Introduction

Subwavelength-scale metallic structures are a basis for manipulating electromagnetic waves [693]. By engineering the geometry of individual structures and their coupling with each other and the environment, it is possible to construct materials that redirect radiation, couple freely propagating waves to highly localized modes and concentrate light into subwavelength-scale “hot spots.” At RF, these concepts have been developed to great maturity, where antenna and transmission line technologies have formed the basis for modern wireless communication [694]. It has been of recent interest to scale these concepts down to IR and even visible wavelengths, to create new functional materials that can be used in photonic and plasmonic circuits [40], field-enhanced spectroscopies [547], beam steering platforms [695] and new types of detectors [201].

Plasmonic nanostructures can be fabricated via two routes. The first is topdown lithographic fabrication, which employs well-developed techniques such as optical lithography, EBL and FIB milling [436]. The second is the chemical synthesis of colloids. NP synthesis dates back to Ancient Roman times where colloidal Ag and Au were used to color glass, famously exemplified by the Lycurgus Cup. Today, physical chemists can synthesize Au and Ag nanostructures with a broad range of shapes and sizes [696]. Top-down nanofabrication will continue to advance developments in nanophotonics, but it possesses intrinsic limitations. One is that the structures are defined in a focal plane and are typically planar. Another is that, for EBL and FIB, structures are written in series and limited to relatively small total areas.

Introduction

Light passing in a small aperture has been the subject of intense scientific interest since the very first introduction of the concept of diffraction by Grimaldi in 1665. This interest is directly sustained by two facts: an aperture in an opaque screen is probably the simplest optical element, and its interaction with electromagnetic radiation leads to a wide range of physical phenomena. As the fundamental comprehension of electromagnetism as well as fabrication techniques evolved during the twentieth century, the interest turned towards apertures of subwavelength dimensions. Bethe gave the first theory of diffraction by an idealized subwavelength aperture in a thin perfect metal layer [17], predicting extremely small transmitted powers as the aperture diameter decreased far below the radiation wavelength. These predictions were refuted by the observation of the so-called extraordinary optical transmission phenomenon by Ebbesen and co-workers in 1998 [23], which in turn stimulated much fundamental research and technology development around subwavelength apertures and nano-optics over the last decade [65]. It is not the aim of this chapter to review the transmission of light through subwavelength apertures. Comprehensive reviews can be found in Refs. [880, 881]. Instead, this chapter will focus on subwavelength apertures to reversibly convert freely propagating optical radiation into localized energy, and tailor light–matter interaction at the nanoscale. This goes within the rapidly growing field of optical antennas [36, 202], which forms the core of this book.

Introduction

Metallic NPs and nanostructures perform a very effective role acting as optical antennas, as has been introduced in previous chapters. Together with their functionality in transferring electromagnetic energy to the far-field in a directional manner [141–143], they can also localize this energy from the far-field into the near-field, an effect of utmost importance in field-enhanced spectroscopies, as we will review in this chapter.

Field enhancement

Optical antennas are able to localize the electromagnetic field by means of excitation of LSPRs in the metal. These matter excitations are associated with oscillations of the surface charge density at the interface between the metal forming the nanostructure and the outer medium. Different metallic nanostructures are arranged in a variety of designs, sometimes mimicking and reproducing previous ones in RF. Depending on the particular role that an optical antenna needs to fulfill, it is possible to find linear antennas for dipolar emission [144], λ4 antennas for omni-directional emission [145], Yagi-Uda antennas for directional emission [81, 143, 146], patch antennas [147] or even parabolic-like nanocups that bend light similarly to parabolic antennas [148]. All these emission properties have their origin in a particular excitation of electromagnetic modes in the nanostructure.

For spectroscopic applications, it is important to consider not only the emission properties of the antenna, but also the localization and strength of the local fields.

Introduction

As extensively discussed in this book, a classic RF antenna provides a means for channeling radio waves to/from a subwavelength receiver/emitter [790]. Similarly, optical antennas bridge the lengthscale difference between the free-space wavelength of light and subwavelength objects, thereby defining the size of the optical antenna to be in the nano to micron regime. But metals, which are the basis for almost all antenna structures, respond differently to electromagnetic waves in the RF and optical frequency ranges. In particular, metal nanostructures support LSPRs for UV, visible and near-IR wavelengths [791]. The LSPRs strongly influence antenna design and offer an unparalleled means to effectively address nanoscopic objects, such as individual molecules, using light [38, 169]. Nanoplasmonic antennas, ranging from single colloidal NPs to elaborate lithographic structures, have therefore become the basis for a variety of surface-enhanced molecular spectroscopies, such as SERS [168, 176, 177], SEIRA [189, 792] and SEF [167]. These methods thus focus on using nanoplasmonic antennas to increase the interaction between external radiation and the molecule, thereby amplifying the strength of the molecular spectroscopic fingerprint. However, the antenna and the molecule is a coupled system, which means that the presence of the molecule will affect the antenna resonance. Nanoplasmonic refractive index sensing is essentially about this effect, that is, to register a change in the dielectric environment of the antenna through an optical measurement of the antenna's LSPR properties.

