Introduction

Quantum optics

The atom is the most elementary constituent of any model that describes the quantum nature of light–matter interaction. Because atoms emit and absorb light at well-defined frequencies, nineteenth century scientists thought of them as collections of harmonically oscillating electric dipole moments or EHDs. In the language of modern physics, the latter represent dipolar transitions among the various quantum mechanical states of an atom.

In a strict definition, the field of quantum optics deals with problems that not only require the quantization of matter but also of the electromagnetic field, with examples such as (i) generation of squeezed light or Fock states, (ii) strong coupling of an atom and a photon, (iii) entanglement of a photon with an atom and (iv) Casimir and van der Waals forces. There are also many other important topics that have been discussed within the quantum optics community but do not necessarily require a full quantum electrodynamic (QED) treatment. Examples are (i) cooling and trapping of atoms, (ii) precision spectroscopy and (iii) modification of spontaneous emission.

The simple picture of a TLS as an EHD remains very insightful and valuable to this day. Indeed, much of what we discuss in this chapter has to do with the interplay between the quantum and classical mechanical characters of dipolar oscillators. For instance, the extinction cross-section of a TLS, given by 3λ2/2π, can be derived just as well using quantum mechanics [70] or classical optics [234]. Another example, albeit more subtle, concerns the spontaneous emission rate.

Introduction

Optical antennas have added a new aspect to the field of light–matter interactions by efficiently coupling localized fields to propagating radiation [202, 203]. Most of their properties can be described in terms of Maxwell equations, which can be solved numerically even for complex antenna geometries (see Chapter 10). The constantly improving understanding of optical antennas has led to a large number of proposed applications that can only be realized by making use of high-precision state-of-the-art nanofabrication tools and techniques, as well as of a subsequent detailed characterization using optical methods to thoroughly verify the intended properties.

Upon illumination, resonant optical antennas can provide very large near-field intensities, resulting from LSPRs that lead to enhanced local surface charge accumulation. Such resonantly enhanced optical fields are the basis for the improved light–matter interaction afforded by optical antennas. Optical antennas are thus exploited in the context of optical spectroscopy, e.g. involving multi-photon processes [33, 34, 350, 353], harmonic generation [171, 329] or Raman scattering [481, 543]. Other applications include the creation of point-like light sources for super-resolved near-field imaging [145, 544] and lithography [545]. Moreover, nanoantennas can act as highly-efficient absorbers in solar-cell and photon-detector technology [435] and they are the ideal interface between far-field propagating photons and guided modes in plasmonic nanocircuitry [546].

Plasmon resonant nanoantennas also exhibit enhanced scattering due to resonantly enhanced plasmonic currents. This property can be exploited in far-field experiments for sensing applications in conjunction with the large sensitivity of the antenna resonance condition to the local dielectric environment [547].

Introduction

The concept of nanoantennas has emerged in optics as an enabling technology for controlling the spatial distribution of light on subdiffraction length scales. Analogously to classical antenna design, the objective of optical antenna design is the optimization and control of the energy transfer between a localized source, acting as receiver or transmitter, and the free radiation field. Most of the implemented optical antenna designs operate in the linear regime that is, the radiation field and the polarization currents are linearly dependent on each other. When this linear dependence breaks down, however, new interesting phenomena arise, such as frequency conversion, switching and modulation. Beyond the ability of mediating between localized and propagating fields, a nonlinear optical antenna provides the additional ability to control the interaction between the two. Figure 8.1 sketches an example where the nonlinear antenna converts the frequency of the incident radiation, thus shifting the frequency of a signal centered at ω1 by a predefined amount Δω into a new frequency band centered at ω2. Here we review the basic properties of nonlinear antennas and then focus on the nonlinearities achievable in either single-NP systems or more complex coupled-NP systems. In practice, the use of nonlinear materials – either metals or dielectrics – in the design of optical antennas is a promising route towards the generation and control of optical information.

Design fundamentals

The study of nonlinear optical antennas is still in its infancy. The design principles are based on the well-established field of nonlinear optics [295, 296] that has its origins in the early 1960s, when SHG was first observed in a piezoelectric crystal [297].

