• CEVU Université

• Physique/Physique/Optique
  
• Physique/Astrophysique
  
• Physique/Relativité Générale et Cosmologie Quantique
  
• Physique/Matière Condensée/Science des matériaux
  
• Physique/Mécanique/Thermique
  
• Physique/Physique des Hautes Energies - Théorie
  
• Physique/Physique Quantique
  
• Sciences de l'ingénieur/ photonique
  
• Sciences de l'ingénieur/Electromagnétisme
  
• Mathématiques
  
• Sciences de l'ingénieur/Mécanique/Thermique
  
• Sciences de l'ingénieur/Microélectronique
  
• Physique/Physique mathématique
  
• Physique
  
• Physique/Matière Condensée/Supraconductivité
  
• Mathématiques/Equations aux dérivées partielles [math.AP]
  
• Physique/Matière Condensée/Systèmes mésoscopiques et effet Hall quantique
  
• Science non linéaire/Dynamique Chaotique [nlin.CD]
  
• Physique/Physique/Physique Numérique
  
• Physique/Matière Condensée/Autre
  
• Mathématiques/Physique mathématique
  
• Physique/Matière Condensée/Gaz Quantiques
  
• Physique/Matière Condensée/Mécanique statistique
  
• Physique/Matière Condensée/Systèmes désordonnés et réseaux de neurones
  
• Sciences de l'ingénieur
  
• Chimie
  

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 reflection as previously stated have to be modified in order to describe the propagation of light through metasurfaces made of diffractive elements. We provide the appropriate laws that take a different form depending on the properties of the metasurface. Our models apply to both periodic and non-periodic metasurfaces. We show that the generalized law of refraction strictly exists only for linear-phase profiles and sawtooth-wave phase profiles under constraints that we specify. It can be approximatively defined for non-linear phase profiles. This document includes the article as the part I and the supporting informations as the part II.

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 from the asymptotic past to the asymptotic future is identified as the so-called heteroclinic orbit connecting the critical points (Ωm=0,γ∞) in the future and (Ωm=1,γ-∞) in the past. The first is an attractor while the second is a saddle point, confirming our earlier results. Further, in the case when a fraction of matter (or DE tracking matter) ϵΩmtot remains unclustered, we find that the limit of the growth index in the past γ-∞ϵ does not depend on the equation of state of DE, in sharp contrast with the case ϵ=0 (for which γ-∞ is obtained). We show indeed that there is a mathematical discontinuity: one cannot obtain γ-∞ by taking limϵ→0γ-∞ϵ (i.e., the limits ϵ→0 and Ωmtot→1 do not commute). We recover in our analysis that the value γ-∞ϵ corresponds to tracking DE in the asymptotic past with constant γ=γ-∞ϵ found earlier.

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 expressions may be useful for the computation of the exciton binding energy in 2D or quasi‐2D materials.

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 even in the presence of a non-negligible decaying mode today. Moreover, γ becomes arbitrarily large deep in the matter era. Only in the limit of a vanishing decaying mode do we get a finite γ, from the past to the future in this case. We find further a condition for γ(Ωm) to be monotonically decreasing (or increasing). This condition can be violated inside GR for varying wDE though generically γ(Ωm) will be monotonically decreasing (like ΛCDM), except in the far future and past. A bump or a dip in Geff can also lead to a significant and rapid change in the slope dγdΩm. On a ΛCDM background, a γ substantially lower (higher) than 0.55 with a negative (positive) slope reflects the opposite evolution of Geff. In Dvali-Gabadadze-Porrati (DGP) models, γ(Ωm) is monotonically increasing except in the far future. While DGP gravity becomes weaker than GR in the future and wDGP→-1, we still get γ∞DGP=γ∞ΛCDM=23. In contrast, despite GeffDGP→G in the past, γ does not tend to its value in GR because dGeffDGPdΩm|-∞≠0.

Metasurfaces have been used for light manipulation and control, from the point of view of planar optics or polarization control, or non-linear light extraction. The properties of metasurfaces is rooted in the presence of resonant basic elements which are responsible for strongly confined electromagnetic surface modes. We propose to use these modes to enhance light-matter interaction in the vicinity of the surface by considering hybrid structure made of a thin layer, such as a 2D quantum material or a thin film with embedded quantum dots. A semi-classical theory will be proposed along with some functionalities attainable with the device.