Introduction

A current mirror is a transistor-based circuit that the current level is controlled in an adjacent transistor, and the adjacent transistor essentially acts as a current source. Such circuits are now considered a commonly used building block in a number of analog integrated circuits (IC). Operational amplifiers, operational transconductance amplifiers, and biasing networks are examples of such circuits that essentially use current mirrors. Analog IC implementation techniques such as current-mode and switched-current circuits use current mirrors as basic circuit elements.

A significant advantage associated with the current mirrors is that they act as a near-ideal current source while fabricated using transistors and can replace large-value passive resistances in analog circuits, saving large chip area.

The later part of the chapter discusses another important analog circuit, namely, differential amplifier. As the name suggests, differential amplifiers amplify the difference between two signals that are applied to their two inputs. In addition to the differential amplification, it is also required that differential amplifiers suppress unwanted signal, which is present on the two input signals in the form of a common-mode signal. A differential amplifier is a particularly very useful and essential part of operational amplifiers. A differential pair is the basic building block of a differential amplifier that comprises of two transistors in a special form of connection.

Thermal and zero-point fluctuations of charges and electromagnetic fields give rise to fluctuation-induced forces, known as dispersion forces. To understand these forces, we first discuss the properties of stationary stochastic fields and derive fluctuation–dissipation theorems for both fields and sources. Fluctuating sources give rise to Johnson noise in resistors and to blackbody radiation and heat transfer. For a pair of polarizable particles, we derive the Casimir–Polder potential and evaluate it for short and large separations, which renders the Van der Waals and the Casimir force, respectively. For a particle moving in a thermal field, we find a viscous force, referred to as vacuum friction. We show that zero-point fluctuations are responsible for shot noise in optical power measurements and for radiation pressure shot noise exerted on irradiated objects. Shot noise is responsible for measurement imprecision and radiation pressure shot noise for measurement backaction, the disturbance of an object by the measuring optical field. We show that imprecision and backaction noise set a limit to measurement accuracies, known as the standard quantum limit, and that their product is fundamentally bound by the so-called Heisenberg limit.

Coupled mode theory considers the interaction between eigensolutions of a system (modes). It is a theoretical framework that underlies many physical phenomena, such as coupled optical cavities and waveguides, cavity optomechanics or the coupling between atoms and cavities. We derive the coupled-mode equations for a system of harmonic oscillators and transform them into Bloch equations, which allows us to represent the solutions on the Bloch sphere. We discuss mode coupling (hybridization) and coherent control protocols, such as Ramsey interferometry and dispersive coupling. We consider time-dependent interactions and analyze adiabatic and diabatic transitions (Landau-Zener tunneling). The control of damping brings us to topics such as time-reversal symmetry breaking, exceptional points and non-Hermitian dynamics. We discuss the limits of ultrastrong coupling and nonlinear interactions and analyze the phenomenon of induced transparency. Finally, we analyze the dynamics of optomechanical systems and discuss the transition to multimode systems and quantum mechanics.

Matter consists of charges that interact with electromagnetic fields. This interaction gives rise to mechanical forces that can be utilized to control matter. Based on Maxwell’s equations we derive a continuity equation for linear momentum, which allows us to calculate the force exerted by an optical field on an arbitrary object. We derive the radiation pressure acting on an irradiated surface and show that if the surface is in motion, it will experience a viscous force known as radiation damping. We then investigate the force acting on a tiny particle characterized by its polarizability $\alpha$, and split this force into conservative and nonconservative parts. This leads to the concepts of gradient and scattering forces, which are widely used for the manipulation of atoms, molecules, and nanoparticles. We discuss the properties of optical tweezers and derive the torque exerted on a particle by a circularly polarized light beam. Finally, we discuss how the motion of a vacuum-trapped particle can be amplified or cooled via feedback and touch on the limits imposed by zero-point fluctuations.

The chapter introduces the significance, theory, and applications of optical antennas. We begin by discussing the necessity of enhancing light–matter interactions, followed by an introduction to elements of classical radio-frequency antenna theory, setting the stage for a deeper exploration of optical antenna theory. We then discuss optical antenna theory, highlighting both similarities and deviations from the radio-frequency regime. This includes a detailed examination of antenna parameters used to describe the performance of antenna designs, as well as the mechanisms behind antenna-enhanced light–matter interactions. The chapter concludes with a discussion of coupled-dipole antennas, emphasizing their unique properties and practical applications.

Optical resonators store electromagnetic energy. The finite response time of optical resonators provides a feedback mechanism for controlling the dynamics of atomic and mechanical systems and to effectively exchange energy between light and matter. This chapter starts with a derivation of the reflection and transmission coefficients of a confocal optical cavity. The spectrum is characterized by multiple resonances and for most applications a single resonance can be singled out. This leads to the single-mode approximation. We derive the energy stored in the cavity and evaluate the fields of a cavity that is internally excited by a radiating dipole. We calculate the LDOS and derive an expression for cavity-enhanced emission (Purcell effect). We continue with an analysis of microsphere resonators with characteristic whispering-gallery modes and review the effective potential approach, which allows us to cast the problem in form of a Schr\“odinger equation, with parallels to quantum tunneling and radioactive decay. The next section is focused on deriving the cavity perturbation formula, which states that a change in energy is accompanied by a frequency shift. Having established a solid understanding of optical resonators we discuss the interplay of optical and mechanical degrees of freedom within the context of cavity optomechanics. We derive the optomechanical coupling rate and discuss the resolved sideband and the weak-retardation regimes.

