Thirty-eight years ago, together with my colleague the late Robert Sternberg, I wrote a book entitled The Design of Optical Spectrometers. It described the state of the art as it was at that time after the great advances which had come in the previous ten years, and it was intended for people who wished to build a spectrometer tailored to a specific purpose, where perhaps one of the commercial designs was inadequate, unsuitable, unnecessarily cumbersome, or expensive.

When at last the time came to consider a new edition it became clear that the technology had changed so much that the classical optical spectrometer, in the sense of monochromator, was more or less obsolete and that later developments such as the desktop computer and the charge-coupled device had restored the spectrograph to its former eminence. The restoration in noway annulled the optical improvements of the previous 30 years but new constraints posed new problems in design. These problems are now solved and the solutions are presented here.

The fundamentals of optical design have not changed, but the constraints are now all different, and such properties as flat fields are needed where before they could be largely ignored; and focal ratios matter again when previously we could design everything so that such trivia as spherical aberration and coma could be neglected.

The thermal and zero-point motion of electrically charged particles inside materials gives rise to a fluctuating electromagnetic field. Quantum theory tells us that the fluctuating particles can only assume discrete energy states and, as a consequence, the emitted fluctuating radiation takes on the spectral form of blackbody radiation. However, while the familiar blackbody radiation formula is strictly correct at thermal equilibrium, it is only an approximation for non-equilibrium situations. This approximation is reasonable at larger distances from the emitting material (far-field) but it can strongly deviate from the true behavior close to material surfaces (near-field).

Because fluctuations of charge and current in materials lead to dissipation via radiation, no object at finite temperature can be in thermal equilibrium in free space. Equilibrium with the radiation field can only be achieved by confining the radiation to a finite space. However, in most cases the object can be considered to be close to equilibrium and the non-equilibrium behavior can be described by linear response theory. In this regime, the most important theorem is the fluctuation–dissipation theorem. It relates the rate of energy dissipation in a non-equilibrium system to the fluctuations that occur spontaneously at different times in equilibrium systems.

The fluctuation–dissipation theorem is of relevance for the understanding of fluctuating fields near nanoscale objects and optical interactions at nanoscale distances (e.g. van der Waals force). This chapter is intended to provide a detailed derivation of some important aspects in fluctuational electrodynamics.

The scope of this chapter is to discuss optical interactions between nanoscale systems and the properties of the emitted radiation. This is different from Chapter 3 where we considered the focusing and confinement of free propagating radiation. To link the two topics it is also necessary to understand how focused light interacts with nanoscale matter. This is a difficult task since it depends on the particular material properties, the shape of the investigated objects, and also on the strength of interaction. Nevertheless, there are issues that can be discussed from a more or less general point of view.

At the heart of nano-optics are light–matter interactions on the nanometer scale. Optical interactions with nanoscale matter are encountered in various fields of research. For example: the activity of proteins and other macromolecules is followed by optical techniques; optically excited single molecules are used to probe their local environment; and optical interactions with metal nanostructures are actively investigated because of their resonant behavior important for sensing applications. Furthermore, various nanoscale structures are encountered in near-field optics as local light sources.

To rigorously understand light–matter interactions we need to invoke quantum electrodynamics (QED). There are many textbooks that provide a good understanding of optical interactions with atoms or molecules and we especially recommend the books in Refs. [1–3]. Since nanometer-scale structures are often too complex to be solved rigorously by QED we prefer to stick to classical theory and invoke the results of QED in a phenomenological way.

A major problem in nano-optics is the determination of electromagnetic field distributions near nanoscale structures and the associated radiation properties. A solid theoretical understanding of field distributions holds promise for new, optimized designs of near-field optical devices, in particular by exploitation of field enhancement effects and favorable detection schemes. Calculations of field distributions are also necessary for image reconstruction purposes. Fields near nanoscale structures have often to be reconstructed from experimentally accessible far-field data. However, most commonly the inverse scattering problem cannot be solved in a unique way and calculations of field distributions are needed to provide prior knowledge about source and scattering objects and to restrict the set of possible solutions.

Analytical solutions of Maxwell's equations provide a good theoretical understanding but can be obtained for simple problems only. Other problems have to be strongly simplified. A pure numerical analysis allows us to handle complex problems by discretization of space and time but computational requirements (usually given by cpu time and memory) limit the size of the problem and the accuracy of results is often unknown. The advantage of pure numerical methods, such as the finite-difference time-domain (FDTD) method or the finite-element (FE) method, is the ease of implementation. We do not review these pure numerical techniques since they are well documented in the literature. Instead we review two commonly used semi-analytical methods in nano-optics: the multiple multipole method (MMP) and the volume integral method.