Introduction

The purpose of this chapter is to further discuss the concept of the impedance of a nanoantenna. As highlighted in the previous chapter, at RF the impedance plays a key role in two respects: (i) the real part of the impedance is called radiation resistance and quantifies the amount of energy radiated by the antenna; (ii) the interaction between the antenna and the feeding circuit is analyzed using the impedance. The maximum power transmission occurs when an impedance matching condition is satisfied. It is of interest to analyze the light emission assisted by a nanoantenna in terms of impedance for the same reasons: how much power is emitted? What is the effect of the interaction between the source and its environment? When comparing the case of RF and the case of optical emission assisted by a nanoantenna, it is remarkable to realize that we deal with the same fundamental issue: electromagnetic wave emission by electrons. However, in optics we analyze photon emission using very different concepts such as density of states, Purcell factor, lifetime or decay rates.

The aim is twofold: (i) we wish to establish a connection between the two points of view; (ii) we wish to introduce the concept of impedance in optics as a practical tool to analyze the interaction between an antenna and a quantum emitter. Regarding the concept of impedance for nanoantennas, the cases of antennas consisting of two separate parts such as dimers or two rods has been extensively analyzed in the previous chapter and in Refs.

Introduction

At microwaves and RFs, antennas are fundamental devices for wireless communication systems, and they are found around us in everyday use probably more often than we even realize. In our homes and offices we can probably count tens of antennas operating in the same environment, each capable of transmitting and receiving wireless radio signals at different frequencies for a variety of purposes. The Latin word antenna was commonly used well before the discovery of electromagnetic radiation to describe the long stylus on a ship connected to the sail, the sensing appendage of several arthropods in the animal world, as well as the central pole of a tent. For electromagnetic radiation, the term was introduced by the Italian radio-wave pioneer Guglielmo Marconi to describe the vertical pole he was using as the apparatus capable of transmitting and receiving wireless electromagnetic signals at a distance. In general, an antenna is designed as an efficient transducer to convert electromagnetic waves freely propagating in free-space into confined electric signals, and vice versa. From the first attempts to create such a bridge to modern antenna technology, more than a century has passed and antenna technology has evolved tremendously. Nowadays, microwave antenna designers have a variety of powerful tools in order to match the requirements of the specific application of interest.

Recent progress in nanofabrication technology allows the possibility of realizing metallic NPs of arbitrary shape that may provide strong scattering resonances associated with the plasmonic features of metal at optical frequencies.

Introduction

The nanoantenna concept refers to electromagnetic phenomena related to field amplification and confinement at visible or near-IR light by nanometer-sized objects [29, 206]. Nanoantennas rely on electric field enhancement by the LSPR, which takes place in metallic NPs embedded in dielectric media. There is a profuse literature about this topic and several reviews can be found elsewhere [202, 507, 508].

The simplest model for understanding LSPR is to consider the electrostatic problem of a sphere in a dielectric medium under a homogeneous applied field [151, 234, 509]. The solution is a homogeneous internal field modified by the effect of depolarization generated by surface charges. Contrary to this, the external field presents an evanescent character, decaying as r-3 outside the NP. However, the most interesting fact is that internal and surface fields diverge when the medium єd and NP єm dielectric functions are such that 2єd = -єm. From an experimental point of view, this condition can be approximately fulfilled for several metals (mainly Ag, Au and Cu) at some specific frequencies. The electric field at the NP surface can increase up to 1000 times. The resonance condition can be modified by changing the matrix or the shape of the NPs. Therefore, for either oblate or prolate NPs, the resonance condition is given by (1 - L)/єd = -Lєm, where L is the so-called depolarization factor [510], which only depends on the NP geometry. For an irregular shape, the NP is described by several depolarization factors Lk, each with its corresponding LSPR associated with it.

Introduction

The oldest form of imaging is optical imaging, which has been an inseparable part of human life for centuries. People have used flat or curved surfaces of solids and liquids as mirrors and lenses to form several kinds of images for a long time. Naturally, the light utilized in such imaging was the light that we could see, which means the visible spectral range of light. Nature has many interesting things to offer – one of them is the fact that visible light (from near-UV to near-IR) contains an energy that is comparable to the electronic or vibrational energies of most of the naturally existing materials that we interact with in our day-to-day lives. Visible light can therefore interact directly with the electronic or vibronic system of a sample, and can extract information related to the intrinsic properties of the sample. Thus, optical imaging turns out to be the most informative technique, which has gradually improved over time as scientists have developed various kinds of microscopes and telescopes that have enabled us to see tiny objects, such as bacteria, or distant objects, such as planets.

Even though the visible region is the best spectral range of light for informative imaging, it turns out that the rather longer wavelengths associated with this range of light makes it impossible for visible light to interact efficiently with nanomaterials. Thus, even with the fast and remarkable progress of optical imaging techniques, observing a sample at nanoscale resolution with an optical microscope has always remained a dream for scientists.

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.