Local-field calculation of the optical diamagnetic response of a metallic quantum well

Abstract

A theoretical study of the local field inside a metallic quantum well placed on top of a dielectric substrate is presented in the case where the optical diamagnetic response is the dominating one. Taking as a starting point a fundamental integral equation for the local field, the prevailing sand p-p p-polarized case it is demonstrated that the so-called slave approximation gives a result in complete agreement with the exact numerical calculation. In the slave approximation it is assumed that (i) the field-induced motion of the conduction electrons parallel to the plane of the film is independent of the local field across the quantum well and (ii) the motion of the particles across the well is driven by the background field plus the local field caused by the motion of the carriers along the quantum well. On the basis of the homogeneous part of the fundamental integral equation the self-sustaining oscillations in the local field, i.e., the local-field eigenmodes, are investigated. The basic theory for the local field is used to calculate the s- and p-polarized amplitude-reflection coefficients of the quantum well/substrate system, and it is shown that for thin quantum wells a macroscopic two-layer model carrying surface currents as well as surface charges at the vacuum/substrate interface can account for the optical-reflection properties once the surface currents and charges have been determined from microscopic considerations. Numerical calculations of the local field inside the quantum well, the local electric displacement field, the s-polarized energy-reflection coefficient, and the surface-wave dispersion relation are presented for superthin niobium films deposited on crystalline quartz. It is demonstrated that our theory is in excellent agreement with experimental results for the s-polarized reflectivity of the Nb/quartz system recently obtained by Alieva et al. [Phys. Lett. A 152, 89 (1991)].