Vectorial near-field coupling.

The coherent exchange of optical near fields between two neighbouring dipoles plays an essential role in the optical properties, quantum dynamics and thus the function of many naturally occurring and artificial nanosystems. These interactions are challenging to quantify experimentally. They extend over only a few nanometres and depend sensitively on the detuning, dephasing and relative orientation (that is, the vectorial properties) of the coupled dipoles. Here, we introduce plasmonic nanofocusing spectroscopy to record coherent light scattering spectra with 5 nm spatial resolution from the apex of a conical gold nanotaper. The apex is excited solely by evanescent fields and coupled to plasmon resonances in a single gold nanorod. We resolve resonance energy shifts and line broadenings as a function of dipole distance and relative orientation. We demonstrate how these phenomena arise from mode couplings between different vectorial components of the interacting optical near fields, specifically from the coupling of the nanorod to both transverse and longitudinal polarizabilities of the taper apex.

Large-Area Two-Dimensional Plasmonic Meta-Glasses and Meta-Crystals: a Comparative Study.

The geometrical arrangement of metallic nanoparticles plays a crucial role on the optical response of nanoplasmonic samples due to particle-particle interactions. In this work, large-area, two-dimensional meta-glasses (random arrangements) and meta-crystals (periodic arrangements) made of identical metallic nanoparticles are investigated for three different particle densities of 5, 10, and 15 discs/µm2. A direct comparison between random and periodically ordered arrays is presented. The comparison clearly shows that the particle density has the largest influence on the extinction spectra for both periodic and random samples, and that for equal densities, the optical response away from diffraction effects is strikingly similar in both cases. The role of the radial density function and minimum particle distance is also determined. This study elucidates the role of the particle-particle interactions on the response of plasmonic nanoparticles and indicates how to control position and shape of the plasmonic resonance.

Reflection and Phase Matching in Plasmonic Gold Tapers.

We investigate different dynamic mechanisms, reflection and phase matching, of surface plasmons in a three-dimensional single-crystalline gold taper excited by relativistic electrons. Plasmonic modes of gold tapers with various opening angles from 5° to 47° are studied both experimentally and theoretically, by means of electron energy-loss spectroscopy and finite-difference time-domain numerical calculations, respectively. Distinct resonances along the taper shaft are observed in tapers independent of opening angles. We show that, despite their similarity, the origin of these resonances is different at different opening angles and results from a competition between two coexisting mechanisms. For gold tapers with large opening angles (above ∼20°), phase matching between the electron field and that of higher-order angular momentum modes of the taper is the dominant contribution to the electron energy-loss because of the increasing interaction length between electron and the taper near-field. In contrast, reflection from the taper apex dominates the EELS contrast in gold tapers with small opening angles (below ∼10°). For intermediate opening angles, a gradual transition of these two mechanisms was observed.

Quantitative and Direct Near-Field Analysis of Plasmonic-Induced Transparency and the Observation of a Plasmonic Breathing Mode.

We investigated experimentally and numerically in the optical near-field a plasmonic model system similar to a dolmen-type structure for phenomena such as plasmon-induced transparency. Through engineering of coupling strength, structure orientation, and incident angle and phase of the excitation source it was possible to control near-field excitation of the dark modes. We showed that quantitative analysis of near-field amplitude and excitation strength provided essential information that allowed identifying the interaction between the bright and the dark mode and how it causes the formation of plasmon-induced transparency features and a Fano resonance. In addition, we introduced a mechanism to excite field distributions in plasmonic structures that cannot be accessed directly using far-field illumination and demonstrated the excitation of a dark mode akin to a symmetry-forbidden plasmonic breathing mode using a linearly polarized far-field source.

Suppression of Radiative Damping and Enhancement of Second Harmonic Generation in Bull's Eye Nanoresonators.

We report a drastic increase of the damping time of plasmonic eigenmodes in resonant bull's eye (BE) nanoresonators to more than 35 fs. This is achieved by tailoring the groove depth of the resonator and by coupling the confined plasmonic field in the aperture to an extended resonator mode such that spatial coherence is preserved over distances of more than 10 µm. Experimentally, this is demonstrated by probing the plasmon dynamics at the field level using broadband spectral interferometry. The nanoresonator allows us to efficiently concentrate the incident field inside the central aperture of the BE and to tailor its local optical nonlinearity by varying the aperture geometry. By replacing the central circular hole with an annular ring structure, we obtain 50-times higher second harmonic generation efficiency, allowing us to demonstrate the efficient concentration of long-lived plasmonic modes inside nanoapertures by interferometric frequency-resolved autocorrelation. Such a light concentration in a nanoresonator with high quality factor has high potential for sensing and coherent control of light-matter interactions on the nanoscale.

