Dynamic dielectric response of an asymmetric double quantum well near the bounding surface of a semi-infinite dynamic plasmalike host medium

We have examined the dynamic, nonlocal dielectric response function of a pair of asymmetric quantum wells embedded in a semi-infinite dynamic (local) host plasmalike medium, near its bounding surface, by carrying out a closed form inversion of the dielectric function of this system explicitly. The resulting random-phase-approximation (RPA) inverse dielectric function ${K(z,z}^{\prime };\mathbf{q},\omega ),$ which depends on lateral wave vector q and frequency ω, is obtained analytically in position representation with ${z,z}^{\prime }$ describing distances into the medium from the bounding surface. In this, we neglect intersubband transitions in the two quantum wells (assumed to be thin) and ignore tunneling effects. The frequency poles of ${K(z,z}^{\prime };\mathbf{q},\omega ),$ describe the collective modes resulting from the coupling of the double quantum well quasi-two-dimensional intrasubband plasmons with the bulk and surface plasmons of the host medium, and the residues at these poles provide the oscillator strengths of such coupled collective modes.