Didier Felbacq

• HdR
• Professor (Full) at Université de Montpellier

A historical background of metamaterials is presented. The story starts at the end of the 90s as a bifurcation in the field of photonic crystals. The basics of the field and a survey of the main realizations of metamaterials are presented. Among these are: the negative refraction effect, the super lens, the invisibility cloak, metasurfaces, and the...

Metamaterials are basically periodic structures. As such they can be analyzed by means of Bloch waves. This approach has limitations due to the existence of losses but provides very interesting insights into the properties of metamaterials. Moreover, a very good understanding of Bloch theory is fundamental for such advanced topics as photonic topol...

The concepts which gave rise to the field of electronic topological insulators have been extended to metamaterials, whether they be photonic, acoustic, or mechanic. The chapter explores the notion of topological insulators by giving numerous examples and explicit calculations.

This chapter aims at presenting some possible applications and experimental realizations of metamaterials: negative refraction, super lens, and cloaking. The chapter is written in a detailed way with complete calculations.

This chapter covers some aspects of non-photonic metamaterials, extending the frontiers of the domain. Namely, aspects of acoustical and mechanical metamaterials are presented. The aim is to give a broad vision of these fields, but also to describe experiments and realizations. In particular, a detailed analysis of theoretical aspects of mechanical...

As seen from the point of view of effective properties, reinforced concrete is a metamaterial, with respect to mechanical properties. The original flavor of metamaterials was concerned with electromagnetic properties but it did not take long for people to generalize the ideas to a large panel of domains. Nowadays there are acoustical, thermal, mech...

Metasurfaces are bidimensional metamaterials, that is, collections of basic resonant structures deposited on a surface. They have been proposed as a viable technological way because they are not pledged by the losses inherent to volume metamaterials. The field has been rapidly evolving, with very interesting experimental realizations. The chapter w...

A new method is proposed to predict the topological properties of 1D periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and zeros. The sequence of poles and zeros of this function is a topological invariant that can be linked to the Berry–Zak phase. S...

Objective: Dentin, enamel and the transition zone, called the dentin-enamel junction (DEJ), have an organization and properties that play a critical role in tooth resilience and in stopping the propagation of cracks. Understanding their chemical and micro-biomechanical properties is then of foremost importance. The aim of this study is to apply Br...

The title paper [Spectrochim. Acta A 213 (2019): 391-396] reports an improvement of the ”Poor Man’s Kramers-Kronig analysis” and of the ”Kramers-Kronig constrained variational analysis” thanks to an ad hoc modification of some analytical formulas existing in the literature. This ad hoc modification is not based on mathematical grounds. In this comm...

Topological excitations in photonic crystals and metamaterials can be observed in many different guises. While passive periodic structures can support essentially topological Bloch modes, the insertion of quantum degrees of freedom can lead to a wealth of topological solutions such as solitons and vortices. We will present a survey of recent result...

This paper presents investigations on the generalized laws of refraction and reflection for metasurfaces made of diffractive elements. It introduces a phenomenological model that reproduces all the features of the experiments dedicated to the generalized Snell-Descartes laws. Our main finding is that the generalized laws of refrac-tion and reflecti...

This paper presents investigations on the generalized laws of refraction and reflection for metasurfaces made of diffractive elements. It introduces a phenomenological model that reproduces all the features of the experiments dedicated to the generalized Snell- Descartes laws. Our main finding is that the generalized laws of refraction and reflecti...

We analyze the global behavior of the growth index of cosmic inhomogeneities in an isotropic homogeneous universe filled by cold nonrelativistic matter and dark energy (DE) with an arbitrary equation of state. Using a dynamical system approach, we find the critical points of the system. That unique trajectory for which the growth index γ is finite...

We analyze the global behaviour of the growth index of cosmic inhomogeneities in an isotropic homogeneous universe filled by cold non-relativistic matter and dark energy (DE) with an arbitrary (and not universal necessarily) equation of state. Using the dynamical system approach, we find the critical points of the system. That unique trajectory for...

We perform here a global analysis of the growth index γ behavior from deep in the matter era till the far future. For a given cosmological model in general relativity (GR) or in modified gravity, the value of γ(Ωm) is unique when the decaying mode of scalar perturbations is negligible. However, γ∞, the value of γ in the asymptotic future, is unique...

We perform here a global analysis of the growth index $\gamma$ behaviour from deep in the matter era till the far future. For a given cosmological model in GR or in modified gravity, the value of $\gamma(\Omega_{m})$ is unique when the decaying mode of scalar perturbations is negligible. However, $\gamma_{\infty}$, the value of $\gamma$ in the asym...