The chapter discusses quantum emitters, exploring their fundamental mechanisms, properties, and applications. Beginning with two-level systems, we introduce the concept of extinction cross-section. To capture phenomena, such as fluorescence, the discussion extends to four-level systems and spontaneous as well as stimulated emission processes, crucial for understanding laser operation. We then examine the dependence of the quantum yield on the local environment. Single-photon emission is scrutinized in terms of the second-order autocorrelation function through both steady-state and time-dependent analyses, providing a comprehensive understanding of this essential feature of quantum emitters. The chapter further addresses the generation of indistinguishable single photons, a key requirement for quantum computing and secure communication. Various types of quantum emitters are then introduced, including fluorescent molecules, semiconductor quantum dots, and color centers in diamond, each with unique properties and applications. Finally, single molecules are presented as probes for localized fields, with an in-depth look at field distributions in a laser focus and sources of strongly localized fields.

This chapter discusses light–matter interactions from a semiclassical point of view. By expanding the electromagnetic field into a Taylor series we derive the multipolar interaction potential and particle-field Hamiltonian. Then, using the Green function formalism, we calculate the fields of an oscillating dipole and, based on Poynting’s theorem, derive a general expression for the rate of energy dissipation in an arbitrary environment. This expression leads to the concept of local density of states (LDOS) and provides a direct link to spontaneous emission and atomic decay rates. The rate of energy dissipation of an oscillating dipole is also used to derive the absorption cross-section in terms of the polarizability. By accounting for radiation reaction and scattering losses, we obtain a compact expression for the dynamic polarizability. Dipole radiation and atomic decay rates can be enhanced via LDOS engineering, and the enhancement factor is referred to as the Purcell factor. We show that if the LDOS gets enhanced in a certain frequency range, it must be reduced in other frequency ranges, a feature described by the LDOS sum rule. After discussing the properties of a single dipole, we continue with analyzing the interaction between multiple dipoles. We derive the interaction potential and calculate the energy transfer rate between dipoles. For short distances we recover the famous Förster energy transfer formula. If the interaction energy becomes sufficiently large, we enter the regime of strong coupling, which gives rise to hybridized and delocalized modes, level splittings, and entanglement.

The chapter introduces the field of plasmonics, focusing on the unique optical properties of noble metals. We begin by describing noble metals as plasmas, introducing concepts such as electronic screening and the ponderomotive force. We then discuss the local optical response of noble metals through their frequency-dependent dielectric function. The chapter progresses to surface plasmons at plane interfaces, detailing the properties of surface plasmon polaritons (SPPs), methods for exciting SPPs, and their practical applications in sensors, particularly their sensitivity and utility in biochemical sensing. Next, we focus on plasmons supported by nanowires and nanoparticles, utilizing the quasistatic approximation and standing plasmon waves. We analyze plasmon resonances in complex nanostructures by introducing the concept of plasmon hybridization. These resonances play a crucial role in surface-enhanced Raman scattering (SERS), enabling the detection of low-concentration analytes. We further explore nonlinear plasmonics, which leads to phenomena such as harmonic generation and four-wave mixing. Finally, we address nonlocal plasmonics, discussing the impact of spatial dispersion and mesoscopic boundary conditions on plasmonic responses at very small scales, highlighting the quantum effects at the metal surface.

This chapter reviews the main concepts of electromagnetic theory relevant for the understanding of this textbook. Based on Maxwell’s equations, we derive the wave equation and discuss homogeneous solutions, such as plane waves and evanescent waves. We derive the boundary conditions at interfaces between homogeneous media and the Fresnel reflection and transmission coefficients. We discuss energy conservation, causality, and reciprocity of electromagnetic fields. Point response functions are introduced (Green functions) in order to derive the inhomogeneous solution of the wave equation. The chapter concludes with the angular spectrum representation, a framework that allows arbitrary fields to be described as a superposition of plane and evanescent waves.

In practice, a radiating source is most commonly placed close to a surface or multiple interfaces. Examples are antennas mounted over ground or molecules placed on dielectric surfaces or waveguides. The topic has a long history dating back to Arnold Sommerfeld’s paper in 1909. To derive the fields of an arbitrary oriented dipole over a layered medium we have to find the corresponding Green function. We start by decomposing the free-space dyadic Green function into $s$ and $p$ polarized parts and then evaluate reflection and transmission for the two polarizations separately. Once the Green function of the layered reference system is found, we proceed to derive the radiated power and the far-fields of the dipole. We analyze the radiation patterns and the modes into which the energy is most effectively coupled. For dipoles over dielectric half-spaces, we find that evanescent field components couple predominantly into supercritical angles, giving rise to what is termed “forbidden light.” We discuss how recorded radiation patterns can be used to determine the orientation of the radiating dipole, such as the orientation of molecules fluorescing near a dielectric surface. The chapter concludes by reviewing the image dipole method and discussing its validity.

The properties of optical materials are determined by the fundamental constituents of matter. In this chapter we discuss how to design materials with unusual optical properties by arranging meta-atoms, smaller than the wavelength of light, fabricated using nanotechnology. Meta-atoms arranged in periodic arrays with lattice constants of the order of the wavelength lead to photonic crystals. Photons in photonic crystals behave analogous to electrons in regular crystals, allowing principles from solid-state physics, such as doping, to be carried over. This results in fascinating effects such as photonic bandgaps and localized states of light. Metamaterials arise if meta-atoms are densely packed such that light propagates as if it were in a homogeneous medium. By tuning the properties of the meta-atoms, these materials can be tailored to exhibit exotic optical properties such as negative or near-zero refractive index. Finally, we introduce metasurfaces which directly mold the flow of light – a property that can be used to create ultraflat optical elements.