Non-imaging metasurface design for collimated beam shaping.

Non-imaging optical lenses can shape the light intensity from incoherent sources to a desired target intensity profile, which is important for applications in lighting, solar light concentration, and optical beam shaping. Their surface curvatures are designed to ensure optimal transfer of energy from the light source to the target. The performance of such lenses is directly linked to their asymmetric freeform surface curvature, which is challenging to manufacture. Metasurfaces can mimic any surface curvature without additional fabrication difficulty by imparting a spatially-dependent phase delay using optical antennas. As a result, metasurfaces are uniquely suited to realize non-imaging optics, but non-imaging design principles have not yet been established for metasurfaces. Here, we take an important step in connecting non-imaging optics and metasurface optics, by presenting a phase-design method for beam shaping based on the concept of optimal transport. We establish a theoretical framework that enables a collimated beam to be redistributed by a metasurface to a desired output intensity profile. The optimal transport formulation leads to metasurface phase profiles that transmit all energy from the incident beam to the output beam, resulting in an efficient beam shaping process. Through a variety of examples, we show that our approach accommodates a diverse range of different input and output intensity profiles. Last but not least, a full field simulation of a metasurface has been done to verify our phase-design framework.

Mode Hybridization in Silicon Core-Gold Shell Nanosphere.

A dielectric core-metal shell nanosphere has attracted scientific and technological interests due to the unique optical resonances arising from the hybridization of surface plasmon modes and cavity modes. The previous studies focus on a low-index dielectric core without its own optical resonances. Here, optical resonances of a core-shell nanosphere with a high refractive index (n ≈ 4) core with the lowest order Mie resonances in the visible range are investigated theoretically and experimentally. Scattering and absorption spectra of a core-shell nanosphere for different values of the core refractive index are first analyzed, and there is a transition of the hybridization scheme around n ≈ 2. Above the value, a characteristic hybridized mode with strong absorption and weak scattering emerges in the near-infrared range. A core-shell nanosphere composed of a silicon core and a gold shell is prepared, and the resonance modes are studied by single particle scattering spectroscopy and electron energy loss spectroscopy (EELS) in a transmission electron microscope. The core-shell nanospheres exhibit the hybridized modes depending on the core diameter. The hybridized mode as well as the higher order one that is not observable in the scattering spectroscopy is observed in the EELS.

Disentangling Cathodoluminescence Spectra in Nanophotonics: Particle Eigenmodes vs Transition Radiation.

Cathodoluminescence spectroscopy performed in an electron microscope has proven a versatile tool for analyzing the near- and far-field optical response of plasmonic and dielectric nanostructures. Nevertheless, the transition radiation produced by electron impact is often disregarded in the interpretation of the spectra recorded from resonant nanoparticles. Here we show, experimentally and theoretically, that transition radiation can by itself generate distinct resonances that, depending on the time-of-flight of the electron beam inside the particle, can result from constructive or destructive interference in time. Superimposed on the eigenmodes of the investigated structures, these resonances can distort the recorded spectrum and lead to potentially erroneous assignment of modal characters to the spectral features. We develop an intuitive analogy that helps distinguish between the two contributions. As an example, we focus on the case of silicon nanospheres and show that our analysis facilitates the unambiguous interpretation of experimental measurements on Mie-resonant nanoparticles.

Nanoelectromechanical modulation of a strongly-coupled plasmonic dimer.

The ability of two nearly-touching plasmonic nanoparticles to squeeze light into a nanometer gap has provided a myriad of fundamental insights into light-matter interaction. In this work, we construct a nanoelectromechanical system (NEMS) that capitalizes on the unique, singular behavior that arises at sub-nanometer particle-spacings to create an electro-optical modulator. Using in situ electron energy loss spectroscopy in a transmission electron microscope, we map the spectral and spatial changes in the plasmonic modes as they hybridize and evolve from a weak to a strong coupling regime. In the strongly-coupled regime, we observe a very large mechanical tunability (~250 meV/nm) of the bonding-dipole plasmon resonance of the dimer at ~1 nm gap spacing, right before detrimental quantum effects set in. We leverage our findings to realize a prototype NEMS light-intensity modulator operating at ~10 MHz and with a power consumption of only 4 fJ/bit.

Importance of substrates for the visibility of "dark" plasmonic modes.

