Impedance matching and emission properties of optical antennas in a nanophotonic circuit

An experimentally realizable prototype nanophotonic circuit consisting of a receiving and an emitting nano antenna connected by a two-wire optical transmission line is studied using finite-difference time- and frequency-domain simulations. To optimize the coupling between nanophotonic circuit elements we apply impedance matching concepts in analogy to radio frequency technology. We show that the degree of impedance matching, and in particular the impedance of the transmitting nano antenna, can be inferred from the experimentally accessible standing wave pattern on the transmission line. We demonstrate the possibility of matching the nano antenna impedance to the transmission line characteristic impedance by variations of the antenna length and width realizable by modern microfabrication techniques. The radiation efficiency of the transmitting antenna also depends on its geometry but is independent of the degree of impedance matching. Our systems approach to nanophotonics provides the basis for realizing general nanophotonic circuits and a large variety of derived novel devices

Electromechanically Tunable Suspended Optical Nano-antenna

Coupling mechanical degrees of freedom with plasmonic resonances has potential applications in optomechanics, sensing, and active plasmonics. Here we demonstrate a suspended two-wire plasmonic nano-antenna acting like a nano-electrometer. The antenna wires are supported and electrically connected via thin leads without disturbing the antenna resonance. As a voltage is applied, equal charges are induced on both antenna wires. The resulting equilibrium between the repulsive Coulomb force and the restoring elastic bending force enables us to precisely control the gap size. As a result the resonance wavelength and the field enhancement of the suspended optical nano-antenna (SONA) can be reversibly tuned. Our experiments highlight the potential to realize large bandwidth optical nanoelectromechanical systems (NEMS)

Evolutionary optimization of optical antennas

The design of nano-antennas is so far mainly inspired by radio-frequency technology. However, material properties and experimental settings need to be reconsidered at optical frequencies, which entails the need for alternative optimal antenna designs. Here a checkerboard-type, initially random array of gold cubes is subjected to evolutionary optimization. To illustrate the power of the approach we demonstrate that by optimizing the near-field intensity enhancement the evolutionary algorithm finds a new antenna geometry, essentially a split-ring/two-wire antenna hybrid which surpasses by far the performance of a conventional gap antenna by shifting the n=1 split-ring resonance into the optical regime.Comment: Also see Supplementary material, as attached to the main pape

Second harmonic generation from plasmonic hotspots by controlled local symmetry breaking

Bonding resonant modes of plasmonic nanoantennas with narrow gaps exhibit very large local field enhancement. These hotspots are highly attractive for boosting optical nonlinearities, such as second harmonic generation. However, for resonant symmetric gap antennas, the strong second harmonic sources created at the gap interfaces oscillate out-of-phase and therefore interfere destructively in the far-field. Here, we use an advanced nanofabrication approach to systematically break the local symmetry of nanoscopic antenna gaps while retaining the bonding resonant antenna mode at the fundamental frequency and the concomitant intensity hotspot. We find that antennas with the strongest local symmetry breaking emit correspondingly intense second harmonic radiation as compared to symmetric reference structures. By combining these findings with second harmonic radiation patterns as well as quantitative nonlinear simulations, we obtain remarkably detailed insights into the mechanism of second harmonic generation at the nanoscale. Our findings open new perspectives for the realization of non-reciprocal nanoscale systems, where local symmetry breaking is crucial to create unique functionalities

Direct electrical modulation of surface response in a single plasmonic nanoresonator

Classical electrodynamics describes the optical response of macroscopic systems, where the boundaries between materials is treated as infinitesimally thin. However, due to the quantum nature of electrons, interfaces acquires a finite thickness. To include non-classical surface effects in the framework of Maxwell's equations, surface-response functions can be introduced, also known as Feibelman $d$-parameters. Surface response impacts systems with strong field localization at interfaces, which is encountered in noble metal nanoparticles supporting surface plasmon polaritons. However, studying surface response is challenging as it necessitates sub-nanometer control of geometric features, e.g. the gap size in a dimer antenna, while minimizing uncertainties in morphology. In contrast, electrical gating is convenient since the static screening charges are confined exclusively to the surface, which alleviates the need for precise control over the morphology. Here, we study the perturbation of Feibelman $d$-parameters by direct electric charging of a single plasmonic nanoresonator and investigate the resulting changes of the resonance in experiment and theory. The measured change of the resonance frequency matches the theory by assuming a perturbation of the tangential surface current. However, we also observe an unforeseen narrowing in the resonance width when adding electrons to the surface of a plasmonic nanoresonator. These reduced losses cannot be explained by electron spill-out within the local-response approximation (LRA). Such an effect is likely caused by nonlocality and the anisotropy of the perturbed local permittivity. Our findings open up possibilities to reduce losses in plasmonic resonators and to develop ultrafast and extremely small electrically driven plasmonic modulators and metasurfaces by leveraging electrical control over non-classical surface effects.Comment: 10 pages, 3 figures, 15 pages Supplementar

