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The interaction of electromagnetic waves and material media can be characterized by many different phenomena such as absorption, scattering, reflection, etc. Of course, these effects are strongly dependent on frequency and on the nature of the materials. Visible light will be reflected by a metal and transmitted by glass. Glass is transparent in the visible but opaque in the infrared, etc. To account for these effects, it is necessary to include in Maxwell equations the relevant information concerning the materials. This takes the form of a relation connecting the polarization and the magnetization of the material with the electric and magnetic fields. These relations contain all the information of the absorption processes and the dispersion effects. Typical models describing metals, crystals and gases are introduced.

The aim of this book is to cover the scope of Nanophotonics, a discipline that has emerged around the turn of the millennium. It results from the merge of different communities working in different aspects of light-matter interaction at the nanoscale. These include near-field optics and super-resolution microscopy, photonic crystals, diffractive optics, plasmonics, optoelectronics, synthesis of metallic and semiconductor nanoparticles, two-dimensional materials and metamaterials. Our feeling when we started the project was that a book covering most of these aspects altogether was lacking. The field is so rapidly evolving that it is impossible to summarize all the recent breakthroughs. The goal of this book is to provide a self-contained discussion of the fundamentals of the different subfields involved in nanophotonics. The current project is a collaborative project between three researchers that have been actively involved in the field from different communities. Henri Benisty has a background in semiconductor physics and optoelectronics, Jean-Jacques Greffet has a background in near-field optics and light scattering, Philippe Lalanne has a background in diffractive optics and photonic crystals. All of them made significant contributions to the advancement of the field. The book material is based on lectures that have been given by them at the Institut d’Optique Graduate School (Palaiseau, Bordeaux and Saint-Etienne).

We consider light-matter interaction processes such as emission, absorption, elastic or inelastic scattering and fluorescence by a quantum object such as an atom, a molecule or a quantum dot. The idea of controlling these processes with a resonator (a cavity or a resonant nanoantenna) is to use an intermediate structure which is coupled both to plane waves in vacuum and to the emitters. In this chapter we use a unified approach to discuss any type of resonator using the concept of Green tensor. We review different models to deal with spontaneous emission with the aim of clarifying the connection between classical and quantum points of view. After this analysis of spontaneous emission, we discuss different light-matter interaction processes such as Raman Scattering and Fluorescence both in the linear regime and in the saturation regime. Finally, we discuss how to optimize absorption and introduce the concept of impedance for an optical nanoantenna.

Waveguides are basically a device (‘a guide’) for transporting electromagnetic energy from a source to another defined point, through a structure that is invariant in one or two directions without any loss in wave intensity. The chapter is intended to provide an introductory self-contained treatment of optical waveguide theory. The slab guide serves as a textbook example to examine fundamental concepts such as the discrete modes and their effective indices. The basis of modal structure decomposition is then underlined: mode orthogonality, mode normalization, role of reciprocity. Several complements introduce more subtle aspects, such as the different group and energy velocities and mode orthogonality in lossy/amplifying cases. The elementary case of the perfect metal walls is also discussed, as well as multimode waveguide applications encountered in integrated optics.

In the last three decades, the advent of nanotechnology has enabled the fabrication of materials and surfaces patterned with meta-atoms with dimensions slightly smaller than the optical wavelength. This scale, which is too coarse for the medium to be considered as homogenous, is very rich in various exotic physical effects. The latter have enabled a plethora of new functionalities and applications, from artificial media with both negative indices, ‘perfect’ lenses, to metasurfaces offering a complete control of the phase and polarisation. In spite of the need to account for a substantial diversity, the chapter scope is also to highlight the fundamentals, by connecting to anterior works on the one hand, and the main applications, by considering the limitations and forces of metallic or dielectric nanostructures on the other hand.