The problem of dipole radiation in or near planar layered media is of significance to many fields of study. It is encountered in antenna theory, single molecule spectroscopy, cavity quantum electrodynamics, integrated optics, circuit design (microstrips), and surface contamination control. The relevant theory was also applied to explain the strongly enhanced Raman effect of adsorbed molecules on noble metal surfaces, and in surface science and electrochemistry for the study of optical properties of molecular systems adsorbed on solid surfaces. Detailed literature on the latter topic is given in Ref.[1]. In the context of near-field optics, dipoles close to a planar interface have been considered by various authors to simulate tiny light sources and small scattering particles. The acoustic analog is also applied to a number of problems such as seismic investigations or ultrasonic detection of defects in materials.

In his original paper, in 1909, Sommerfeld developed a theory for a radiating dipole oriented vertically above a planar and lossy ground. He found two different asymptotic solutions: space waves (spherical waves) and surface waves. The latter had already been investigated by Zenneck. Sommerfeld concluded that surface waves account for long-distance radio wave transmission because of their slower radial decay along the Earth's surface compared with space waves. Later, when space waves were found to reflect at the ionosphere, the contrary was confirmed. Nevertheless, Sommerfeld's theory formed the basis for all subsequent investigations. In 1911 Hörschelmann, a student of Sommerfeld, analyzed the horizontal dipole in his doctoral dissertation and likewise used expansions in cylindrical coordinates.

Why should we care about nano-optics? For the same reason we care about optics! The foundations of many fields of the contemporary sciences have been established using optical experiments. To give an example, think of quantum mechanics. Blackbody radiation, hydrogen lines, or the photoelectric effect were key experiments that nurtured the quantum idea. Today, optical spectroscopy is a powerful means to identify the atomic and chemical structure of different materials. The power of optics is based on the simple fact that the energy of light quanta lies in the energy range of electronic and vibrational transitions in matter. This fact is at the core of our abilities for visual perception and is the reason why experiments with light are very close to our intuition. Optics, and in particular optical imaging, helps us to consciously and logically connect complicated concepts. Therefore, pushing optical interactions to the nanometer scale opens up new perspectives, properties and phenomena in the emerging century of the nanoworld.

Nano-optics aims at the understanding of optical phenomena on the nanometer scale, i.e. near or beyond the diffraction limit of light. It is an emerging new field of study, motivated by the rapid advance of nanoscience and nanotechnology and by their need for adequate tools and strategies for fabrication, manipulation and characterization at the nanometer scale. Interestingly, nano-optics predates the trend of nanotechnology by more than a decade.

Near-field optical probes, such as laser-irradiated metal tips, are the key components of near-field optical microscopes discussed in the previous chapter. No matter whether the probe is used as a local illuminator, a local collector, or both, the optical spatial resolution solely depends on the confinement of the optical energy at the apex of the probe. This chapter discusses light propagation and light confinement in different probes used in near-field optical microscopy. Where applicable we study fundamental properties using electromagnetic theories (see Chapter 15) and provide an overview of current methods used for the fabrication of optical probes. We hope to provide the basic knowledge to develop a clear sense of the potentials and the technical limitations of the respective probes. The most common optical probes are (1) uncoated fiber probes, (2) aperture probes, (3) pointed metal and semiconductor probes, and (4) nano-emitters, such as single molecules or nanocrystals. The reciprocity theorem of electromagnetism states that a signal remains unchanged upon exchange of source and detector. Therefore, it suffices to investigate a given probe in only one mode of operation. In the majority of applications it is undesirable to expose the sample surface on a large scale due to the risk of photo-damage or long-range interference effects complicating image reconstruction. Therefore, we will preferentially consider the local illumination configuration.

Dielectric probes

Dielectric, i.e. transparent, tips are an important class of near-field optical probes and are the key components for the fabrication of more complex probes, e.g. aperture probes.

In recent years, artificial optical materials and structures have enabled the observation of various new optical effects and experiments. For example, photonic crystals are able to inhibit the propagation of certain light frequencies and provide the unique ability to guide light around very tight bends and along narrow channels. The high field strengths in optical microresonators lead to nonlinear optical effects that are important for future integrated optical networks. This chapter explains the basic underlying principles of these novel optical structures. For a more detailed overview the reader is referred to review articles and books listed in the references.