Introduction

In order for antennas to operate in the visible and near-IR wavelength range (optical antennas), the devices need to be subwavelength in size. Recently, nanofabrication tools have been developed to create optical antennas with unprecedented properties which have enabled many applications [202]. For example, optical antennas can be used as nanoscale energy transmitters or scatterers for SNOM and spectroscopy with subwavelength resolution and directional emission of single photons [68, 143, 146, 256]. The antennas can also operate as receivers to collect and concentrate EM energy into nanoscale volumes for photovoltaics, photo-detection and nonlinear optical devices [34, 171, 201, 435, 668].

Over the past decade, a variety of optical antenna designs have been investigated for different applications. These structures include: (i) metal NPs (NPs) that support LSPRs, which can act as receivers to enhance optical absorption for active materials as well as transmitters to enhance emission rates of nearby dipole emitters (see Fig. 16.1a) [68]. (ii) NP dimers that can result in significant field enhancements of the incident light in the nanoscale gap separating the NPs (see Figs. 16.1b–d) [34, 167, 171]. (iii) nanoscale apertures in a metallic film that can also operate as receivers to convert optical energy from propagating waves into nano-localized spots. (see Fig. 16.1e) [669]. (iv) nano-rod arrays that can function as miniaturized Yagi–Uda antennas and result in directional radiation (see Fig. 16.1f) [143, 146].

Introduction

Nano-optical devices have a great potential for technological applications [201, 597, 598]. Consequently, the investigation of plasmonic excitations in nanostructures and on surfaces has evolved into a tremendous research field, made possible only by the progress in nanotechnology. Nowadays, nanoantennas with highly complex shapes are fabricated with an extremely high accuracy by standardized procedures [564]. The spectral features and near-field properties of such optical antennas are determined on a length scale that is intrinsically smaller than the diffraction limit of electromagnetic waves. However, experimental access to the spatial properties of these antennas on the nanoscale is essential for an understanding of the underlying mechanisms that lead to strong near-field enhancements, interferences and mode hybridization. Thus, there is a particular need for a real-space microscopy technique that delivers information about near-field distribution within and in the vicinity of nanostructures, with a resolution below the diffraction limit. In addition to pure imaging of static field distributions, knowledge of the dynamical properties of electronic excitations is relevant for encoding and manipulation of information on the nanoscale. The microscopic understanding of the associated dynamics is crucial for many other research fields, such as molecular biology or catalytic chemistry. Considering technological applications, well-tuned spectral properties and high reproducibility of the nanostructures is most important. Smallest differences on the nanoscale of individual structures (e.g. induced by the fabrication process) lead to strong variations of their optical response.

Introduction

Today there is significant effort put into understanding the optical properties of molecules interacting with optical antennas. This interest is largely driven by many potential applications of such interactions, as well as a scientific curiosity for obtaining a detailed understanding of the complicated physics and chemistry arising in these unique systems. Establishing a detailed fundamental understanding of the optical properties in these mixed molecule–metal complexes will be essential in order to apply these materials to energy harvesting [435], nanoscale optical circuits [436] and ultra-sensitive chemical and biological sensors [437, 438].

The optical properties of molecules are characterized by localized excitations that reflect the electronic structure of the molecules. These localized electronic transitions can be engineered by introducing electron donating or electron withdrawing groups into the molecule by means of chemical synthesis. This allows for molecules to be designed with tailored optical properties. In contrast, the optical properties of metallic nanoantennas are dominated by the collective excitations of the conduction electrons, also known as SPPs. The excitation of a LSPR results in strong absorption in the UV–visible region and thus are responsible for NP's brilliant optical properties. The LSPR excitation is sensitive to the size, shape, material and surroundings of the NP, which provides significant opportunities for designing materials with optimum optical properties. This is possible due to significant advances in fabrication techniques as well as efficient classical electromagnetic simulation techniques. This feature makes plasmonic antennas uniquely suited for a wide range of applications in catalysis, optics, chemical and biological sensing and medical therapeutics.