The patterning toolbox FIB-o-mat: Exploiting the full potential of focused helium ions for nanofabrication

Focused beams of helium ions are a powerful tool for high-fidelity machining with spatial precision below 5 nm. Achieving such a high patterning precision over large areas and for different materials in a reproducible manner, however, is not trivial. Here, we introduce the Python toolbox FIB-o-mat for automated pattern creation and optimization, providing full flexibility to accomplish demanding patterning tasks. FIB-o-mat offers high-level pattern creation, enabling high-fidelity large-area patterning and systematic variations in geometry and raster settings. It also offers low-level beam path creation, providing full control over the beam movement and including sophisticated optimization tools. Three applications showcasing the potential of He ion beam nanofabrication for two-dimensional material systems and devices using FIB-o-mat are presented

The patterning toolbox FIB-o-mat: Exploiting the full potential of focused helium ions for nanofabrication

Focused beams of helium ions are a powerful tool for high-fidelity machining with spatial precision below 5 nm. Achieving such a high patterning precision over large areas and for different materials in a reproducible manner, however, is not trivial. Here, we introduce the Python toolbox FIB-o-mat for automated pattern creation and optimization, providing full flexibility to accomplish demanding patterning tasks. FIB-o-mat offers high-level pattern creation, enabling high-fidelity large-area patterning and systematic variations in geometry and raster settings. It also offers low-level beam path creation, providing full control over the beam movement and including sophisticated optimization tools. Three applications showcasing the potential of He ion beam nanofabrication for two-dimensional material systems and devices using FIB-o-mat are presented

Optimierung von Nano-Antennen zur Fokussierung von Licht: Neue Ansätze: Von Evolution zu Moden-Anpassung

