Title: Granular permittivity representation in extremely near-field light-matter interactions processes,
Abstract: Light-matter interaction processes are significantly affected by surrounding
electromagnetic environment. Dielectric materials are usually introduced into
an interaction picture via their classical properties, e.g. permittivity,
appearing in constitutive relations. While this approach was proven to be
applicable in many occasions, it might face limitations when an emitter is
situated very close to a material boundary. In this case nonlocal extend of a
quantum wave function of an emitter becomes comparable with a distance to a
boundary and a lattice constant of a material. Here a semi-classical model,
taking into account material's granularity, is developed. In particular,
spontaneous emission process in the vicinity of flat boundaries is considered.
The material boundary is divided into a pair areas - far zone is modeled as a
continuous phase, while the near zone next to a nonlocal emitter is represented
with a discrete array of polarizable particles. This array resembles optical
properties of the continuous phase under the standard homogenization procedure.
Local field effects were shown to lead orders of magnitude corrections to
spontaneous emission rates in the case of sub-nanometer emitter-surface
separation distances. The developed mesoscopic model enables addressing few
aspects of local field corrections in quite complex scenarios, where quantum ab
initio techniques yet face challenges owing to involved computational
complexity. The developed method could be utilized for designs of quantum
sources and networks, enhanced with structured electromagnetic environment.