The chapter aims at introducing students to the basic of electronic wavefunctions and energy bands in semiconductors. The Bloch mode is the key point, with the band edges and the bandgap. The Fermi-Dirac statistics based on the Fermi level is introduced to account for the population with the help of the relevant density-of-states. Doping is explained. The optical transitions, their rule and their dynamics are outlined. The focus is then more on heterojunctions, notably double heterojunctions and quantum wells, circumventing the textbook description of space charges, as they are suppressed in injected devices. Quantum wells are discussed in relation with laser diodes anr their threshold current, showing why the separate confinement heterostructure (SCH) combining a guide with quantum wells, stands as an early nanophotonic device design. The confinement factor of the optical mode relates this chapter to that on guided modes. Silicon and III-V semiconductors are contrasted throughout.

Periodic Waveguides are an important building-block of modern photonics, combining waveguides and gratings. They are logical candidates to implement miniature photonic functions, either in-plane or to couple guided waves with extended waves of the outer space. Their operation is quite conceptually complex, as they support guided modes like the classical waveguides (chapter 6) as well as resonant modes with finite lifetime. The chapter attempts to emphasize the underlying physical processes, stressing conceptual aspects, and develop the mathematical analysis to parallel the physical intuition. It also provides a comprehensive description of several illustrative optical components whose principle of operation fundamentally relies on the coupling between free-space and an almost confined electromagnetic field, with a complement on light extraction from LEDs.

Chapter 16 focusses on the properties of photonic gaps and band edges. We introduce the gap modes with a complex-valued propagation constant. With a simplified two-wave approach, we give analytical expressions of the essential features of bandgaps in one-dimension, e.g. the gap width and the penetration depth that is related to the effective indices of evanescent Bloch modes. The presentation is complemented by a discussion of various flavours of slow light propagation, occurring typically but not exclusively near band edges.

Plasmonic-based nanostructures are of considerable interest because of their unique capability of confining light at a deep subwavelength scale, something that cannot be achieved with conventional lenses in 2D and photonic microcavities in 3D which are diffraction-limited. This feature can be used to perform near-field imaging beyond the diffraction limit, to implement nanoscale light sources, enhance the capacity of data storage devices or guide light at nanoscale to name a few examples. The confinement of light comes with another important property: the enhancement of the field. We introduce the main figure of merits of nanoparticle and discuss how they can be designed to control localized electromagnetic resonances at nanoscale.

A powerful theoretical tool to compute the electromagnetic field in the near field is the integral formulation of the field equations. A nice feature of this formulation is that it allows gaining some physical insight into the scattering mechanisms. It proves convenient to introduce the tensor describing the electric field radiated by a point-like dipole, known as Green tensor. Then, we apply these concepts to the study of scattering of light by arbitrary systems. This provides a framework to discuss the possibility of performing super-resolution imaging by using far-field data and solving the inverse problem. The second part of this chapter deals with the analysis of the link between the Green tensor and the local density of electromagnetic states. This quantity plays a key role in the study of spontaneous emission in the presence of nanostructures in the weak coupling regime.

In its simplest one-dimensional form, propagation describes the transformation of a spatial field f(x) at time t=0 over time as a function of time in the special form f(x-vt) where v is the wavevelocity. In this chapter, we generalize this elementary definition to include propagation in a three-dimensional vacuum and discuss the connection with diffraction. We also introduce the concept of evanescent waves. We then consider propagation in a dispersive and lossy medium. This leads to the introduction of a complex refractive index in the frequency domain and to the introduction of a dispersion relation. We discuss several definitions of the velocity. We finally introduce the quasinormal modes in lossy media.

This chapter deals with surface waves propagating along a metallic interface called surface plasmon polaritons. We first introduce the concept of polariton, a mixed light-matter excitation of solids which has remarkable properties in order to confine electromagnetic energy. We discuss in detail its dispersion relation. We then discuss gap surface plasmon polaritons propagating between two parallel metallic planes with subwavelength separation. We finally briefly introduce plasmons on graphene, surface phonon polaritons and discuss the contribution of surface polaritons to the local density of states.

The purpose of this chapter is to briefly summarize the basics of electrodynamics. Maxwell equations are written using a classical and microscopic description of matter. The potentials and their connection to the longitudinal and transverse fields are then introduced. In section 3, a spatial averaging procedure is used to derive macroscopic fields from the microscopic fields. It is shown that these averaged fields obey macroscopic Maxwell equations where additional terms (polarization and magnetization) appears as a result of the spatial average of the microscopic charge and current densities. The key concepts about energy conservation of electromagnetic fields are then introduced as well as the reciprocity theorem. The chapter ends with the description of a few generic topics: radiation treated in chapter 2, propagation and diffraction treated in chapter 4, reflection and transmission treated in chapter 5, scattering treated in chapter 12.