Excitation of Mesoscopic Plasmonic Tapers by Relativistic Electrons: Phase Matching versus Eigenmode Resonances.

We investigate the optical modes in three-dimensional single-crystalline gold tapers by means of electron energy-loss spectroscopy. At the very proximity to the apex, a broad-band excitation at all photon energies from 0.75 to 2 eV, which is the onset for interband transitions, is detected. At large distances from the apex, though, we observe distinct resonances with energy dispersions roughly proportional to the inverse local radius. The nature of these phenomena is unraveled by finite difference time-domain simulations of the taper and an analytical treatment of the energy loss in fibers. Our calculations and the perfect agreement with our experimental results demonstrate the importance of phase-matching between electron field and radiative taper modes in mesoscopic structures. The local taper radius at the electron impact location determines the selective excitation of radiative modes with discrete angular momenta.

Toward plasmonics with nanometer precision: nonlinear optics of helium-ion milled gold nanoantennas.

Plasmonic nanoantennas are versatile tools for coherently controlling and directing light on the nanoscale. For these antennas, current fabrication techniques such as electron beam lithography (EBL) or focused ion beam (FIB) milling with Ga(+)-ions routinely achieve feature sizes in the 10 nm range. However, they suffer increasingly from inherent limitations when a precision of single nanometers down to atomic length scales is required, where exciting quantum mechanical effects are expected to affect the nanoantenna optics. Here, we demonstrate that a combined approach of Ga(+)-FIB and milling-based He(+)-ion lithography (HIL) for the fabrication of nanoantennas offers to readily overcome some of these limitations. Gold bowtie antennas with 6 nm gap size were fabricated with single-nanometer accuracy and high reproducibility. Using third harmonic (TH) spectroscopy, we find a substantial enhancement of the nonlinear emission intensity of single HIL-antennas compared to those produced by state-of-the-art gallium-based milling. Moreover, HIL-antennas show a vastly improved polarization contrast. This superior nonlinear performance of HIL-derived plasmonic structures is an excellent testimonial to the application of He(+)-ion beam milling for ultrahigh precision nanofabrication, which in turn can be viewed as a stepping stone to mastering quantum optical investigations in the near-field.

Interplay between strong coupling and radiative damping of excitons and surface plasmon polaritons in hybrid nanostructures.

We report on the interplay between strong coupling and radiative damping of strongly coupled excitons (Xs) and surface plasmon polaritons (SPPs) in a hybrid system made of J-aggregates and metal nanostructures. The optical response of the system is probed at the field level by angle-resolved spectral interferometry. We show that two different energy transfer channels coexist: coherent resonant dipole-dipole interaction and an incoherent exchange due to the spontaneous emissions of a photon by one emitter and its subsequent reabsorption by another. The interplay between both pathways results in a pronounced modification of the radiative damping due to the formation of super- and subradiant polariton states. This is confirmed by probing the ultrafast nonlinear response of the polariton system and explained within a coupled oscillator model. Such a strong modification of the radiative damping opens up interesting directions in coherent active plasmonics.

k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy.

We investigate the radiation patterns of sharp conical gold tapers, which were designed as adiabatic nanofocusing probes for scanning near-field optical microscopy (SNOM). Field calculations show that only the lowest order eigenmode of such a taper can reach the very apex and thus induce the generation of strongly enhanced near-field signals. Higher-order modes are coupled into the far field at finite distances from the apex. Here, we demonstrate experimentally how to distinguish and separate between the lowest and higher-order eigenmodes of such a metallic taper by filtering in the spatial frequency domain. Our approach has the potential to considerably improve the signal-to-background ratio in spectroscopic experiments at the nanoscale.

Vibrational near-field mapping of planar and buried three-dimensional plasmonic nanostructures.

