Role of electron back action on photons in hybridizing double-layer graphene plasmons with localized photons

In this paper, we deal with the electromagnetic coupling between an incident surface-plasmon-polariton wave and relativistic electrons in two graphene layers. Our previous investigation was limited to single-layer graphene (Iurov et al 2017 Phys. Rev. B 96 081408). However, the present work, is both an expanded and extended version of this previous Phys. Rev. B paper after having included very detailed theoretical formalisms and extensive comparisons of results from either one or two graphene layers embedded in a dielectric medium. The additional retarded Coulomb interaction between two graphene layers will compete with the coupling between the single graphene layer and the surface of a conductor. Consequently, some distinctive features, such as triply-hybridized absorption peaks and a new acoustic-like graphene plasmon mode within the anticrossing region, have been found for the double-layer graphene system. Physically, our theory is self-consistent, in comparison with a commonly adopted perturbative theory, for studying hybrid light-plasmon modes and the electron back action on photons. Instead of usual radiation or grating-deflection field coupling, a surface-plasmon-polariton localized field coupling is introduced with completely different dispersion relations for radiative (small wave numbers) and evanescent (large wave numbers) field modes. Technically, the exactly calculated effective scattering matrix for this theory can be employed to construct an effective-medium theory in order to improve the accuracy of the well-known finite-difference time-domain method for solving Maxwell's equations numerically. Practically, the predicted triply-hybridized absorption peaks can excite polaritons only, giving rise to a possible polariton-condensation based laser.