Anchen Effect Research Articles

Photonic spin Hall effect in bilayer graphene moiré superlattices

The formation of a superstructure - with a related Moir\'e pattern - plays a crucial role in the extraordinary optical and electronic properties of twisted bilayer graphene, including the recently observed unconventional superconductivity. Here we put forward a novel, interdisciplinary approach to determine the Moir\'e angle in twisted bilayer graphene based on the photonic spin Hall effect. We show that the photonic spin Hall effect exhibits clear fingerprints of the underlying Moir\'e pattern, and the associated light beam shifts are well beyond current experimental sensitivities in the near-infrared and visible ranges. By discovering the dependence of the frequency position of the maximal photonic spin Hall effect shift on the Moir\'e angle, we argue that the latter could be unequivocally accessed via all-optical far-field measurements. We also disclose that, when combined with the Goos-H\"anchen effect, the spin Hall effect of light enables the complete determination of the electronic conductivity of the bilayer. Altogether our findings demonstrate that sub-wavelength spin-orbit interactions of light provide a unprecedented toolset for investigating optoelectronic properties of multilayer two-dimensional van der Waals materials.

Goos-Hänchen-like shifts at a metal/superconductor interface

At a normal-metal/superconductor interface, an incident electron from the normal-metal (N) side can be normally reflected as an electron or Andreev reflected as a hole. We show that pronounced lateral shifts along the interface between the incident and the reflected quasiparticles can happen in both reflection processes, which are analogous to the Goos-H\"anchen effect in optics. Two concrete model systems are considered. For the simplest model in which the N side is of the two-dimensional electron gas, we find that while the shift in Andreev reflection stays positive, the shift in normal reflection can be made either positive or negative, depending on the excitation energy. For the second model with the N side taken by graphene, the shift in Andreev reflection can also be made negative, and the shifts have rich behavior due to the additional sublattice pseudospin degree of freedom. We show that the shift strongly modifies the dispersion for the confined waveguide modes in an SNS structure. We also suggest a possible experimental setup for detecting the shift.

Goos-Hänchen effect in light transmission through biperiodic photonic-magnonic crystals

We present a theoretical investigation of the Goos-H\"anchen effect, i.e., the lateral shift of the light beam transmitted through one-dimensional biperiodic multilayered photonic systems consisting of equidistantmagnetic layers separated by finite size dielectric photonic crystals. We show that the increase of the number of periods in the photonic-magnonic structure leads to increase of the Goos-H\"anchen shift in the vicinity of the frequencies of defect modes located inside the photonic band gaps. Presence of the linear magnetoelectric coupling in the magnetic layers can result in a vanishing of the positive maxima of the cross-polarized contribution to the Goos-H\"anchen shift.

Topological insulators are tunable waveguides for hyperbolic polaritons

Layered topological insulators, for example, Bi$_2$Se$_3$ are optically hyperbolic materials in a range of THz frequencies. Such materials possess deeply subdiffractional, highly directional collective modes: hyperbolic phonon-polaritons. In thin crystals the dispersion of such modes is split into discrete subbands and is strongly influenced by electron surface states. If the surface states are doped, then hybrid collective modes result from coupling of the phonon-polaritons with surface plasmons. The strength of the hybridization can be controlled by an external gate that varies the chemical potential of the surface states. Momentum-dependence of the plasmon-phonon coupling leads to a polaritonic analog of the Goos-H\"anchen effect. Directionality of the polaritonic rays and their tunable Goos-H\"anchen shift are observable via THz nanoimaging.

Influence of magnetic surface anisotropy on spin wave reflection from the edge of ferromagnetic film

We study propagation of the Gaussian beam of spin waves and its reflection from the edge of thin yttrium-iron-garnet film with in-plane magnetization perpendicular to this edge. We have performed micromagnetic simulations supported by analytical calculations to investigate the influence of the surface magnetic anisotropy present at the film edge on the reflection, especially in the context of the Goos-H\"anchen effect. We have shown the appearance of a negative lateral shift between reflected and incident spin wave beams' spots. This shift is particularly sensitive to the surface magnetic anisotropy value and is a result of the Goos-H\"anchen shift which is sensitive to the magnitude of the anisotropy and of the bending of the spin wave beam. We have demonstrated that the demagnetizing field provided a graded increase of the refractive index for spin waves, which is responsible for the bending.

Optical conductivities and signatures of topological insulators with hexagonal warping

In this work we study the effect of the hexagonal warping term on the optical conductivities of topological insulators (TIs). The possible optical signatures in the spectra are also discussed in detail. We begin with systematical analyses of the optical conductivities of the TIs by using Kubo's formula. Then, based on the features of the optical conductivities, we study the possible optical signatures due to the warping term. We explore the reflection spectra from a TI thin film growing on a metamaterial. We find that by properly tuning the refraction index of the metamaterial, all features of the warping effect on the conductivities can be detected and identified from the reflection spectra at an experimentally accessible level. Finally, we discuss the possibility of using the Goos-H\anchen effect and the Brewster angle measurement to determine the possible optical signatures of the warping term on the imperfectly quantized optical Hall conductivity.

