The quaternionic Goos–Hänchen shift
Department of Applied Mathematics, State of University of Campinas, Campinas, Brazil
2 Center of Mathematics, Computation and Cognition, Federal University of ABC, Santo André, Brazil
Accepted: 5 September 2020
Published online: 15 September 2020
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–Hänchen shift.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020