The chapter reviews selected key technologies for nanophotonics applications in passive or emitting devices. The chapter introduces the scientific principles and the figures of merit of these devices, in which guides, gratings, plasmonic systems, periodic guides of previous chapters are the ingredients. It details the issue of sensing, a very heuristic topic. It then provides clues for a practical, applications-based approach to the design and operation of integrated photonic circuits and their electro-optic functions. In the area of active devices, it deals with the factors that determine the device efficiency. For edge-emitting lasers, it shows how guide and gratings are assembled in the emblematic DFB laser diodes. Vertical emitting lasers (VCSELs) are also discussed, connecting their structure to fundamentals of light-matter interaction and to periodicity. The important issue of light extraction is eventually revisited across several kinds of devices, LEDs of course, but also other specialized emitting systems.

The chapter encompasses a rigorous approach to model the non-Hermitian resonators that leaks energy in open spaces, as well as a simplified phenomenological approach valid in the limit of weak leakage. The rigorous treatment relies on the concept of normalized quasinormal modes. It is detailed for the intuitive example of a Fabry-Perot cavity. The relationship to the key LDOS concept – the local density-of-states – is given. The phenomenological model has an attractive simplicity to describe coupling phenomena through time constants. It addresses a variety of issues such as weak, strong and critical couplings. The correspondence with the classical textbook Fabry-Perot physics and related concepts such as finesse and quality factors is also outlined.

This chapter aims at introducing structures where the electron is confined in two or three dimensions, the so-called quantum wires and quantum dots. The basics of the density-of-states are explained, as its strong structure distinguishes these systems from higher-dimensional ones, in addition of the large interface/volume ratio. Fabrication routes of different nature are presented, either self-organised or epitaxial, and the tunability of photonic properties that result from variable size and shape is underlined. The semiconductor families and the applications of each route are presented. The emblematic case of InAs growth on III-V substrates provides the key phenomena of interest. The II-VI colloidal quantum dots are the other emblematic case, leading to the evolving uses of quantum dots, e.g. in displays or as nanoprobes. The description of porous silicon as a lower-dimensional version of silicon is used to introduce the reader to more subtle interplays of electronic and photonic properties.

The concept of evanescent waves, which plays a key role in the description of the electromagnetic field at the nanoscale, is introduced in the first section. The second section offers an alternative introduction to near-field optics by examining the radiation of an electric dipole. These two sections can also be viewed as a discussion of the concepts of near field either in Fourier space (evanescent waves) or in direct space (dipole radiation). In the third section, we establish a connection between the quasi-electrostatic and quasi-magnetostatic approximations familiar in the regime of low frequencies and the near-field regime used in optics for TE and TM polarization. Finally, in the last part of the chapter, we highlight some particular properties of the near field. It will be seen that the familiar concepts of phase, Fresnel reflection factor, field structure, polarization need to be revisited in the near field.

Chapter 15 introduces the Bloch modes of photonic crystals for the very important textbook example of one-dimensional photonic crystals. The originality of the present presentation lies in the dual view that is adopted. Bloch modes are described by deriving either complex-valued wavevectors for fixed real frequencies (like the waveguide modes of Chapter 6) or complex-valued frequencies for fixed real wavevectors (like the quasinormal modes of Chapter 7). This synoptic description is then used to study the first and second-order homogenisation of multidimensional crystals in the long wavelength limit, the properties of the gap and the band edge being left for the following chapter. The last part focuses on the conditions for which diffraction gratings, first reminded, can be approximately replaced by homogeneous thin films, a generic problem that is encountered in the design of many optical components and prepares the readers to the applications of metasurfaces discussed in chapter 18.

