Abstract. The analogies between optical and electronic Goos-Hänchen effects are established based on electron wave optics in semiconductor or graphene-based nanostructures. In this paper, we give a brief overview of the progress achieved so far in the field of electronic Goos-Hänchen shifts, and show the relevant optical analogies. In particular, we present several theoretical results on the giant positive and negative Goos-Hänchen shifts in various semiconductor or graphen-based nanostructures, their controllability, and potential applications in electronic devices, e.g. spin (or valley) beam splitters.

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The quantum Goos-Hänchen shift for ballistic electrons is investigated in a parabolic potential well under a uniform vertical magnetic field. It is found that the Goos-Hänchen shift can be negative as well as positive, and becomes zero at transmission resonances. The beam shift depends not only on the incident energy and incidence angle, but also on the magnetic field and Landau quantum number. Based on these phenomena, we propose an alternative way to realize the spin beam splitter in the proposed spintronic device, which can completely separate spin-up and spin-down electron beams by negative and positive Goos-Hänchen shifts.

Using Yasumoto and Õishi's energy flux method, a generalized analytical formulation for analyzing the Goos-Hänchen (GH) shift in frustrated total internal reflection is provided, from which the GH shift given by Artman's stationary phase method is shown to equal the GH calculated by Renard's conventional energy flux method plus a self-interference shift. The self-interference shift, originating from the interference between the incident and reflected beams, sheds light on the asymptotic behavior of the GH shift in such optical tunneling process in term of energy flux.

Controlling the motional state of a particle in a multidimensional space is key for fundamental science and quantum technologies. Applying a recently found two-dimensional invariant combined with linear invariants, we propose protocols to drive a particle in two dimensions so that the final harmonic trap is translated and rotated with respect to the initial one. These protocols realize a one-to-one mapping between initial and final eigenstates at some predetermined time and avoid any final excitations.