Propagators and spectra of surface polaritons in metallic slabs: Effects of quantum-mechanical nonlocality

A transparent and compact method for the calculation of the electromagnetic-field propagator in presence of a thin metallic slab is developed. Electron wave functions for the slab are obtained numerically by using density-functional theory within the local density approximation, and used to construct the slab conductivity tensor. Expressions for the free-photon Green’s function and photon self-energy (i.e., slab conductivity tensor) in terms of electronic wave functions are derived analytically, taking advantage of the symmetry of the problem and separating it in s and p polarizations. Dyson equation for the polariton propagator is analytically prepared to be solved in two steps: first, solving the Dyson equation with only paramagnetic (nonlocal) part of photon self-energy included, and second, renormalizing such propagator because of its interaction with diamagnetic (local) polarizations. Such approach allows us to take both polarization mechanisms into account as well as their mutual influence. Long-wavelength and quasistatic limits of our results are derived and compared with previous results. Finally, the method is used to calculate spectra of polaritons, i.e., electromagnetic excitations produced by an oscillating dipole placed in the vicinity or inside a metallic slab