In this introductory chapter we will try to define computational photonics and to position it within a broad field of photonics. We will briefly summarize several subfields of photonics (with the main emphasis on optical fibre communication) to indicate potential possibilities where computational photonics can significantly contribute by reducing cost of designing new devices and speeding up their development.

What is photonics?

We start our discussion from a broader perspective by articulating what photonics is, what the current activities are and where one can get the most recent information.

Photonics is the field which involves electromagnetic energy, such as light, where the fundamental object is a photon. In some sense, photonics is parallel to electronics which involves electrons. Photonics is often referred to as optoelectronics, or as electro-optics to indicate that both fields have a lot in common. In fact, there is a lot of interplay of photonics and electronics. For example, a laser is driven by electricity to produce light or to modulate that light to transmit data.

Photonics applications use the photon in a similar way to that which electronic applications use the electron. However, there are several advantages of optical transmission of data over electrical. Furthermore, photons do not interact between themselves (which is both good and bad), so electromagnetic beams can pass through each other without interacting and/or causing interference.

Introduction

As outlined in the previous two chapters, the traditional understanding of antennas originates from their RF developments [73]. Transmitting antennas are viewed as transducers that convert voltages and currents into electromagnetic waves. On the other hand, receiving antennas are viewed as transducers that convert electromagnetic waves into voltages and currents. There has been considerable attention given recently to optical antennas (see Ref. [36] and references therein). For instance, standard resonant antennas, i.e. ones whose characteristic length is near a multiple of a half-wavelength, such as dipoles and bowties, have been studied by many groups [33, 74]. They are ones that are the most accessible to nanofabrication processes; and, hence, their simulated properties have been experimentally verified. Dimers are another well-studied example of optical antennas specifically designed for large enhancements of local fields [37, 75, 76]. More recent examples include transitioning directive RF antennas to the optical regime, such as Yagi-Uda antennas [77, 78], arrays [79–81] and simple radiators combined with electromagnetic bandgap structures [82]. Even more traditional schemes, such as using an antenna to excite an RF waveguide, have been extended to optical frequencies [83]. Furthermore, nonlinear loads have been incorporated into optical antennas to control their emission properties, as well as to create harmonic generation [55, 84].

Given the intrinsic nature of the excitation of the majority of optical antennas studied to date, most RF engineers would view them simply as nano-scatterers, which have been designed to create large local fields.

Introduction

As outlined in the previous chapters, optical antennas concentrate incident light within a small spatial volume. As shown throughout this book, these nanostructures may lead to strong local field enhancements depending on their size and shape. Because of that connection, one often encounters figures plotting the near-field as if it were a purely intrinsic property of an optical antenna. However, this viewpoint does not provide a complete description, because the incident radiation must also have an influence. In this chapter, we deal with the question of how one can make use of the degrees of freedom present in the external field in order to manipulate the spatial and temporal properties of the excited near-field. Specifically, we will discuss the usage of shaped femtosecond laser pulses as they contain a broad bandwidth of different frequencies that can be modulated. It will turn out that amplitude, phase and polarization properties are relevant for controlling nano-optical excitations coherently.

It is intuitively clear that the external field must be relevant for the properties of antenna fields. For example, using monochromatic incident light, the local oscillation frequency is the same as that of the external field in the limit of linear response. Upon changing the frequency, however, the amplitude of the local field changes even when the external spectral field amplitude is kept constant, because the field enhancement factor in general varies while moving into or out of material resonances. Furthermore, a phase difference can exist between the external and local field, i.e. their oscillation maxima need not occur at the same time.

Introduction

At the heart of light–matter interaction lies the absorption or emission of a photon by an electronic transition, e.g. in an atom, molecule, QD or color center. Because these are generally much smaller than the wavelength of light, they interact weakly and omni-directionally with light, limiting both their absorption and emission rate. At RF similar issues were encountered and addressed long ago. Electrical circuits radiate little because they are much smaller than the corresponding wavelength. To enable wireless communication, they are connected to antennas that have dimensions in the order of the wavelength. These antennas are designed to effectively convert electrical signals into radiation and vice versa. Exactly the same concept can be applied in optics.

Hence the central idea of this chapter is that the interaction of a quantum emitter with light can be improved by near-field coupling it to the LSPR modes of a metal NP. The key idea is that the LSPRs of a metal NP create a strong local field at the NP. If an emitter is placed in this field, its absorption and emission of radiation are enhanced. The function of the NP is then analogous to an optical antenna. In this way, excitation and emission rates can be increased, and the angular, polarization and spectral dependence controlled.

This chapter first outlines these optical antenna concepts and next provides several concrete examples of how such antennas can be used to control and improve the interaction of single quantum emitters with light.

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.