Chun-Fang Li

Electronic analogy of the Goos–Hänchen effect: a review

The analogies between optical and electronic Goos–Hanchen 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–Hanchen shifts, and show the relevant optical analogies. In particular, we present several theoretical results on the giant positive and negative Goos–Hanchen shifts in various semiconductor or graphene-based nanostructures, their controllability, and potential applications in electronic devices, e.g. spin (or valley) beam splitters.

Gauge transformation and A-B effect

Abstract The aim of this paper is to show that the vector potential in the so-called Aharonov-Bohm (A-B) effect is not a gauge transformation of the vacuum, even when α = integer(≠0) (where α = Φ / Φ 0 represents the magnetic flux in the long cylindrical solenoid and Φ 0 = h / e ). To this end, it is discussed that the wave function of the electron and the gauge function in a gauge transformation are required to be single-valued so that the Schrodinger wave mechanics and the Maxwell electromagnetic theory are well-formulated. It is also discussed that the gauge transformation of wave functions and the representation change of operators of Kobes meaning are the same thing.

Unified theory for Goos-Hanchen and imbert-fedorov effects

A unified theory is advanced to describe both the lateral Goos-Haenchen (GH) effect and the transverse Imbert-Fedorov (IF) effect, through representing the vector angular spectrum of a three-dimensional light beam in terms of a two-form angular spectrum consisting of its two orthogonal polarized components. From this theory, the quantization characteristics of the GH and IF displacements are obtained, and the Artmann formula for the GH displacement is derived. It is found that the eigenstates of the GH displacement are the two orthogonal linear polarizations in this two-form representation, and the eigenstates of the IF displacement are the two orthogonal circular polarizations. The theoretical predictions are found to be in agreement with recent experimental results.

Controllable Goos-Hanchen shifts and spin beam splitter for ballistic electrons in a parabolic quantum well under a uniform magnetic field

The quantum Goos-Hanchen shift for ballistic electrons is investigated in a parabolic potential well under a uniform vertical magnetic field. It is found that the Goos-Hanchen 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-Hanchen shifts.

Negative phase time for particles passing through a potential well

Abstract It is reported that the phase time of particles passing through a potential well is negative when the energy of incident particles and the thickness of potential well satisfy certain conditions. Similar results are also found in a fully-relativistic optical analog. The 2-dimensional optical case gives rise to a lateral shift of the wave packet. It is shown that the phase-time associated lateral shift can also be negative.

Transmission gap, Bragg-like reflection, and Goos-Hanchen shifts near the Dirac point inside a negative-zero-positive index metamaterial slab

Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), the reflection, transmission, and Goos-Haenchen (GH) shifts inside the NZPIM slab are investigated. Due to the linear Dirac dispersion, the transmission as the function of the frequency has a gap, thus, the corresponding reflection has a frequency or wavelength window for the perfect reflection, which is similar to the Bragg reflection in the one-dimensional photonic crystals. Near the DP, the associated GH shifts in the transmission and reflection can be changed from positive to negative with increasing the wavelength. These negative and positive shifts can also be enhanced by transmission resonances when the frequency is far from that at the DP. All these phenomena will lead to some potential applications in the integrated optics and optical devices.

Voltage-tunable lateral shifts of ballistic electrons in semiconductor quantum slabs

It is investigated that the lateral shifts of the ballistic electrons transmitted through semiconductor quantum slabs can be negative as well as positive, which are analogous to the anomalous lateral shifts of the transmitted light beam through a dielectric slab. The necessary condition for the shift to be negative is advanced. It is shown that the lateral shifts depend not only on the structure parameters of semiconductor quantum slab but also on the incidence angle and the incident energy. Numerical calculations further indicate that the lateral shifts can be tuned from negative to positive by the external applied electric field. The voltage-tunable lateral shifts may lead to potential applications in quantum electronic devices.

Representation theory for vector electromagnetic beams

A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a 3x2 mapping matrix and a two-component Jones-like vector. The mapping matrix has one degree of freedom that can be described by the azimuthal angle of a fixed unit vector with respect to the wave vector. This degree of freedom allows us to find out such a beam solution in which every plane-wave component is specified by the same fixed unit vector I and has the same normalized Jones-like vector. The angle theta(I) between the fixed unit vector I and the propagation axis acts as a parameter that describes the vectorial property of the beam. The impact of theta(I) is investigated on a beam of angular-spectrum field scalar that is independent of the azimuthal angle. The field vector in position space is calculated in the first-order approximation under the paraxial condition. A transverse effect is found that a beam of elliptically polarized angular spectrum is displaced from the center in the direction that is perpendicular to the plane formed by the fixed unit vector and the propagation axis. The expression of the transverse displacement is obtained. Its paraxial approximation is also given.

Guided modes in a symmetric five-layer left-handed waveguide

The guided modes are investigated in a symmetric five-layer slab waveguide with a core of negative refractive index material surrounded by four normal dielectrics. The graphical method is applied to determine the guided optical modes. The left-handed material waveguide supports both oscillating and surface guided modes. For oscillating guided modes the fundamental mode can be supported. Mode double-degeneracy appears and some modes are absent in the five-layer waveguide. High-order surface guided modes exist due to the oscillating electric field in the inner claddings. Energy flux for the oscillating and surface guided modes is also discussed in detail.

A traversal time for tunneling particles through a potential barrier

A new kind of traversal time for tunneling particles through a potential barrier that has no problem of superluminality is introduced. Its physical significance is investigated. Several limits are considered, which are physically meaningful. Comparisons with dwell time and phase time are also made.