There is a number of works about exciton-plasmon hybrid excitations (polaritons) in nanostructures, for example:
In these papers, exciton and plasmon are assumed to couple via electromagnetic field. However it is known that:
1) any configuration of electric field can be decomposed into longitudinal and transverse fields (Helmholtz decomposition);
2) plasmons interact only with the longitudinal electric field (density response), while excitons interact only with the transverse field.
So how excitons and plasmons couple to each other electromagnetically?