Photonic crystals

Photonic crystals are materials with a spatial periodicity in their dielectric constant. Under certain conditions, photonic crystals can create a photonic bandgap, i.e. a frequency window in which propagation of light through the crystal is inhibited. Light propagation in a photonic crystal is similar to the propagation of electrons and holes in a semiconductor. An electron passing through a semiconductor experiences a periodic potential due to the ordered atomic lattice. The interaction between the electron and the periodic potential results in the formation of energy bandgaps. It is not possible for the electron to pass through the crystal if its energy falls in the range of the bandgap. However, defects in the periodicity of the lattice can locally destroy the bandgap and give rise to interesting electronic properties.

As early as 1619 Johannes Kepler suggested that the mechanical effect of light might be responsible for the deflection of the tails of comets entering our Solar System. The classical Maxwell theory showed in 1873 that the radiation field carries with it momentum and that “light pressure” is exerted on illuminated objects. In 1905 Einstein introduced the concept of the photon and showed that energy transfer between light and matter occurs in discrete quanta. Momentum and energy conservation was found to be of great importance in microscopic events. Discrete momentum transfer between photons (X-rays) and other particles (electrons) was experimentally demonstrated by Compton in 1925 and the recoil momentum transferred from photons to atoms was observed by Frisch in 1933. Important studies on the action of photons on neutral atoms were made in the 1970s by Letokhov and other researchers in the former USSR and in the group of Ashkin at the Bell Laboratories, USA. The latter group proposed bending and focusing of atomic beams and trapping of atoms in focused laser beams. Later work by Ashkin and coworkers led to the development of “optical tweezers”. These devices allow optical trapping and manipulation of macroscopic particles and living cells with typical sizes in the range of 0.1–10 micrometers. Milliwatts of laser power produce piconewtons of force. Due to the high field gradients of evanescent waves, strong forces are to be expected in optical near-fields.

In near-field optical micro-copy, a local probe has to be brought into close proximity to the sample surface. Typically, the probe–sample distance is required to be smaller than the size of lateral field confinement and thus smaller than the spatial resolution to be achieved. As in other types of scanning probe techniques, an active feedback loop is required to maintain a constant distance during the scanning process. However, the successful implementation of a feedback loop requires a sufficiently short-ranged interaction between optical probe and sample. The dependence of this interaction on probe–sample distance should be monotonous in order to ensure a unique distance assignment. A typical block-diagram of a feedback loop applied to scanning probe microscopy is shown in Fig. 7.1. A piezoelectric element P(ω) is used to transform an electric signal into a displacement, whilst the interaction measurement I(ω) takes care of the reverse transformation. The controller G(ω) is used to optimize the speed of the feedback loop and to ensure stability according to well-established design rules. Most commonly, a so-called PI controller is used, which is a combination of a proportional gain (P) and an integrator stage (I).

Using the (near-field) optical signal itself as a distance-dependent feedback signal seems to be an attractive solution at first glance. However, it turns out that: (1) In the presence of a sample of unknown and inhomogeneous composition, unpredictable variations in the near-field distribution give rise to non-monotonous distance dependence.

Having discussed the propagation and focusing of optical fields, we now start to browse through the most important experimental and technical configurations employed in high-resolution optical microscopy. Various topics discussed in the previous chapters will be revisited from an experimental perspective. We shall describe both far-field and near-field techniques. Far-field microscopy, scanning confocal optical microscopy in particular, is discussed because the size of the focal spot routinely reaches the diffraction limit. Many of the experimental concepts that are used in confocal microscopy have naturally been transferred to near-field optical microscopy. In a near-field optical microscope a nanoscale optical probe is raster scanned across a surface much as in AFM or STM. There is a variety of possible experimental realizations in scanning near-field optical microscopy while in AFM and STM a (more or less) unique set-up exists. The main difference between AFM/STM and near-field optical microscopy is that in the latter an optical near-field has to be created at the sample or at the probe apex before any interaction can be ineasured. Depending how the near-field is measured, one distinguishes between different configurations. These are summarized in Table 5.1.

Far-field illumination and detection

Confocal microscopy

Confocal microscopy employs far-field illumination and far-field detection and has been discussed previously in Section 4.3. Despite the limited bandwidth of spatial frequencies imposed by far-field illumination and detection, confocal microscopy is successfully employed for high-position-accuracy measurements as discussed in Section 4.5 and for high-resolution imaging by exploiting nonlinear or saturation effects as discussed in Section 4.2.3.