Optische Antennen arbeiten ähnlich wie Antennen für Radiowellen und wandeln elektromagnetische Strahlung in elektrische Wechselströme um. Ladungsdichteansammlungen an der Antennen-Oberfläche führen zu starken und lokalisierten Nahfeldern. Da die meisten optischen Antennen eine Ausdehnung von wenigen hundert Nanometern besitzen, ermöglichen es ihre Nahfelder, Licht auf ein Volumen weit unterhalb des Beugungslimits zu fokussieren, mit Intensitäten, die mehrere Größenordnungen über dem liegen, was man mit klassischer beugender und reflektierender Optik erreichen kann. Die Aufgabe, die Abstrahlung eines Quantenemitters zu maximieren, eines punktförmigen Objektes, welches einzelne Photonen absorbieren und emittieren kann, ist identisch mit der Aufgabe, die Feldintensität am Ort des Quantenemitters zu maximieren. Darum ist es erstrebenswert, den Fokus optischer Antennen zu optimieren Optimierte Radiofrequenz-Antennen, welche auf Größenordnungen von wenigen 100 Nanometern herunterskaliert werden, zeigen bereits eine gute Funktionalität. Jedoch liegen optische Frequenzen in der Nähe der Plasmafrequenz von den Metallen, die für optische Antennen genutzt werden und die Masse der Elektronen kann nicht mehr vernachlässigt werden. Dadurch treten neue physikalische Phänomene auf. Es entstehen gekoppelte Zustände aus Licht und Ladungsdichte-Schwingungen, die sogenannten Plasmonen. Daraus folgen Effekte wie Volumenströme und kürzere effektive Wellenlängen. Zusätzlich führt die endliche Leitfähigkeit zu thermischen Verluste. Das macht eine Antwort auf die Frage nach der optimalen Geometrie für fokussierende optische Antennen schwer. Jedoch stand vor dieser Arbeit der Beweis noch aus, dass es für optische Antennen bessere Alternativen gibt als herunterskalierte Radiofrequenz-Konzepte. In dieser Arbeit werden optische Antennen auf eine bestmögliche Fokussierung optimiert. Dafür wird ein Ansatz gewählt, welcher bei Radiofrequenz-Antennen für komplexe Anwendungsfelder (z.B. isotroper Breitbandempfang) schon oft Erfolg hatte: evolutionäre Algorithmen. Die hier eingeführte erste Implementierung erlaubt eine große Freiheit in Bezug auf Partikelform und Anzahl, da sie quadratische Voxel auf einem planaren, quadratischen Gitter beliebig anordnet. Die Geometrien werden in einer binären Matrix codiert, welche als Genom dient und somit Methoden wie Mutation und Paarung als Verbesserungsmechanismus erlaubt. So optimierte Antennen-Geometrien übertreffen vergleichbare klassische Dipol-Geometrien um einen Faktor von Zwei. Darüber hinaus lässt sich aus den optimierten Antennen ein neues Funktionsprinzip ableiten: ein magnetische Split-Ring-Resonanz kann mit Dipol-Antennen leitend zu neuartigen und effektiveren Split-Ring-Antennen verbunden werden, da sich ihre Ströme nahe des Fokus konstruktiv überlagern. Im nächsten Schritt wird der evolutionäre Algorithmus so angepasst, so die Genome real herstellbare Geometrien beschreiben. Zusätzlich wird er um eine Art ''Druckertreiber'' erweitert, welcher aus den Genomen direkt Anweisungen zur fokussierten Ionenstrahl-Bearbeitung von einkristallinen Goldflocken erstellt. Mit Hilfe von konfokaler Mikroskopie der Zwei-Photonen-Photolumineszenz wird gezeigt, dass Antennen unterschiedlicher Effizienz reproduzierbar aus dem evolutionären Algorithmus heraus hergestellt werden können. Außerdem wird das Prinzip der Split-Ring-Antenne verbessert, indem zwei Ring-Resonanzen zu einer Dipol-Resonanz hinzugefügt werden. Zu guter Letzt dient die beste Antenne des zweiten evolutionäre Algorithmus als Inspiration für einen neuen Formalismus zur Beschreibung des Leistungsübertrages zwischen einer optischen Antenne und einem Punkt-Dipol, welcher sich als "dreidimensionaler Modenüberlapp" beschreiben lässt. Damit können erstmals intuitive Regeln für die Form einer optischen Antenne aufgestellt werden. Die Gültigkeit der Theorie wird analytisch für den Fall eines Dipols nahe einer metallischen Nano-Kugel gezeigt. Das vollständige Problem, Licht mittels einer optischen Antenne zu fokussieren, lässt sich so auf die Erfüllung zweier Modenüberlapp-Bedingungen reduzieren -- mit dem Feld eines Punktdipols, sowie mit einer ebenen Welle. Damit lassen sich zwei Arten idealer Antennenmoden identifizieren, welche sich von der bekannten Dipol-Antennen-Mode grundlegend unterscheiden. Zum einen lässt sich dadurch die Funktionalität der evolutionären und Split-Ring-Antennen erklären, zum lassen sich neuartige plasmonische Hohlraum-Antennen entwerfen, welche zu besserer Fokussierung von Licht führen. Dies wird numerisch im direkten Vergleich mit einer klassischen Dipolantennen-Geometrie gezeigt.Optical antennas work similar to antennas for the radio-frequency regime and convert electromagnetic radiation into oscillating electrical currents. Charge density accumulations form at the antenna surface leading to strong and localized near-fields. Since most optical antennas have dimensions of a few hundred nanometers, their near-fields allow the focusing of electromagnetic fields to volumes much smaller than the diffraction limit, with intensities several orders of magnitude larger than achievable with classical diffractive and refractive optical elements. The task to maximize the emission of a quantum emitter, a point-like entity capable of reception and emission of single photons, is identical to the task to maximize the field intensity at the position of the quantum emitter. Therefore it is desirable to optimize the capabilities of focusing optical antennas. Radio-frequency-antenna designs scaled to optical dimensions of several hundred nanometers show already a decent performance. However, optical frequencies lie near the plasma frequency of the metals used for optical antennas and the mass of electrons cannot be neglected anymore. This leads to new physical phenomena. Light can couple to charge density oscillations, yielding a so-called Plasmon. Effects emerge which have no equivalent in the very advanced field of radio-frequency-technology, e.g.~volume currents and shortened effective wavelengths. Additionally the conductivity is not infinite anymore, leading to thermal losses. Therefore, the question for the optimal geometry of a focusing optical antenna is not easy to answer. However, up to now there was no evidence that there exist better alternatives for optical antennas than down-scaled radio-frequency designs. In this work the optimization of focusing optical antennas is based on an approach, which often proved successful for radio-frequency-antennas in complex applications (e.g.~broadband and isotropic reception): evolutionary algorithms. The first implementation introduced here allows a large freedom regarding particle shape and count, as it arranges cubic voxels on a planar, square grid. The geometries are encoded in a binary matrix, which works as a genome and enables the methods of mutation and crossing as mechanism of improvement. Antenna geometries optimized in this way surpass a comparable dipolar geometry by a factor of 2. Moreover, a new working principle can be deduced from the optimized antennas: a magnetic split-ring resonance can be coupled conductively to dipolar antennas, to form novel and more effective split-ring-antennas, as their currents add up constructively near the focal point. In a next step, the evolutionary algorithm is adapted so that the binary matrices describe geometries with realistic fabrication constraints. In addition a 'printer driver' is developed which converts the binary matrices into commands for focused ion-beam milling in mono-crystalline gold flakes. It is shown by means of confocal two-photon photo-luminescence microscopy that antennas with differing efficiency can be fabricated reliably directly from the evolutionary algorithm. Besides, the concept of the split-ring antenna is further improved by adding this time two split-rings to the dipole-like resonance. The best geometry from the second evolutionary algorithm inspires a fundamentally new formalism to determine the power transfer between an antenna and a point dipole, best termed 'three-dimensional mode-matching'. Therewith, for the first time intuitive design rules for the geometry of an focusing optical antenna can be deduced. The validity of the theory is proven analytically at the case of a point dipole in from of a metallic nano sphere. The full problem of focusing light by means of an optical antenna can, thus, be reduced to two simultaneous mode-matching conditions -- on the one hand with the fields of a point dipole, on the other hand with a plane wave. Therefore, two types of ideal focusing optical antenna mode patterns are identified, being fundamentally different from the established dipolar antenna mode. This allows not only to explain the functionality of the evolutionary antennas and the split-ring antenna, but also helps to design novel plamonic cavity antennas, which lead to an enhanced focusing of light. This is proven numerically in direct comparison to a classical dipole antenna design

