Localized gradient enhancement near anisotropic scatterers

This work investigates time-harmonic electromagnetic scattering governed by the Maxwell system in the presence of bounded anisotropic electromagnetic scatterers embedded in an intermediate anisotropic electromagnetic layer. We focus on the localized enhancement of the gradients of the total electric and magnetic fields in small boundary-attached neighborhoods of finitely many prescribed points on the outer interface of the surrounding layer. We show that, through a suitable construction of incident electromagnetic waves, the gradients of both the total electric field and the total magnetic field can be made arbitrarily large in these neighborhoods. Moreover, the localization radius may be chosen according to the prescribed gradient magnitude, thereby describing a localized high-gradient concentration mechanism for electromagnetic fields near anisotropic scatterers.
The main strategy is based on the introduction of auxiliary boundary-attached electromagnetic neighborhoods and the associated electric and magnetic fields, which exhibit strong gradient variation near the prescribed points. Using the approximation property of Maxwell Herglotz wave functions, these auxiliary fields are then approximated by physically admissible incident waves in the neighborhood of the scatterers. Together with the well-posedness and continuous dependence of the anisotropic scattering problem, this implies that the corresponding scattered field can be controlled to be sufficiently weak in the relevant layer region. Consequently, the total field is dominated by the incident field near the prescribed points and inherits its large-gradient behavior.