Monoatomically thin polarizable sheets

Abstract

We consider a flat lattice of dipoles modeled by harmonic oscillators interacting with the electromagnetic field in the dipole approximation. Eliminating the variables from the coupled equations of motion, we come to effective Maxwell equations. These allow for taking the lattice spacing $a$ to zero. As a result, we obtain reflection coefficients for the scattering of electromagnetic waves off the sheet. These are a generalization of that known from the hydrodynamic model. For instance, we get a nontrivial scattering for polarizability perpendicular to the sheet. Also, we show that the case of polarizability parallel to the sheet can be obtained in a natural way from a plasma layer of finite thickness. As an alternative approach, we discuss the elimination of the electromagnetic fields resulting in effective equations for the oscillators. These are shown, for $a\ensuremath{\rightarrow}0$, divergent behavior, resulting from the electrostatic interaction of the dipoles.