The screened Coulomb potential plays a crucial role in the binding energies of excitons in a thin dielectric slab. The asymptotic behavior of this potential is studied when the thickness of the slab is very small as compared to the exciton Bohr radius. A regularized expression is given and the exact effective 2D potential is derived. These expressi...

The screened Coulomb potential plays a crucial role in the binding energies of excitons in a thin dielectric slab. The asymptotic behavior of this potential is studied when the thickness of the slab is very small as compared to the exciton Bohr radius. A regularized expression is given and the exact effective 2D potential is derived. These expressi...

This note is a reply to the paper arXiv:1801.05590: "The equivalence of the Power-Zineau-Woolley picture and the Poincar{\'e} gauge from the very first principles" by G. K{\'o}nya, et al. In a recent paper [2], we have shown that the Power-Zienau-Woolley Hamiltonian does not derived from the minimal-coupling hamiltonian with the help of a gauge tra...

This article deals with the fundamental problem of light-matter interaction in the quantum theory. Although it is described through the vector potential in quantum electrodynamics, it is believed by some that a hamiltonian involving only the electric and the magnetic fields is preferable. In the literature this hamiltonian is known as the Power-Zie...

It is now well established that the homogenization of a periodic array of parallel dielectric fibers with suitably scaled high permittivity can lead to a (possibly) negative frequency-dependent effective permeability. However this result based on a two-dimensional approach holds merely in the case of linearly polarized magnetic fields, reducing thu...

The ray dynamics in a photonic crystal was investigated. Chaos occurs for perfectly periodic crystals, the rays dynamics being very sensitive to the initial conditions. Depending on the filling factor, the ray dynamics can exhibit stable paths near (fully) chaotic motion. The degree of chaoticity is quantified through the computation of Lyapunov ex...

Metamaterials made of periodic collections of dielectric nanorods are considered theoretically. When quantum resonators are embedded within the nanorods, one obtains a quantum metamaterial, whose electromagnetic properties depend upon the state of the quantum resonators. The theoretical model predicts that when the resonators are pumped and reach t...

This book provides a set of theoretical and numerical tools useful for the study of wave propagation in metamaterials and photonic crystals. While concentrating on electromagnetic waves, most of the material can be used for acoustic (or quantum) waves. For each presented numerical method, numerical code written in MATLAB® is presented. The codes ar...

We study a device that consist of quantum resonators coupled to a mesoscopic photonic structure, such as a metasurface or a 2D metamaterial. For metasurfaces, we use surface Bloch modes in order to reach various coupling regimes between the metasurface and a quantum emitter, modelized semi-classically by an oscillator. Using multiple scattering the...

It has been demonstrated by many theoretical and experimentals works that Mie resonances are at the heart of the effective properties of dielectric metamaterials. These resonances indeed allow for the onset of tailorable macroscopic magnetic properties. They were shown to provide a convenient way to study the transition between photonic crystals an...

THz-based technologies are promising enabling tools with a broad spectrum of applications, ranging from security and defense to telecommunications and non-destructive control [1]. About two decades ago, M. Dyakonov and M. Shur developped an elegant perturbative theory [2] and successfully predicted the detection of electromagnetic THz radiation bas...

Light can be transmitted through disordered media with high efficiency due to the existence of open channels, but quantitative agreement with theory is difficult to obtain because of the large number of channels to control. By measuring, by digital holography, the correlations of the transmitted field, we are able to determine the number of channel...

Quantum metamaterials generalize the concept of metamaterials (artificial optical media) to the case when their optical properties are determined by the interplay of quantum effects in the constituent 'artificial atoms' with the electromagnetic field modes in the system. The theoretical investigation of these structures demonstrated that a number o...

Quantum metamaterials generalize the concept of metamaterials (artificial optical media) to the case when their optical properties are determined by the interplay of quantum effects in the constituent 'artificial atoms' with the electromagnetic field modes in the system. The theoretical investigation of these structures demonstrated that a number o...

Open channels are peculiar incidents modes that are transmitted by a diffusing medium with high efficiency (up to 100%). Digital holography is used to analyze the correlations of the transmitted field, and to test open channel theory. Quantitative agreement is obtained.

It is now well established that the homogenization of a periodic array of parallel dielectric fibers with suitably scaled high permittivity can lead to a (possibly) negative frequency-dependent effective permeability. However this result based on a two-dimensional approach holds merely in the case of linearly polarized magnetic fields, reducing thu...

