Quantum-well enhancement of the Goos-Hänchen shift for p-polarized beams in a two prism configuration

It is predicted that the Goos-Hänchen effect can be resonantly enhanced by placing a metallic quantum well (ultrathin film) at the dielectric-vacuum (air) interface. We study the enhancement of the phenomenon, as it appears in frustrated total internal reflection with p-polarized light, both theoretically and numerically. Starting from boundary conditions for the electromagnetic field, which in a self-consistent manner take into account the quantum-well dynamics, we derive new expressions for the amplitude reflection and transmission coefficients of light, and from these the stationary phase approximation to the Goos-Hänchen shifts is obtained. It is shown that large peaks appear in the Goos-Hänchen shift below the critical angle in reflection, and these are located at the minima for the enrergy reflection coefficient. Both positive and negative shifts may occur, and the number of peaks depends on the gap width. To determine the accuracy of the simple stationary phase approximation, we carry out a rigorous stationary energy-transport calculation of the Goos-Hänchen shift. Although the overall agreement between the two approaches is good, the stationary phase approach mostly overestimates the peak heights. For a Gaussian incident beam, the resonance displacement of the reflected beam can be as large as the Gaussian width parameter. It is suggested that the possible relation between the Goos-Hänchen effect and the optical tunneling phenomenon in the two-prism configuration should be reinvestigated by depositing quantum wells on the glass-vacuum interfaces to obtain a better spatial photon localization.