Super-resolution in structured media, and small volume asymptotics

Eric Bonnetier (1)

1 EDP - Equations aux Dérivées Partielles

We consider the Helmholtz equation in a medium that contains a periodic array of scatterers, surrounded by a reference medium. We show that a dielectric defect, placed in the region where the scatterers are distributed, is felt in the far field as a dipole, that radiates in an effective medium. Its refractive index combines the material properties of the ambient medium and of the scatterers. Their presence thus affects the focusing properties of light around the defect. We discuss how this mechanism may be related to super-resolution phenomena that have been observed in recent time-reversal experiments.

Domaines: Equations aux dérivées partielles [math.AP]

Eric Bonnetier. Super-resolution in structured media, and small volume asymptotics. Some mathematical problems of material science: effects of multiple scales and extreme aspect ratios, Feb 2010, Banff, Canada. ⟨hal-00750510⟩