Imbert-Fedorov Shifts Research Articles

Generic optical singularities and beam-field phenomena due to general paraxial beam reflection at a plane dielectric interface

A single paraxial beam reflection at a plane dielectric interface, configured appropriately, can lead to the formation of a polarization singularity in the inhomogeneously polarized output beam field for any central angle of incidence. In this paper we derive the necessary condition to realize this effect. We explore the phase singularity characteristics associated with this polarization-singular field and explore the dynamics of the singularities due to controlled variations of the input polarization. The simulation-generated exact field information lead to the exploration of the unique Goos-H\"anchen, Imbert-Fedorov, and spin shifts of the optical-singular fields and the anticipation of an exact mathematical characterization of spin-orbit interaction phenomena involved therein. The formation of a phase singularity independent of a polarization singularity is explained subsequently. Interrelating these seemingly unconnected beam-field phenomena and generic optical singularities can lead to a significant and fundamental understanding of the inhomogeneously polarized beam field; additionally, our singularity generation method can find potential application in experimental characterization of the involved dielectric media.

Enhanced and tunable Imbert-Fedorov shift based on epsilon-near-zero response of Weyl semimetal

We theoretically investigate the reflected spatial Imbert–Fedorov (IF) shift of transverse-electric (TE)-polarized beam illuminating on a bulk Weyl semimetal (WSM). The spatial IF shift is enhanced significantly at two different frequencies close to the epsilon-near-zero (ENZ) frequency, where large values of reflection coefficients |r pp|/|r ss| are obtained due to the ENZ response induced different rapid increasing trends of |r pp| and |r ss|. Particularly, the tunable ENZ effect with tilt degree of Weyl cones and Fermi energy enables the enhanced spatial IF shift at different frequencies. The enhanced spatial IF shift also shows the adjustability of WSM thickness, incident angle and Weyl node separation. Our findings provide easy and available methods to enlarge and adjust the reflected IF shift of TE-polarized light with a WSM.

Bistable reflection and beam shifts with excitation of surface plasmons in a saturable absorbing medium.

We investigate the nonlinear reflection of a light beam from a Kretschmann configuration with saturable absorbing medium. The absorption of medium has direct influence on the intrinsic loss of the system, thus affecting the reflectivity and the phase variation when the surface plasmons are resonantly excited. As the incident power changes, the reflectivity can be switched between high and low values and exhibits absorptive optical bistability as a result of the inherent positive feedback by the intensity-dependent saturation effect. The Goos-Hänchen and the Imbert-Fedorov shifts of the reflected beam have the same bistable behavior as the reflectance. The effects of the thickness of metal film and the linear absorption coefficient on the hysteresis loop are analyzed in detail by considering the system losses and the saturated absorption. The bistable reflection and beam shifts may have applications in all-optical devices, such as optical switching.

A semiclassical approach to surface Fermi arcs in Weyl semimetals

We present a semiclassical explanation for the morphology of the surface Fermi arcs of Weyl semimetals. Viewing the surface states as a two-dimensional Fermi gas subject to band bending and Berry curvatures, we show that it is the non-parallelism between the velocity and the momentum that gives rise to the spiral structure of Fermi arcs. We map out the Fermi arcs from the velocity field for a single Weyl point and a lattice with two Weyl points. We also investigate the surface magnetoplasma of Dirac semimetals in a magnetic field, and find that the drift motion, the chiral magnetic effect and the Imbert-Fedorov shift are all involved in the formation of surface Fermi arcs. Our work not only provides an insightful perspective on the surface Fermi arcs and a practical way to find the surface dispersion, but also paves the way for the study of other physical properties of the surface states of topological semimetals, such as transport properties and orbital magnetization, using semiclassical methods.

Transformation from asymmetric spin splitting to symmetric spin splitting with phase compensation in photonic spin Hall effect.

Generally, when an arbitrary polarized light beam is reflected or refracted from an isotropic interface, the spin splitting in photonic spin Hall effect (SHE) shows asymmetry properties. In this paper, we theoretically propose a phase compensation scheme to achieve the transformation from asymmetric spin splitting to symmetric spin splitting in photonic SHE. We experimentally acquire the spin splitting after phase compensation in the case of a 45 degrees linear polarized Gaussian light beam totally internally reflected from a prism-air interface. Particularly, whether or not phase compensation, the transverse shift of total barycenter of reflected field [i.e., the Imbert-Fedorov (IF) shift] does not change. These findings can solve this problem that asymmetric spin splitting cannot be observed by weak measurements.