Observation of nonspecular effects for Gaussian Schell-model light beams

We investigate experimentally the role of spatial coherence on optical beam shifts. This topic has been the subject of recent theoretical debate. We consider Gaussian Schell-model beams, with different spatial degrees of coherence, reflected at an air-glass interface. We prove that the angular Goos-H\"anchen and the angular Imbert-Fedorov effects are affected by the spatial degree of coherence of the incident beam, whereas the spatial Goos-H\"anchen effect does not depend on incoherence. Our data unambiguously resolve the theoretical debate in favour of one specific theory.

Observation of the Goos-Hänchen Shift with Neutrons

The Goos-Hänchen effect is a spatial shift along an interface resulting from an interference effect that occurs for total internal reflection. This phenomenon was suggested by Sir Isaac Newton, but it was not until 1947 that the effect was experimentally observed by Goos and Hänchen. We provide the first direct, absolute, experimental determination of the Goos-Hänchen shift for a particle experiencing a potential well as required by quantum mechanics: namely, wave-particle duality. Here, the particle is a spin-polarized neutron reflecting from a film of magnetized material. We detect the effect through a subtle change in polarization of the neutron. Here, we demonstrate, through experiment and theory, that neutrons do exhibit the Goos-Hänchen effect and postulate that the associated time shift should also be observable.

Optical signature of topological insulators

The axion coupling in topological insulators couples electric polarization with magnetic field, and magnetization with electric field. As a result, the usual laws of electromagnetic wave propagation are modified. We report on the Fresnel formula for the reflection of electromagnetic wave at the interface of materials with different axion couplings. The Brewster angle and the Goos-H\anchen effect are also studied. We find that, because of the axion coupling, in order to realize the Brewster-angle condition, the incident polarization should be rotated away from the plane of incidence. The maximum angle of rotation is $\ensuremath{\pi}/4$ when both materials have nearly the same refraction indices. This offers a convenient way to determine the axion angle by optical measurement.

Negative refraction in two-dimensional photonic crystals: Role of lattice orientation and interface termination

Negative refraction at the interface between air and a two-dimensional photonic crystal is analyzed at frequencies corresponding to the second photonic band. In the study, several lattice orientations and interface terminations of a photonic crystal slab are considered. Finite-difference time-domain simulations are carried out and compared to an analysis using equifrequency contours. The results show that negative refraction and the resulting focusing effects occur under certain conditions but the photonic crystal does not behave in general as an effective refractive medium because the propagation inside the crystal strongly depends on the interface termination. In addition, the Goos-H\anchen effect must be taken into account to obtain the effective index of refraction for a finite photonic crystal slab when negative refraction occurs.

Observation of the Goos-Hänchen Effect in a Phase-Conjugate Mirror

The Goos-H\anchen shift between a supercritically incident beam and its reflection in a total-internal-reflection mirror comprising a material interface is well established. We experimentally demonstrate that the Goos-H\anchen effect can also occur between the probe beam and the phase-conjugate beam in a phase-conjugate mirror. Controlled lateral displacements of up to $218\ensuremath{\mu}\mathrm{m}$ were measured using photorefractive four-wave mixing with a frequency-detuned Gaussian probe beam.

Measurement of the Nonlinear Goos-Hänchen Effect for Gaussian Optical Beams.

The nonlinear Goos-H\anchen effect is experimentally isolated for the total reflection of a Gaussian beam at an interface between a linear medium and a negative Kerr-type nonlinear medium. The evolution of this nonlinear spatial shift versus light intensity is measured for both TE and TM polarizations. The results are in good agreement with a simple model based on nonlinear Artmann's formulas.

Direct measurement of the optical Goos-Hänchen effect in lasers.

The Goos-H\anchen longitudinal shift at total reflection of an optical Gaussian beam is experimentally investigated for only one reflection. The differential experimental method uses the high sensitivity of the eigenstates of a quasi-isotropic laser to small perturbations to measure an intracavity Goos-H\anchen effect for angles of incidence both below and above the critical angle. The measurements are in good agreement with our calculations of the longitudinal shift for Gaussian laser beams.

Spatial displacement of electrons due to multiple total reflections

A theoretical investigation is made of the spatial displacements of a Dirac electron which undergoes a series of total internal reflections from finite potential barriers of arbitrary smoothness. These displacements are analogous to the shifts observed for optical total reflection (the Goos-H\"anchen effect). For an electron, the polarization states that are invariant to a single-reflection process are identified and the change in polarization for an arbitrary incident polarized state is determined. A calculation of longitudinal and transverse shifts is made for a double-reflection process from surfaces with a specified orientation. This calculation is based on a phase-shift analysis in which a localization form-invariance argument for the wave packet is used to determine both the eigenpolarization states of the double-reflection process and the relevant phase shifts. An unpolarized beam of electrons will be spatially split into these geometry-dependent eigenpolarization states. In general, it is found that the total spatial displacement of the wave-packet center for each eigenstate consists of two parts, each of which has longitudinal and transverse components. There is a common shift (dependent on the potential) which near critical reflection is of the order of the de Broglie wavelength, and a polarization-dependent shift (independent of the potential) that causes a split that is at most of the order of a Compton wavelength. There is no splitting for reflections between parallel surfaces. In principle, a macroscopically observable common shift can be produced through multiple reflections.