Cooperative Bond Activation Reactions with Ruthenium Carbene Complex PhSO₂(Ph₂PNSiMe₃)CRu(<i>p</i>‑cymene): RuC and N–Si Bond Reactivity

The synthesis of ruthenium carbene complex PhSO₂(Ph₂PNSiMe₃)­CRu­(<i>p</i>-cymene) (<b>3</b>) and its application in cooperative bond activation reactions were studied. Compound <b>3</b> is accessible via salt metathesis using the dilithium methandiide ligand or alternatively via dehydrohalogenation of the corresponding chlorido complex <b>2</b>. The carbene complex was studied by X-ray crystallography, multielement NMR spectroscopy, and DFT studies, all of which confirm the presence of a RuC double bond. The polarization of the RuC bond is less pronounced than in an analogous carbene complex with a thiophosphoryl instead of the iminophosphoryl moiety. This should be beneficial for realizing reversible activation processes by the addition of element-hydrogen bonds across the RuC double bond. Accordingly, <b>3</b> is more stable and the RuC linkage less reactive in the activation of aromatic alcohols and elemental dihydrogen, showing reversible processes and longer reaction times. Despite the selective addition of dihydrogen across the Ru–C bond, the activation of O–H bonds was accompanied by hydrolysis of the N–Si linkage. The reaction of <b>3</b> with water led to the hydrolysis of the N–Si bond as well as protonative cleavage of the central P–C bond in the ligand backbone, thus resulting in the formation of an unusual dinuclear ruthenium–imido complex