The quaternionic Goos–Hänchen shift

Abstract

We investigate the lateral displacement of electronic waves when partially and totally reflected by a quaternionic potential. Following the analogy between Quantum Mechanics and Optics we introduce a refractive index for the complex and the pure quaternionic case. For incidence greater than the critical one (total reflection) the quaternionic potentials amplify the lateral displacement found in the complex case. For incidence below the critical angle, we find, in the quaternionic case, an additional shift. The analytical formula found for the quaternionic lateral displacement gives the possibility to observe quantitative and qualitative differences between the complex and quaternionic Goos-Haenchen shift.