The aim of this chapter is to derive the electromagnetic fields generated by timedependent sources. Here, we consider that the sources are known and that they radiate in vacuum. This typically corresponds to the problem of a wire antenna in vacuum. The procedure to compute the fields is based on the fact that Maxwell equations are linear. It follows that a key role is played by the field radiated by a point-like source, as any source can be decomposed into a linear superposition of point-like sources. We also introduce in this chapter a concept that plays a fundamental role in electrodynamics: the electric dipole moment.

In this chapter, we deal with reflection and refraction of electromagnetic waves at a planar interface between two homogeneous media described by a linear and isotropic permittivity and permeability. We will derive the general form of the fields in both media and derive the form of their complex amplitudes, namely the Fresnel reflection and transmission factors. We use complex refractive indices in order to include in the discussion the losses.

We provide in this Supplemental document more details on the properties of a quartic dispersion relation, as well as additional numerical calculations, in particular the impact of rounded corners on the dispersion curve.

Compact sources in the mid-wave infrared (MWIR) are needed for applications ranging from spectroscopy to free-space communication. Ultrathin incandescent metasurfaces are promising candidates, offering the possibility to tune the emission spectrum, directivity, and modulation speed. However, control over polarization remains a challenge, especially when it comes to the emission of circularly polarized light. Here, we report the emission of polarized MWIR radiation from a 700 nm thick incandescent chiral metasurface. The degree of polarization is above 0.5 with degree of circular polarization of 0.38 at 5 µm. The metasurface is heated by the Joule effect, and the emission can be modulated beyond 10 MHz. This could enable detection techniques that use polarization as an additional degree of freedom.

We report an experimental and theoretical study of light emission by a patterned ensemble of colloidal quantum dots (cQDs). This system modifies drastically the emission spectrum and polarization as compared to a planar layer of cQDs. It exhibits bright, directional and polarized emission including a degree of circular polarization in some directions. We introduce a model of light emission based on a local Kirchhoff law which reproduces accurately all the features of the experiment. The model provides a figure of merit to assess quantitatively the emitted power. This work paves the way to the systematic design of efficient ultrathin light emitting metasurfaces with controlled polarization, spectrum and directivity.

We report on the synthesis of hybrid light emitting particles with a diameter ranging between 100 and 500 nm, consisting in a compact semiconductor CdSe/CdS/CdZnS nanocrystal aggregate encapsulated by a controlled nanometric size silica and gold layers. We first characterize the Purcell decay rate enhancement corresponding to the addition of the gold nanoshell as a function of the particle size and find a good agreement with the predictions of numerical simulations. Then, we show that the contribution corresponding to Förster resonance energy transfer is inhibited.

Coupling quantum emitters and nanostructures, in particular cold atoms and waveguides, has recently raised a large interest due to unprecedented possibilities of engineering light-matter interactions. However, the implementation of these promising concepts has been hampered by various theoretical and experimental issues. In this work, we propose a new type of periodic dielectric waveguide that provides strong interactions between atoms and guided photons with an unusual dispersion. We design an asymmetric comb waveguide that supports a slow mode with a quartic (instead of quadratic) dispersion and an electric field that extends far into the air cladding for an optimal interaction with atoms. We compute the optical trapping potential formed with two guided modes at frequencies detuned from the atomic transition. We show that cold Rubidium atoms can be trapped as close as 100 nm from the structure in a 1.3-mK-deep potential well. For atoms trapped at this position, the emission into guided photons is largely favored, with a beta factor as high as 0.88 and a radiative decay rate into the slow mode 10 times larger than the free-space decay rate., Comment: 14 pages, 6 figures

National audience

The authors propose a general absorption-coherence relation to show that spatial coherence emission by molecules on a metallic film is due to the excitation of surface plasmon polaritons and is reduced in the presence of strong coupling.

While spatially coherent emission has been experimentally observed for several photoluminescent devices composed of metallic nanostructures, no model is currently able to compute the spatial coherence function of the emitted fields, and thus to explain its origin. We introduce a model of light emission by thermalized ensembles of emitters which connects the coherence of the fields at two positions to the power absorbed by the system when illuminated by two sources. We can apply it to the study of the spatial coherence properties of the light emitted by a layer of molecular dyes deposited on top of a silver layer.