its applicability in an example of Er:YAG and Er:YLF dielectric crystals, potential radiation converters for thermophotovoltaic applications. In our experiments, the (80 at.%) Er:YAG crystal was opaque between 1.45 μm and 1.64 μm. In this spectral range, i…
The optical characterization of dielectric periodic line-gratings for which the period of the grating is significantly larger than the probing wavelength is investigated experimentally, numerically, and analytically. The experimental diffraction efficiencies are analyzed in transmission with the help of a closed-form approximate solution within a single scattering picture. In particular, the angular width of significant scattering and the haze are analyzed for samples of increasing grating profile amplitude.
This paper is withdrawn by the authors. We theoretically examine graphene plasmon polaritons (GPP) supported by a sheet of graphene sandwiched between two dielectric media. The influence of the dielectric environment on GPP's is studied within local and nonlocal descriptions of graphene's conductivity. We demonstrate that a local-response approximation invariably leads, counter-intuitively, to a substrate-independent surface plasmon frequency. On the other hand, the nonlocal description of the electron gas allows the presence of non-vertical inter-band transitions which changes the results qua…
We perform a study of the achievable field enhancement of plasmonic cascade nanolenses in the quantum and classical regimes, and explore the limits enforced at larger sizes by retardation and at smaller sizes by nonlocality and other quantum effects. We compare the near field response of a sodium nanolens within a local and nonlocal formalism and find that the increased electron- surface scattering decreases the field enhancements by over an order of magnitude. The large parameter space is explored, within the local approximation, for a number of plasmonic metals as well as the polar dielectri…
Epsilon-near-zero (ENZ) metamaterial slabs at visible frequencies based on metal-dielectric multilayers are experimentally realized. Transmission, reflection and absorption spectra are measured and used to determine the complex refractive indices and the effective permittivities of the ENZ slabs, which agree with the results obtained from both the numerical simulations and the optical nonlocalities analysis. Furthermore, light propagation in ENZ slabs and directional emission from ENZ prisms are also analyzed. The accurate determination of the ENZ wavelength for metal-dielectric multilayer met…
Probing the temperature dependence of dielectric function of ternary transition metal dichalcogenides: towards thermo-driven ultrathin photonic components
Yerevan State University（埃里温国立大学）；National University of Singapore（新加坡国立大学）
When mid-infrared light interacts with nanoscale polar dielectric structures optical phonon propagation cannot be ignored, leading to a rich nonlocal phenomenology which we have only recently started to uncover. In properly crafted nanodevices this includes the creation of polaritonic excitations with hybrid longitudinal-transverse nature, which are predicted to allow energy funnelling from longitudinal electrical currents to far-field transverse radiation. In this work we study the physics of these longitudinal-transverse polaritons in a dielectric nanolayer in which the nonlocality strongly …
Polar dielectrics are a promising platform for mid-infrared nanophotonics, allowing for nanoscale electromagnetic energy confinement in oscillations of the crystal lattice. We recently demonstrated that in nanoscopic polar systems a local description of the optical response fails, leading to erroneous predictions of modal frequencies and electromagnetic field enhancements. In this Paper we extend our previous work providing a scattering matrix theory of the nonlocal optical response of planar, anisotropic, layered polar dielectric heterostructures. The formalism we employ allows for the calcul…
Probing mesoscopic nonlocal screening in van der Waals heterostructures with polaritons
Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR)（材料研究工程研究所，科学技术研究局）；Quantum Innovation Centre (Q. InC), Agency for Science, Technology and Research (A*STAR)（量子创新中心，科学技术研究局）；School of Materials Science and Engineering, Nanyang Technological University（南洋理工大学材料科学与工程学院）；Department of Materials Science and Engineering, National University of Singapore（新加坡国立大学材料科学与工程系）；National Key Laboratory of Microwave Photonics & College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics（南京航空航天大学微波光子学国家重点实验室与电子信息学院）；School of Electrical and Electronic Engineering, Nanyang Technological University（南洋理工大学电气与电子工程学院）；Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences（中国科学院上海光学精密机械研究所）；Department of Mechanical Engineering, The Hong Kong Polytechnic University（香港理工大学机械工程系）
