Interference of optically induced electric and magnetic modes in high-index all-dielectric nanoparticles offers unique opportunities for tailoring directional scattering and engineering the flow of light. In this article we demonstrate theoretically and experimentally that the interference of electric and magnetic optically induced modes in individual subwavelength silicon nanodisks can lead to the suppression of resonant backscattering and to enhanced resonant forward scattering of light. To this end we spectrally tune the nanodisk’s fundamental electric and magnetic resonances with respect to each other by a variation of the nanodisk aspect ratio. This ability to tune two modes of different character within the same nanoparticle provides direct control over their interference, and, in consequence, allows for engineering the particle’s resonant and off-resonant scattering patterns. Most importantly, measured and numerically calculated transmittance spectra reveal that backward scattering can be suppresse...

Tailoring Directional Scattering through Magnetic and Electric Resonances in Subwavelength Silicon Nanodisks

Understanding how light interacts with matter at the nanometre scale is a fundamental issue in optoelectronics and nanophotonics. In particular, many applications (such as bio-sensing, cancer therapy and all-optical signal processing) rely on surface-bound optical excitations in metallic nanoparticles. However, so far no experimental technique has been capable of imaging localized optical excitations with sufficient resolution to reveal their dramatic spatial variation over one single nanoparticle. Here, we present a novel method applied on silver nanotriangles, achieving such resolution by recording maps of plasmons in the near-infrared/visible/ultraviolet domain using electron beams instead of photons. This method relies on the detection of plasmons as resonance peaks in the energy-loss spectra of subnanometre electron beams rastered on nanoparticles of well-defined geometrical parameters. This represents a significant improvement in the spatial resolution with which plasmonic modes can be imaged, and provides a powerful tool in the development of nanometre-level optics.

Mapping surface plasmons on a single metallic nanoparticle

The discovery of optical second harmonic generation in 1961 started modern nonlinear optics. Soon after, R. C. Miller found empirically that the nonlinear susceptibility could be predicted from the linear susceptibilities. This important relation, known as Miller's Rule, allows a rapid determination of nonlinear susceptibilities from linear properties. In recent years, metamaterials, artificial materials that exhibit intriguing linear optical properties not found in natural materials, have shown novel nonlinear properties such as phase-mismatch-free nonlinear generation, new quasi-phase matching capabilities and large nonlinear susceptibilities. However, the understanding of nonlinear metamaterials is still in its infancy, with no general conclusion on the relationship between linear and nonlinear properties. The key question is then whether one can determine the nonlinear behaviour of these artificial materials from their exotic linear behaviour. Here, we show that the nonlinear oscillator model does not apply in general to nonlinear metamaterials. We show, instead, that it is possible to predict the relative nonlinear susceptibility of large classes of metamaterials using a more comprehensive nonlinear scattering theory, which allows efficient design of metamaterials with strong nonlinearity for important applications such as coherent Raman sensing, entangled photon generation and frequency conversion.

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Predicting nonlinear properties of metamaterials from the linear response.

Developments of optical detection and spectroscopy methods for single nano-objects are key advances for applications and fundamental understanding of the novel properties exhibited by nanosize systems. These methods are reviewed, focusing on far-field optical approaches based on light absorption and elastic scattering. The principles of the main linear and nonlinear methods are described and experimental results are illustrated in the case of metal nanoparticles, stressing the key role played by the object environment, such as the presence of a substrate, bound surface molecules or other nano-objects. Special attention is devoted to quantitative methods and correlation of the measured optical spectra of a nano-object with its morphology, characterized either optically or by electron microscopy, as this permits precise comparison with theoretical models. Application of these methods to optical detection and spectroscopy for single semiconductor nanowires and carbon nanotubes is also presented. Extension to ultrafast nonlinear extinction or scattering spectroscopies of single nano-objects is finally discussed in the context of investigation of their nonlinear optical response and their electronic, acoustic and thermal properties.

Optical absorption and scattering spectroscopies of single nano-objects

This article reviews the state of the recently developed discontinuous Galerkin finite element method for the efficient numerical treatment of nanophotonic systems. This approach combines the accurate and flexible spatial discretisation of classical finite elements with efficient time stepping capabilities. We describe in detail the underlying principles of the discontinuous Galerkin technique and its application to the simulation of complex nanophotonic structures. In addition, formulations for both time- and frequency-domain solvers are provided and specific advantages and limitations of the technique are discussed. The potential of the discontinuous Galerkin approach is illustrated by modelling and simulating several experimentally relevant systems.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/lpor.201000045

Discontinuous Galerkin methods in nanophotonics

Efficient low-storage Runge-Kutta schemes with optimized stability regions

Antennas convert propagating radiation to localized electromagnetic energy and to heat. To unambiguously separate between these two aspects, one needs to quantitatively determine the antenna scattering and absorption cross-section spectra. By using a spatial modulation technique combined with a common-path interferometer and lithographically fabricated individual gold nanoantennas, we experimentally determine the scattering and absorption cross-section spectra of different optical antennas simultaneously and quantitatively for the first time.

Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas.

Metamaterials are artificial media which can provide optical properties not available from natural materials. These properties often result from the resonant excitation of plasmonic modes in the metallic building blocks (“metaatoms”) of the metamaterial. Electromagnetic interactions between the metaatoms significantly modify the resonances of the individual metaatoms and influence the optical properties of the whole metamaterial. To better understand these interactions, we study in this Letter the evolution of the plasmonic near-field in the course of the transition from an isolated metaatom, in our case a split-ring resonator (SRR), to a photonic metamaterial via electron energy-loss spectroscopy. For small SRR ensembles, we observe the formation of discrete optical bright and dark modes due to coupling of the metaatoms. Large SRR arrays reveal a quasi-continuum of modes in the interior and distinct edge modes at the boundaries of the array. Our experimental results are in excellent agreement with numeri...

From isolated metaatoms to photonic metamaterials: evolution of the plasmonic near-field.

Comparison of Low-Storage Runge-Kutta Schemes for Discontinuous Galerkin Time-Domain Simulations of Maxwell's Equations

The Discontinuous Galerkin (DG) approach is a variation of the classical finite‐element method, which allows to combine an unstructured higher‐order spatial discretization with an explicit time‐stepping scheme. This feature is particularly relevant for the time‐domain analysis of plasmonic structures, where the electromagnetic field varies strongly on rather small length scales. Here, we present our recent advances in further improving the spatial discretization of the DG method. In particular, we demonstrate how three‐dimensional curvilinear elements can be used to improve the accuracy when dealing with rounded structures.

Richard Diehl

Papers

Efficient low-storage Runge-Kutta schemes with optimized stability regions

Quantitative experimental determination of scattering and absorption cross-section spectra of individual optical metallic nanoantennas.

From isolated metaatoms to photonic metamaterials: evolution of the plasmonic near-field.

Comparison of Low-Storage Runge-Kutta Schemes for Discontinuous Galerkin Time-Domain Simulations of Maxwell's Equations

Using Curved Elements in the Discontinuous Galerkin Time-Domain Approach