Dark plasmonic modes have interesting properties, including longer lifetimes and narrower linewidths than their radiative counterpart, and little to no radiative losses. However, they have not been extensively studied yet due to their optical inaccessibility. In this work, we systematically investigated the dark radial breathing modes (RBMs) in monocrystalline gold nanodisks, specifically their outcoupling behavior into the far-field by cathodoluminescence spectroscopy. Increasing the substrate thickness resulted in an up to 4-fold enhanced visibility. This is attributed to breaking the mirror symmetry by the high-index substrate, creating an effective dipole moment. Furthermore, the resonance energy of the dark RMBs can be easily tuned by varying the nanodisk diameter, making them promising candidates for nanophotonic applications.

Slow light using magnetic and electric Mie resonances.

The ability to slow down light leads to strong light-matter interaction, which is important for a number of optical applications such as sensing, nonlinear optics, and optical pulse manipulation. Here, we show that a dramatic reduction in the speed of light can be realized through the interference of electric and magnetic dipole resonances in Mie-type resonators made of a dielectric material with a high refractive index. We present a general theory that links the maximal speed reduction of light to resonator radiation losses and then consider a specific realization based on silicon nanodisk arrays.

DNA-Assembled Plasmonic Waveguides for Nanoscale Light Propagation to a Fluorescent Nanodiamond.

Plasmonic waveguides consisting of metal nanoparticle chains can localize and guide light well below the diffraction limit, but high propagation losses due to lithography-limited large interparticle spacing have impeded practical applications. Here, we demonstrate that DNA-origami-based self-assembly of monocrystalline gold nanoparticles allows the interparticle spacing to be decreased to ∼2 nm, thus reducing propagation losses to 0.8 dB per 50 nm at a deep subwavelength confinement of 62 nm (∼λ/10). We characterize the individual waveguides with nanometer-scale resolution by electron energy-loss spectroscopy. Light propagation toward a fluorescent nanodiamond is directly visualized by cathodoluminescence imaging spectroscopy on a single-device level, thereby realizing nanoscale light manipulation and energy conversion. Simulations suggest that longitudinal plasmon modes arising from the narrow gaps are responsible for the efficient waveguiding. With this scalable DNA origami approach, micrometer-long propagation lengths could be achieved, enabling applications in information technology, sensing, and quantum optics.

Resonant laser printing of bi-material metasurfaces: from plasmonic to photonic optical response.

Metasurfaces are nanostructured surfaces with engineered optical properties - currently impacting many branches of optics, from miniaturization of optical components to realizing high-resolution structural colors. The optical properties of metasurfaces can be traced to the individual meta-atoms, which set the nature of the optical response, e.g., plasmonic for metallic meta-atoms or photonic for dielectric meta-atoms. Combining multiple types of responses opens up new horizons in design of optical materials, but has so far been avoided due to the fabrication difficulties associated with constructing a metasurface composed of several meta-atom materials. Here, we present a multi-material design approach by optically post-processing a metasurface constructed from self-assembled polystyrene spheres coated with silver. Using our concept of resonant laser printing, we locally alter the initial plasmonic response of the meta-atoms to a pure photonic response. Our work constitutes a conceptually different way of designing metasurfaces and can pave the way for realizing multi-material metasurfaces on large areas while being cost effective.

Thermoplasmonic Ignition of Metal Nanoparticles.

Explosives, propellants, and pyrotechnics are energetic materials that can store and quickly release tremendous amounts of chemical energy. Aluminum (Al) is a particularly important fuel in many applications because of its high energy density, which can be released in a highly exothermic oxidation process. The diffusive oxidation mechanism (DOM) and melt-dispersion mechanism (MDM) explain the ways powders of Al nanoparticles (NPs) can burn, but little is known about the possible use of plasmonic resonances in NPs to manipulate photoignition. This is complicated by the inhomogeneous nature of powders and very fast heating and burning rates. Here, we generate Al NPs with well-defined sizes, shapes, and spacings by electron beam lithography and demonstrate that their plasmonic resonances can be exploited to heat and ignite them with a laser. By combining simulations with thermal-emission, electron-, and optical-microscopy studies, we reveal how an improved control over NP ignition can be attained.

Purcell effect for active tuning of light scattering from semiconductor optical antennas.

Subwavelength, high-refractive index semiconductor nanostructures support optical resonances that endow them with valuable antenna functions. Control over the intrinsic properties, including their complex refractive index, size, and geometry, has been used to manipulate fundamental light absorption, scattering, and emission processes in nanostructured optoelectronic devices. In this study, we harness the electric and magnetic resonances of such antennas to achieve a very strong dependence of the optical properties on the external environment. Specifically, we illustrate how the resonant scattering wavelength of single silicon nanowires is tunable across the entire visible spectrum by simply moving the height of the nanowires above a metallic mirror. We apply this concept by using a nanoelectromechanical platform to demonstrate active tuning.

