Granular Permittivity Representation in Extremely Near-Field Light-Matter Interaction Processes

Light-matter interactions are significantly affected by surrounding electromagnetic material bodies, which are usually introduced into a model via their classical constitutive relations. While this approach is applicable in many cases, it faces limitations when emitters are situated very close to material boundaries and nonlocal quantum wave functions become comparable in size with distances to boundaries and materials' lattice constants. Here a semiclassical model taking into account a material's granularity is developed, and spontaneous emission processes next to flat boundaries are analyzed. The material is divided into a pair of areas: the 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. Local field effects were shown to provide orders of magnitude corrections to spontaneous emission rates in the case of sub-nanometer emitter-surface distances. The developed mesoscopic model addresses aspects of local field corrections in scenarios where quantum ab initio techniques face challenges.