Tunable giant two-dimensional optical beam shift from a tilted linear polarizer

We demonstrate an intriguing giant optical beam shift in a tilted polarizer system analogous to the Imbert-Fedorov shift in partial reflection around the Brewster's angle of incidence. We explain this giant shift using a generalized theoretical treatment for beam shift in a tilted uniaxial anisotropic material incorporating the three-dimensional orientation of its optic axis in the laboratory frame. A regulated control and tunability of both the magnitude and direction of the shifts are demonstrated further by wisely tuning the input polarization and the corresponding orientation angles. These findings open up the possibility of precise micron-level beam steering using a simple linear polarizer.

Determination of tilt degree and Weyl-node separation by the spatial Imbert-Fedorov shift near the Brewster angle

The Imbert-Fedorov (IF) shift at the optical interface of Weyl semimetal (WSM) is extremely significant to recognize the optical characteristics of WSM. In this paper, we have studied the spatial IF shift on the surface of a bulk WSM by theoretically deriving a 4 \ifmmode\times\else\texttimes\fi{} 4 magneto-optic matrix. It is found that the phenomenon of spatial IF shift changing from positive to negative occurs at an incident angle near the Brewster angle. Remarkably, this special phenomenon can be regulated by changing the frequency of incident light, tilt degree, and Weyl node separation. Specially, for a fixed Weyl node separation, the phenomena of spatial IF shift changing from positive to negative can be realized at different tilt degrees by simply changing the frequency, and there exists one-to-one correspondence between the tilt degree and frequency at these situations. Similarly, for a fixed tilt degree, these phenomena can be achieved at different Weyl node separations by changing the frequency, and there also exists one-to-one correspondence between the Weyl node separation and frequency. Therefore, these tunable phenomena of spatial IF shift changing from positive to negative enable the feasibility of accurate determination of tilt degree and Weyl node separation. Our study can also provide a reference for the research of IF shift in such similar structures.

Topological Imbert–Fedorov shifts in silicene

In this paper, we study the topological Imbert–Fedorov (IF) shifts of a light beam reflected from a silicene–substrate system in the presence of an externally applied electric field and circularly polarized beam. Silicene is a topological material and due to the strong spin–orbit interaction has a rich phase diagram. Using the famous Kubo formalism, we derive analytical expressions for the longitudinal and transverse Hall conductivities of silicene. By employing angular spectrum analysis, the analytical expression of the spatial IF shift is obtained. We show that electric field/circularly polarized light beam modulated positive and negative spatial beam shifts can be obtained by tuning the angle of incidence near the Brewster angle and the incident photonic energy in the terahertz regime. Furthermore, we also investigate the IF shifts in different topological phases of the silicene by driving the system through distinct topological quantum phase transitions (TQPTs), i.e., from topologically nontrivial to a semi-metallic state and further to a band insulating state by manipulating the interplay between the electric field and circularly polarized light beam. We believe these results are helpful for developing novel optoelectronic, spintronic, and valleytronic devices and may provide a possible technique for probing Berry curvature, topological Chern numbers, and TQPTs by direct optical measurement.

Goos–Hänchen and Imbert–Fedorov shifts in tiltedWeyl semimetals

We establish the beam models of Goos–Hänchen (GH) and Imbert–Fedorov (IF) effects in tilted Weyl semimetals (WSMs), and systematically study the influences of Weyl cone tilting and chemical potential on the GH and IF shifts at a certain photon energy 1.96 eV. It is found that the GH and IF shifts in tilted type-I and type-II WSMs are both almost symmetric about the Weyl cone tilting. Meanwhile, the GH and IF shifts in type-I WSMs almost do not change with the tilt degree of Weyl cones, while those in type-II WSMs are extremely dependent on tilt degree. These trends are mainly due to the nearly symmetric distribution of WSMs conductivities, where the conductivities keep stable in type-I WSMs and gradually decrease with tilt degree in type-II WSMs. By adjusting the chemical potential, the boundary between type-I and type-II WSMs widens, and the dependence of the beam shifts on the tilt degree can be manipulated. Furthermore, by extending the relevant discussions to a wider frequency band, the peak fluctuation of GH shifts and the decrease of IF shifts occur gradually as the frequency increases, and the performance of beam shifts at photon energy 1.96 eV is equally suitable for other photon frequencies. The above findings provide a new reference for revisiting the beam shifts in tilted WSMs and determining the types of WSMs.

