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

Abstract

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 tensor͒ 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 ͑nonlocal͒ part of photon self-energy included, and second, renormalizing such propagator because of its interaction with diamagnetic ͑local͒ 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.

Nonlocal microscopic theory of Casimir forces at finite temperature

“…We do not deal explicitly with the intraslab interactions since they are included in the surface polariton propagators. 30 We also show that s(TE) and p(TM) contributions to the Casimir energy can be separated, which enables us to study them quantitatively.…”

“…Paramagnetic contribution (currentcurrent response matrix) 30 for the metallic slab has the form para…”

“…30. The propagator of the electromagnetic field near some polarizable medium can be expressed as a series of Feynman diagrams, shown in Fig.…”

“…Here, we extend this method to treat the retarded interaction so that response functions and polariton propagators become matrices, but these can also be taken from Ref. 30.…”

“…The expression for Casimir interaction includes both diamagnetic and paramagnetic contributions, 30 which enable us to separate and investigate, with a high level of accuracy, two kinds of corrections to the local Casimir energy. The diamagnetic term is sensitive to the details of the chargedensity profile at the surface and the paramagnetic term arises from the intraband and interband electronic transitions, and contains essential nonlocal corrections.…”