Resonance effects on total internal reflection and lateral (Goos-Hänchen) beam displacement at the interface between nonlocal and local dielectric

The lateral (Goos-H\"anchen) displacement of a Gaussian laser beam propagating from a denser spatially dispersive medium to a rarer, frequency-dispersive medium is studied using the angular spectrum representation of the fields. Analytical expressions are obtained for the Goos-H\"anchen shift for upper and lower polariton (UP and LP) branches using an incident-beam plane polarized perpendicular to the plane of incidence. Various limiting cases corresponding to |k₀Wᵣδ|1 and |k₀Wᵣδ|1 are examined. Here k₀=ωc, Wᵣ is the width of the beam, and δ is proportional to the difference between the angle of incidence θ and the critical angle θc. Numerical results are obtained for the lateral shifts, D̄₁₁(θ,ω) and D̄₂₂(θ,ω) corresponding to UP and LP, respectively, using material parameters of CdS and GaAs. Frequency ranges close to the A-exciton resonance, and in the pseudogap region ω₀<ω<ωₗ, are studied and strongly dispersive shifts are predicted in the resonance region. The magnitude of the shift can be increased by nearly 10² compared with usual nonresonance case. Large negative Goos-H\"anchen shifts are predicted in the resonance region. Resonance-enhanced Goos-H\"anchen shifts can be used to determine the additional boundary conditions. Surface roughness will cause measurable deviations from our predicted results and can be detected via the changed shifts. Transverse shifts are also expected to be resonance enhanced and much more easily measurable.