There is a number of works about exciton-plasmon hybrid excitations (polaritons) in nanostructures, for example:
https://aip.scitation.org/doi/abs/10.1063/1.4895061?journalCode=jap
https://www.degruyter.com/view/j/nanoph.2018.7.issue-1/nanoph-2017-0059/nanoph-2017-0059.xml
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?