Recent years have witnessed a tremendous progress in nanofabrication, as well as in the theoretical and experimental understanding of light–matter interaction at the nanoscale. The field of nano-optics has thrived during these times and one of the most exciting related advances in this area has been the concept, design and application of optical antennas, or nanoantennas. Starting within the onset of field-enhanced spectroscopy and near-field optics, the concept has rapidly evolved into a sophisticated tool to enhance and direct spontaneous emission from quantum light sources, boost light–matter interaction and optical nonlinearities at the nanoscale, as well as implement realistic optical communication links. The amount of research activity on optical antennas has grown very rapidly in the last few years, and currently spans a broad range of areas, including optics, physics, chemistry, electrical engineering, biology and medicine, to cite a few. The rapid progress and inherent multidisciplinarity of nanoantennas have produced a situation in which the involved research communities do not necessarily speak the same language. If electrical engineers have an established formalism based on circuit and radiation concepts developed over decades of antenna engineering and design, in optics, physics or chemistry many of the same phenomena are described in very different terms. It is exactly this interdisciplinarity, however, that may lead to groundbreaking findings and applications in a variety of fields of modern science.

Introduction

Many optoelectronic devices and systems exhibit a large mismatch between critical optical and electronic length scales that limit their performance. Particularly severe issues in this regard have emerged in scaling electronic circuitry for information technology and in the development of ultra-thin devices for solar energy harvesting. For example, the stringent electronic power and speed requirements on photodetectors used in an optical link set demanding limits on the size of these components. Ideally, one would scale these detectors to the size of an electronic transistor (~10 nm) or in fact build optically controlled transistors. The fundamental laws of diffraction – which state that light waves cannot be focused beyond about half a free-space wavelength (typically a few hundreds of nanometers) – seems to indicate that an efficient coupling to such tiny devices is physically impossible. Similar challenges occur in ultra-thin film solar cells that are realized with the aim of reducing processing and materials costs compared with thicker crystalline cells. Unfortunately their low energy conversion efficiencies still prevent rapid large-scale implementation. The key reason for their relatively poor performance is that the absorption depth of light in the most popular, deposited semiconductors films used in these cells is significantly longer than the electronic (minority carrier) diffusion length (particularly for photon energies close to the bandgap). As a result, charge extraction from optically thick cells is challenging due to carrier recombination in the bulk of the semiconductor.

Introduction

For radio engineers it is a common task to combine several antennas to form an antenna array. This gives them several degrees of freedom for shaping the radiation pattern according to their needs. By selecting different types of individual elements, their relative position in space, their respective orientation, and the amplitude and phase of the induced currents, one can engineer the radiated beam properties [262]. In the new research field of optical nanoantennas, the possibilities of arraying antennas have hardly been explored yet. This is mainly due to the challenges in fabricating and driving the arrays, as well as the yet limited possibilities of characterization. Nevertheless, application of RF antenna array concepts into optical regimes promises tremendous technological advances: increasing the directivity and gain aids in distant signal transmission and reception (similarly to the concepts used in satellite communication), coupling nanoemitters and nanoreceivers to antenna arrays enhances their efficiency with the potential of bridging the size gap between optical radiation and subwavelength emitters or detectors and employing phase retarders allows for steering of optical beams.

In this chapter, we introduce the concepts of array theory and scale them to optical frequencies. We start with a short introduction on RF antenna array theory and discuss the differences that have to be accounted for at optical frequencies. Subsequently, the possibility of beam shaping at optical frequencies is discussed. Numerical and experimental studies on a closely spaced 1D array of plasmonic dipole antennas, whose design is analogous to the well-known RF Yagi–Uda antenna [233], give insight into the dynamics of the optical modes that are supported by the antenna structure.

Introduction

In the past few years, tremendous progress has been made on the utilization, fabrication and understanding of these devices that can focus energy from the far-field onto nanoscale regions and, conversely, enhance the radiation from subwavelength sources into the far-field. While the development of reliable and flexible nanofabrication techniques has been essential for this progress, it has also often been guided by extensive modeling based on computational electrodynamics.

The objective of this chapter is to describe the requirements for accurate electrodynamic modeling of optical antennas, to draw attention to specific pitfalls that can occur in that endeavor and to illustrate some recent modeling results. This chapter is organized as follows: after a brief introduction that describes the challenges associated with the electromagnetic modeling of optical antennas, we review in Sec. 10.2 some of the popular methods used for the electromagnetic simulation of plasmonic antennas, and emphasize in Sec. 10.3 the importance of assessing the convergence of a method and the accuracy of the results it produces. Section 10.4 illustrates the modeling of realistic optical antennas and the utilization of reciprocity to further check the accuracy of numerical results. Section 10.5 provides some typical results on the interaction between an optical antenna and its environment. The chapter concludes with some perspectives on what will be the next challenge in the electromagnetic simulation of plasmonic antennas.

From a computational electromagnetic point of view, the study of optical antennas requires the solving of Maxwell equations for the somewhat complex geometry of the antenna.