Nanoantennas confine electromagnetic fields at visible and infrared wavelengths to volumes of only a few cubic nanometres. Assessing their near-field distribution offers fundamental insight into light-matter coupling and is of special interest for applications such as radiation engineering, attomolar sensing and nonlinear optics. Most experimental approaches to measure near-fields employ either diffraction-limited far-field methods or intricate near-field scanning techniques. Here, using diffraction-unlimited far-field spectroscopy in the infrared, we directly map the intensity of the electric field close to plasmonic nanoantennas. We place a patch of probe molecules with 10 nm accuracy at different locations in the near-field of a resonant antenna and extract the molecular vibrational excitation. We map the field intensity along a dipole antenna and gap-type antennas. Moreover, this method is able to assess the near-field intensity of complex buried plasmonic structures. We demonstrate this by measuring for the first time the near-field intensity of a three-dimensional plasmonic electromagnetically induced transparency structure.

Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible.

Plasmonics has become one of the most vibrant areas in research with technological innovations impacting fields from telecommunications to medicine. Many fascinating applications of plasmonic nanostructures employ electric dipole and higher-order multipole resonances. Also magnetic multipole resonances are recognized for their unique properties. Besides these multipolar modes that easily radiate into free space, other types of electromagnetic resonances exist, so-called toroidal eigenmodes, which have been largely overlooked historically. They are strongly bound to material structures and their peculiar spatial structure renders them practically invisible to conventional optical microscopy techniques. In this Letter, we demonstrate toroidal modes in a metal ring formed by an oligomer of holes. Combined energy-filtering transmission electron microscopy and three-dimensional finite difference time domain analysis reveal their distinct features. For the study of these modes that cannot be excited by optical far-field spectroscopy, energy-filtering transmission electron microscopy emerges as the method of choice. Toroidal moments bear great potential for novel applications, for example, in the engineering of Purcell factors of quantum-optical emitters inside toroidal cavities.

Reciprocity theory of apertureless scanning near-field optical microscopy with point-dipole probes.

Near-field microscopy offers the opportunity to reveal optical contrast at deep subwavelength scales. In scanning near-field optical microscopy (SNOM), the diffraction limit is overcome by a nanoscopic probe in close proximity to the sample. The interaction of the probe with the sample fields necessarily perturbs the bare sample response, and a critical issue is the interpretation of recorded signals. For a few specific SNOM configurations, individual descriptions have been modeled, but a general and intuitive framework is still lacking. Here, we give an exact formulation of the measurable signals in SNOM which is easily applicable to experimental configurations. Our results are in close analogy with the description Tersoff and Hamann have derived for the tunneling currents in scanning tunneling microscopy. For point-like scattering probe tips, such as used in apertureless SNOM, the theory simplifies dramatically to a single scalar relation. We find that the measured signal is directly proportional to the field of the coupled tip-sample system at the position of the tip. For weakly interacting probes, the model thus verifies the empirical findings that the recorded signal is proportional to the unperturbed field of the bare sample. In the more general case, it provides guidance to an intuitive and faithful interpretation of recorded images, facilitating the characterization of tip-related distortions and the evaluation of novel SNOM configurations, both for aperture-based and apertureless SNOM.

Breaking the mode degeneracy of surface plasmon resonances in a triangular system.

In this paper, we present a systematic investigation of symmetry-breaking in the plasmonic modes of triangular gold nanoprisms. Their geometrical C(3v) symmetry is one of the simplest possible that allows degeneracy in the particle's mode spectrum. It is reduced to the nondegenerate symmetries C(v) or E by positioning additional, smaller gold nanoprisms in close proximity, either in a lateral or a vertical configuration. Corresponding to the lower symmetry of the system, its eigenmodes also feature lower symmetries (C(v)), or preserve only the identity (E) as symmetry. We discuss how breaking the symmetry of the plasmonic system not only breaks the degeneracy of some lower order modes, but also how it alters the damping and eigenenergies of the observed Fano-type resonances.

Plasmonic grating as a nonlinear converter-coupler.

The paper introduces a wavelength converter composed of a metallic finite 2-dimensional particle grating on top of an optical waveguide. The particles sustain plasmonic resonances which will result in the near-field enhancement and therefore, high conversion efficiency. Due to near-field interaction of the grating field with the propagating modes of the waveguide, the generated third harmonic wave is phase-matched to a propagating mode of the waveguide, while the fundamental frequency component is not coupled into the output waveguide of the structure. The performance of this structure is numerically investigated using a full-wave transmission line method for the linear analysis and a three-dimensional finite-difference time-domain method for the nonlinear analysis.