Historically, the field of plasmonics has been relying on the framework of classical electrodynamics, with the local-response approximation of material response being applied even when dealing with nanoscale metallic structures. However, when approaching the atomic-scale confinement of the electromagnetic radiation, mesoscopic effects are anticipated to become observable, e.g., those associated with the nonlocal electrodynamic surface response of the electron gas. We investigate nonlocal effects in propagating gap surface plasmon modes in ultrathin metal--dielectric--metal planar waveguides, e…
A nonlocal quantum model is presented for calculating the atomic dielectric response to a strong laser electric field. By replacing the Coulomb potential with a nonlocal potential in the Schrodinger equation, a 3+1D calculation of the time-dependent electric dipole moment can be replaced with a 0+1D integral equation, offering significant computational savings. The model is benchmarked against an established ionization model and \textit{ab initio} simulation of the time-dependent Schrodinger equation. The reduced computational overhead makes the model a promising candidate to incorporate full …
We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material that propagate to the surface. Specific values of these coefficients correspond to various additional boundary conditions (ABC) for Maxwell's equations. We derive the electromagnetic reflection and transmission coefficients at the boundary and investigate their dependence on material parameters and ABC. We also investigate the electromagnetic zero-point and t…
The stationary problem of light interaction with a dense collection of two-level atoms embedded in a dielectric is treated semiclassically. The effect of dielectric absorption on the phenomenon of intrinsic optical bistability is discussed in terms of the complex local-field enhancement factor. The calculations accounting propagation effects (nonlocal regime) show that even low dielectric absorption results in elimination of response instabilities.
We investigate theoretically and experimentally the optical beam propagation in the nematic liquid crystal with negative dielectric anisotropy, which is aligned homeotropically in a $80μm$-thickness planar cell in the presence of an externally voltage. It is predicted that the nonlocal nonlinearity of liquid crystal undergo an oscillatory response function with a negative nonlinear refractive index coefficient. We found that the oscillatory nonlocal nonlinearity can support stable bright solitons, which are observed in experiment. We also found that abnormal modulation instability occurs with …
Nonlocal electromagnetic effects of graphene arise from its naturally dispersive dielectric response. We present semi-analytical solutions of nonlocal Maxwell's equations for graphene nano-ribbons array with features around 100 nm, where we found prominent departures from its local response. Interestingly, the nonlocal corrections are stronger for light polarization parallel to the ribbons, which manifests as additional broadening of the Drude peak. For the perpendicular polarization case, nonlocal effects lead to blue-shifts of the plasmon peaks. These manifestations provide a physical measur…
Material losses in metals are a central bottleneck in plasmonics for many applications. Here we propose and theoretically demonstrate that metal losses can be successfully mitigated with dielectric particles on metallic films, giving rise to hybrid dielectric--metal resonances. In the far field, they yield strong and efficient scattering, beyond even the theoretical limits of all-metal and all-dielectric structures. In the near field, they offer high-Purcell-factor (${>}5000$), high-quantum-efficiency (${>}90\%$), and highly directional emission at visible and infrared wavelengths. Their quali…
We present an approach for the description of fluorescence from optically active material embedded in layered periodic structures. Based on an exact electromagnetic Green's tensor analysis, we determine the radiative properties of emitters such as the local photonic density of states, Lamb shifts, line widths etc. for a finite or infinite sequence of thin alternating plasmonic and dielectric layers. In the effective medium limit, these systems may exhibit hyperbolic dispersion relations so that the large wave-vector characteristics of all constituents and processes become relevant. These inclu…
We investigate second harmonic generation, low-threshold multistability, all-optical switching, and inherently nonlocal effects due to the free-electron gas pressure in an epsilon-near-zero (ENZ) metamaterial slab made of cylindrical, plasmonic nanoshells illuminated by TM-polarized light. Damping compensation in the ENZ frequency region, achieved by using gain medium inside the shells' dielectric cores, enhances the nonlinear properties. Reflection is inhibited and the electric field component normal to the slab interface is enhanced near the effective pseudo-Brewster angle, where the effecti…
Istituto Italiano di Tecnologia（意大利理工大学）；University of Southern Denmark（南丹麦大学）；Fritz Haber Institute of the Max Planck Society（马克斯·普朗克学会弗里茨·哈伯研究所）；Consiglio Nazionale delle Ricerche (CNR)（意大利国家研究委员会）
