LOCAL-FIELD CALCULATION OF THE OPTICAL DIAMAGNETIC RESPONSE OF A METALLIC QUANTUM-WELL

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 s tarting point a fundamental integral equation for the local field, the prevailing s- and p-polarized fields in the quantum well are determin ed. In the p-polarized case it is demonstrated that the so-called slav e approximation gives a result in complete agreement with the exact nu merical 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 b y the background field plus the local field caused by the motion of th e carriers along the quantum well. On the basis of the homogeneous par t of the fundamental integral equation the self-sustaining oscillation s in the local field, i.e., the local-field eigenmodes, are investigat ed. The basic theory for the local field is used to calculate the s- a nd p-polarized amplitude-reflection coefficients of the quantum well/s ubstrate system, and it is shown that for thin quantum wells a macrosc opic two-layer model carrying surface currents as well as surface char ges at the vacuum/substrate interface can account for the optical-refl ection properties once the surface currents and charges have been dete rmined from microscopic considerations. Numerical calculations of the local field inside the quantum well, the local electric displacement f ield, the s-polarized energy-reflection coefficient, and the surface-w ave dispersion relation are presented for superthin niobium films depo sited on crystalline quartz. It is demonstrated that our theory is in excellent agreement with experimental results for the s-polarized refl ectivity of the Nb/quartz system recently obtained by Alieva et al. [P hys. Lett. A 152, 89 (1991)].