A meta-surface made of a collection of nano-resonators characterized an electric dipole and a magnetic dipole was studied in the regime where the wavelength is large with respect to the size of the resonators. An effective description in terms of an impedance operator was derived.

Meta{surfaces or 2D metamaterials are generally seen as a device able to control the far-field behavior of light. Several studies have shown the possibility of controlling the polarization state, the directivity, the light-by-light manipulation or the generation of second harmonic signal. However, because of their resonant properties, meta{ surface...

A simple numerical method for solving diffraction problems was developed. It is based on a multiple scattering approach and a fundamental result in homogenization theory. The method is easily implemented and is efficient for complex inhomogeneous objects.

More than two decades ago, Dyakonov and Shur described a model predicting the possibility to emit or detect THz radiation by use of a Field Effect Transistor (FET). This model did not take into account any resistive term. The adding of a resistive term to the Dyakonov-Shur system was investigated and it was shown that it increases the stability of...

Meta--surfaces are the bidimensional analogue of metamaterials. They are made on resonant elements periodically disposed on a surface. They have the ability of controlling the polarization of light and to generalized refraction laws as well. They have also been used to enhance the generation of the second harmonic. It seems however that their near-...

Meta–surfaces or 2D metamaterials are generally considered in the far-field. Because of their resonant properties, they possess also an interesting band structure in the near-field. A meta–surface made of a set of parallel nano- wires deposited on a surface was studied. Bloch waves localized on the surface exist in the vicinity of the anti-resonanc...

A periodic layer of resonant scatterers is considered in the dipolar approximation. An asymptotic expression for the field diffracted is given in terms of an impedance operator. It is shown that surface Bloch modes appear as a collective effect due to the resonances of the scatterers.

The homogenization of arrays of rods was studied. By means of an asymptotic analysis, a simplified form of the transfer matrix was obtained.

A layered waveguide supported hybrid modes between a surface plasmon and a confined guided mode is studied. The condition for the strong coupling regime are described. The Green function is obtained and decomposed along the continuous and discrete spectrum.

The effect of confinement on surface plasmon polariton in a planar nanocavity was studied. The generalized modes were obtained and studied in detail. In this work, we study the effect of confinement on surface plasmons in a planar cavity with a wall coated with a lossy metal as well as with two walls coated with a lossy metal. The dispersion curves...

The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from an asymptotic theory and an optimization algorithm. Detailed numerical results are given for resonant scatterers and the spatial dispersion is investigated.

The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from three different points of view. Specifically tools for multiple scattering theory, functional analysis, differential geometry and optimization are used. Detailed numerical results are given and the connections between the different approach...

A layered structured made of a dielectric waveguide and a layer of metal was studied from the point of view of the guided modes. A detailed asymptotic study of the dispersion curve was given.

It is shown that it is possible to realize strong coupling between a surface plasmon and a guided mode in a layered structure. The dispersion relation of such a structure is obtained through the S-matrix algorithm combined with the Cauchy integral technique that allows for rigorous computations of complex poles. The strong coupling is demonstrated...

The focus of this book lies at the meeting point of electromagnetic waveguides and photonic crystals. Although these are both widely studied topics, they have been kept apart until recently. The purpose of the first edition of this book was to give state-of-the-art theoretical and numerical viewpoints about exotic fibres which use “photonic crystal...

We employ a time-domain method to compute the near field on a contour enclosing infinitely long cylinders of arbitrary cross section and constitution. We therefore recover the cylindrical Hankel coefficients of the expansion of the field outside the circumscribed circle of the structure. The recovered coefficients enable the wideband analysis of co...

A metal-dielectric - waveguide layered structure is considered. It is shown that the regime of weak and strong coupling between the modes confined in the dielectric waveguide and the surface plasmon can be obtained. The strong coupling allows the spatial exchange of energy and opens a way towards the quantum control of plasmon, i.e. quantum plasmon...

We discuss how the thermalization of an elementary quantum system is modified when the system is placed in an environment out of thermal equilibrium. To this aim we provide a detailed investigation of the dynamics of an atomic system placed close to a body of arbitrary geometry and dielectric permittivity, whose temperature $T_M$ is different from...

The homogenization of arrays of metallic rods was studied. Using standard homogenization theory, the effective permittivity was obtained. The onset of resonances was evidenced and showned to be linked with the negative sign of the real part of the permittivity. Numerical computations were performed to test the homogeneous model. © (2011) COPYRIGHT...