We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order. Specifically, by resorting to a suitable multiscale technique, we show that medium effective permittivity tensor and the first and second order tensors describing spatial dispersion can be evaluated by averaging suitable spatially rapidly-varying fields each satysifing electrostatic-like equations within the metamaterial unit cell. For metamaterials with ne…
Photonic devices rarely provide both elaborate spatial control and sharp spectral control over an incoming wavefront. In optical metasurfaces, for example, the localized modes of individual meta-units govern the wavefront shape over a broad bandwidth, while nonlocal lattice modes extended over many unit cells support high quality-factor resonances. Here, we experimentally demonstrate nonlocal dielectric metasurfaces in the near-infrared that offer both spatial and spectral control of light, realizing metalenses focusing light exclusively over a narrowband resonance while leaving off-resonant f…
The magneto-optical activity, namely the polarization conversion capabilities of high-index, non-absorbing, core-shell dielectric nanospheres is theoretically analyzed. We show that, in analogy with their plasmonic counterparts, the polarization conversion in resonant dielectric particles is linked to the amount of electromagnetic field probing the magneto-optical material in the system. However, in strong contrast with plasmon nanoparticles, due to the peculiar distribution of the internal fields in resonant dielectric spheres, the magneto-optical response is fully governed by the magnetic (d…
Surface plasmons on metals can concentrate light into sub-nanometric volumes and on these near atomic length scales the electronic response at the metal interface is smeared out over a Thomas-Fermi screening length. This nonlocality is a barrier to a good understanding of atomic scale response to light and complicates the practical matter of computing the fields. In this letter, we present a local analogue model and show that spatial nonlocality can be represented by replacing the nonlocal metal with a composite material, comprising a thin dielectric layer on top of a local metal. This method …
Our theoretical examination of second and third harmonic generation from metal-based nanostructures predicts that nonlocal and quantum tunneling phenomena can significantly exceed expectations based solely on local, classical electromagnetism. Mindful that the diameter of typical transition metal atoms is approximately 3Å, we adopt a theoretical model that treats nanometer-size features and/or sub-nanometer size gaps or spacers by taking into account: (i) the limits imposed by atomic size to fulfill the requirements of continuum electrodynamics; (ii) spillage of the nearly-free electron cloud …
We develop a theory of nonlocal homogenization for metamaterial consisting of parallel metallic wires with dielectric coating. It is demonstrated that manipulation of dielectric contrast between wire dielectric shell and host material results in switching of metamaterial dispersion regime from elliptic to the hyperbolic one, i.e. the topological transition takes place. We confirm our theoretical predictions by full-wave numerical simulations.
In a recent Letter [Phys. Rev. Lett. 103, 097403 (2009)], we outlined a computational method to calculate the optical properties of structures with a spatially nonlocal dielectric function. In this Article, we detail the full method, and verify it against analytical results for cylindrical nanowires. Then, as examples of our method, we calculate the optical properties of Au nanostructures in one, two, and three dimensions. We first calculate the transmission, reflection, and absorption spectra of thin films. Because of their simplicity, these systems demonstrate clearly the longitudinal (or vo…
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). 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 t…
We study in this work the near-field radiative heat transfer between two semi-infinite parallel planes of highly n-doped semiconductors. Using a nonlocal model of the dielectric permittivity, usually used for the case of metallic planes, we show that the radiative heat transfer coefficientsaturates as the separation distance is reduced for high doping concentration. These results replace the 1/d${}^2$ infinite divergence obtained in the local model case. Different features of the obtained results are shown to relate physically to the parameters of the materials, mainly the doping concentration…
Nonlocality is a fundamental concept in photonics. For instance, nonlocal wave-matter interactions in spatially modulated metamaterials enable novel effects, such as giant electromagnetic chirality, artificial magnetism, and negative refraction. Here, we investigate the effects induced by spatial nonlocality in {\em temporal} metamaterials, i.e., media with a dielectric permittivity rapidly modulated in time. Via a rigorous multiscale approach, we introduce a general and compact formalism for the nonlocal effective medium theory of temporally periodic metamaterials. In particular, we study two…
