Monolayers polarizable perpendicularly: The Maxwellian response functions

Abstract

We set up a model for a flat, amorphous, insulating monolayer of nonrelativistic oscillators dipolarizable (only) perpendicularly to the layer, minimally coupled to the electromagnetic field obeying Maxwell’s equations. For given surface-parallel wave vector k we use the Coulomb-gauge Hamiltonian of the model to determine, exactly, the eigenvalue equation for the frequencies ωb(k) of the surface-bound normal modes; the polarizability X(k,ω) at frequency ω; and, for light above the threshold frequency ck, the scattering phase-shift δ(k,ω) and the reflection amplitude R(k,ω). As is typical for insulators, the appropriate local field plays a central role. Explicit approximations to the ωb(k) are found well away from or just below threshold. Scattering resonances identify metastable modes; their widths confirm that, as has long been known, they decay much faster than an isolated oscillator.Though calculations in the Coulomb gauge need never touch on radiative reaction, one can see retrospectively that at each oscillator the reactive part of the field it itself has emitted, call it the self-field, is appreciably different from (though comparable to) that of an isolated oscillator with the same history. The difference is crucial to deriving exact results, because it invalidates the assumption, common in other approaches, that the two fields are the same, or that the reactive self-fields in the monolayer are zero.