Apertureless near-field optical microscopy: differences between heterodyne interferometric and non-interferometric images.

We analyze simulations of the image generation process in apertureless Scanning Near-Field Optical Microscopy to study the differences between heterodyne interferometric and non-interferometric detection schemes implemented in experiments. Beyond the well-known possibilities of interferometry to enhance signals and extract optical phase information, we find that heterodyne interferometric detection may in fact lead to more robust and easier to interpret experimental results. Further, our results illustrate how simulations that do not include the use of interferometric detection in a given experiment can lead to significant disagreements with the measurements.

Hybridized metal slit eigenmodes as an illustration of Babinet's principle.

By energy-filtering transmission electron microscopy (EFTEM), we observe Fabry-Pérot-like surface plasmon resonances (SPRs) along the length of rectangular single and double slits drilled into free-standing thin silver films. These eigenmodes hybridize in closely situated slits. The nature of their lateral coupling is uncovered from finite-element simulations, which show that the symmetry and energy sequence of hybrid modes is governed by Babinet complementarity principles. Interestingly, the modes of a double slit system, being proto-self-complementary, may alternatively be explained by magnetic interactions between slit fields or by electrostatic interactions across the metallic bridge separating the slits.

Long-distance indirect excitation of nanoplasmonic resonances.

In nanoscopic systems, size, geometry, and arrangement are the crucial determinants of the light-matter interaction and resulting nanoparticles excitation. At optical frequencies, one of the most prominent examples is the excitation of localized surface plasmon polaritons, where the electromagnetic radiation is coupled to the confined charge density oscillations. Here, we show that beyond direct near- and far-field excitation, a long-range, indirect mode of particle excitation is available in nanoplasmonic systems. In particular, in amorphous arrays of plasmonic nanodiscs we find strong collective and coherent influence on each particle from its entire active neighborhood. This dependency of the local field response on excitation conditions at distant areas brings exciting possibilities to engineer enhanced electromagnetic fields through controlled, spatially configured illumination.

Near-field dynamics of optical Yagi-Uda nanoantennas.

We present near-field measurements of optical Yagi-Uda nanoantennas that are used in receiving mode. The eigenmode imaging of amplitude and phase by apertureless scanning near-field optical microscopy allows us to investigate the dynamics of the local out-of-plane electric field components and to visualize the temporal evolution of this time-harmonic reception process. The antenna directionality manifests itself by the dependence of the local field enhancement at the feed element on the illumination direction. Simulations taking into account the substrate confirm our observation of the directionality. Our work demonstrates the possibility to characterize multielement nanoantennas by electromagnetic antenna near-field scanners.

3D optical Yagi-Uda nanoantenna array.

Future photonic circuits with the capability of high-speed data processing at optical frequencies will rely on the implementation of efficient emitters and detectors on the nanoscale. Towards this goal, bridging the size mismatch between optical radiation and subwavelength emitters or detectors by optical nanoantennas is a subject of current research in the field of plasmonics. Here we introduce an array of three-dimensional optical Yagi-Uda antennas, fabricated using top-down fabrication techniques combined with layer-by-layer processing. We show that the concepts of radiofrequency antenna arrays can be applied to the optical regime proving superior directional properties compared with a single planar optical antenna, particularly for emission and reception into the third dimension. Measuring the optical properties of the structure reveals that impinging light on the array is efficiently absorbed on the subwavelength scale because of the high directivity. Moreover, we show in simulations that combining the array with suitable feeding circuits gives rise to the prospect of beam steering at optical wavelengths.

Plasmonic oligomers: the role of individual particles in collective behavior.

We present a comprehensive experimental study of the optical properties of plasmonic oligomers. We show that both the constitution and configuration of plasmonic oligomers have a large influence on their resonant behavior, which draws a compelling analogy to molecular theory in chemistry. To elucidate the constitution influence, we vary the size of individual nanoparticles and identify the role of the target nanoparticle from the spectral change. To illustrate the configuration influence, we vary the positions and numbers of nanoparticles in a plasmonic oligomer. Additionally, we demonstrate experimentally a large spectral redshift at the transition from displaced nanoparticles to touching ones. The oligomeric design strategy opens up a rich pathway for the implementation of optimized optical properties into complex plasmonic nanostructures for specific applications.