Electron energy-loss spectroscopy of branched gap plasmon resonators.

The miniaturization of integrated optical circuits below the diffraction limit for high-speed manipulation of information is one of the cornerstones in plasmonics research. By coupling to surface plasmons supported on nanostructured metallic surfaces, light can be confined to the nanoscale, enabling the potential interface to electronic circuits. In particular, gap surface plasmons propagating in an air gap sandwiched between metal layers have shown extraordinary mode confinement with significant propagation length. In this work, we unveil the optical properties of gap surface plasmons in silver nanoslot structures with widths of only 25 nm. We fabricate linear, branched and cross-shaped nanoslot waveguide components, which all support resonances due to interference of counter-propagating gap plasmons. By exploiting the superior spatial resolution of a scanning transmission electron microscope combined with electron energy-loss spectroscopy, we experimentally show the propagation, bending and splitting of slot gap plasmons.

Multipole plasmons and their disappearance in few-nanometre silver nanoparticles.

Electron energy-loss spectroscopy can be used for detailed spatial and spectral characterization of optical excitations in metal nanoparticles. In previous electron energy-loss experiments on silver nanoparticles with radii smaller than 20 nm, only the dipolar surface plasmon resonance was assumed to play a role. Here, applying electron energy-loss spectroscopy to individual silver nanoparticles encapsulated in silicon nitride, we observe besides the usual dipole resonance an additional surface plasmon resonance corresponding to higher angular momenta for nanoparticle radii as small as 4 nm. We study the radius and electron beam impact position dependence of both resonances separately. For particles smaller than 4 nm in radius the higher-order surface plasmon mode disappears, in agreement with generalized non-local optical response theory, while the dipole resonance blueshift exceeds our theoretical predictions. Unlike in optical spectra, multipole surface plasmons are important in electron energy-loss spectra even of ultrasmall metallic nanoparticles.

Slow-light plasmonic metamaterial based on dressed-state analog of electromagnetically induced transparency.

We consider a simple configuration for realizing one-dimensional slow-light metamaterials with large bandwidth-delay products using stub-shaped Fabry-Perot resonators as building blocks. Each meta-atom gives rise to large group indices because of a classical analog of the dressed-state picture of electromagnetically induced transparency. By connecting up to eight meta-atoms, we find bandwidth-delay products over unity and group indices approaching 100. Our approach is quite general and can be applied to any type of Fabry-Perot resonators and tuned to different operating wavelengths.

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.

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.

Extremely confined gap surface-plasmon modes excited by electrons.

High-spatial and energy resolution electron energy-loss spectroscopy (EELS) can be used for detailed characterization of localized and propagating surface-plasmon excitations in metal nanostructures, giving insight into fundamental physical phenomena and various plasmonic effects. Here, applying EELS to ultra-sharp convex grooves in gold, we directly probe extremely confined gap surface-plasmon (GSP) modes excited by swift electrons in nanometre-wide gaps. We reveal the resonance behaviour associated with the excitation of the antisymmetric GSP mode for extremely small gap widths, down to ~5 nm. We argue that excitation of this mode, featuring very strong absorption, has a crucial role in experimental realizations of non-resonant light absorption by ultra-sharp convex grooves with fabrication-induced asymmetry. The occurrence of the antisymmetric GSP mode along with the fundamental GSP mode exploited in plasmonic waveguides with extreme light confinement is a very important factor that should be taken into account in the design of nanoplasmonic circuits and devices.

Nonlocal response of metallic nanospheres probed by light, electrons, and atoms.

Inspired by recent measurements on individual metallic nanospheres that cannot be explained with traditional classical electrodynamics, we theoretically investigate the effects of nonlocal response by metallic nanospheres in three distinct settings: atomic spontaneous emission, electron energy loss spectroscopy, and light scattering. These constitute two near-field and one far-field measurements, with zero-, one-, and two-dimensional excitation sources, respectively. We search for the clearest signatures of hydrodynamic pressure waves in nanospheres. We employ a linearized hydrodynamic model, and Mie-Lorenz theory is applied for each case. Nonlocal response shows its mark in all three configurations, but for the two near-field measurements, we predict especially pronounced nonlocal effects that are not exhibited in far-field measurements. Associated with every multipole order is not only a single blueshifted surface plasmon but also an infinite series of bulk plasmons that have no counterpart in a local-response approximation. We show that these increasingly blueshifted multipole plasmons become spectrally more prominent at shorter probe-to-surface separations and for decreasing nanosphere radii. For selected metals, we predict hydrodynamic multipolar plasmons to be measurable on single nanospheres.

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.

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.