Voltage controllable Goos Hänchen and Imbert Fedorov shifts based on capacitor structure

The polarization properties and optical spot position of a 1550 nm linearly polarized laser beam reflected from ITO-Au(100 nm)/Ti(30 nm) interdigital electrodes-SiO2 glass (ITO-IE) or ITO-SiO2 microspheres-Au(100 nm)/Ti(30 nm) interdigital electrodes-SiO2 glass (ITO-SiO2-IE) are studied by a Thorlabs PAX 5710 IR3 polarimeter and a Thorlabs BP209-IR slit beam profiler detector under external direct current (DC) voltage. The Au is used as a reflective layer and the Ti is used as a buffer layer. The Au/Ti interdigital electrodes are prepared on SiO2 glass by thick film, printed circuit board and MEMS process. The surface morphology of the ITO-IE and ITO-SiO2-IE is obtained by a polarized light microscope. The polarization parameters' change of the linearly polarized laser beam reflected from ITO-IE is larger than that of the ITO-SiO2-IE. The maximum Goos Hänchen (GH) and Imbert Fedorov (IF) shifts of the linearly polarized laser beam reflected from the ITO-IE are 135.79 μm and −127.7 μm, while the GH and IF shifts of the linearly polarized laser beam reflected from ITO-SiO2-IE are 96.75 μm and −103.48 μm, when the external DC voltage increases from 0 to 3.0 V. The polarization properties and spatial position of the linearly polarized laser beam reflected from the ITO-IE and ITO-SiO2-IE capacitors show different trends. It is very important for the manufacture and design of optical displacement sensors.

Ultrasensitive Optical Temperature Transducers Based on Surface Plasmon Resonance Enhanced Composited Goos-Hänchen and Imbert-Fedorov Shifts

The spatial and angular Goos-Hänchen and Imbert-Fedorov shifts occur simultaneously for the light beam reflected from a lossy surface (e.g., metal surface). The mixture of spatial and angular Goos-Hänchen (Imbert-Fedorov) shifts, referred to as composited Goos-Hänchen (Imbert-Fedorov) shift, has been experimentally confirmed in recent years. The temperature-dependent composite Goos-Hänchen and Imbert-Fedorov shifts for a light beam reflected from the prism-gold interface in the Kretschmann-Raether configuration are theoretically investigated. The spatial and angular Goos-Hänchen and Imbert-Fedorov shitfs of p-polarized incident light are significantly enhanced around the resonant angle with the generation of surface plasmon resonance. The ultrahigh temperature sensitivities of 0.79 cm/K and 188 μm/K are obtained with the composite Goos-Hänchen and Imbert-Fedorov shift, respectively, which are about 5 orders higher than those obtained with a bare gold surface. The ultrahigh temperature sensitivity is mostly contributed by the angular shift effect. Our results demonstrated the importance of angular shift effect in achieving an ultrahigh sensitivity. This work can serve as a guidance for the design of temperature sensor, chemical sensor and biosensor based on composite Goos-Hänchen and Imbert-Fedorov shifts.

Negative group delay of reflected Weyl quasiparticles

When an electron is incident from a Weyl material to an insulator and totally reflected, it suffers a reflection group delay and a reflection shift (Goos–Hänchen and/or Imbert–Fedorov shifts). We found the group delay is negative for half of the incident states. The negative group delay does not mean the electron is bounced back before its injection, but is an effective acceleration of the electron near the interface induced by self-interference. The reflection shift orients circulating the points at which the surface-bulk state transition occurs. The reflection shift and the group delay cause velocity correction of the bound states in the Weyl material sandwiched by two insulators. The velocity correction features induced by the negative group delay were verified by a tight-binding calculation, in which the concept of group delay is not used.

Shifting beams at normal incidence via controlling momentum-space geometric phases

When hitting interfaces between two different media, light beams may undergo small shifts. Such beam shifts cannot be described by the geometrical optics based on Snell’s law and their underlying physics has attracted much attention. Conventional beam shifts like Goos-Hänchen shifts and Imbert-Fedorov shifts not only require obliquely incident beams but also are mostly very small compared to the wavelength and waist size of the beams. Here we propose a method to realize large and controllable polarization-dependent lateral shifts for normally incident beams with photonic crystal slabs. As a proof of the concept, we engineer the momentum-space geometric phase distribution of a normally incident beam by controlling its interaction with a photonic crystal slab whose momentum-space polarization structure is designed on purpose. The engineered geometric phase distribution is designed to result in a large shift of the beam. We fabricate the designed photonic crystal slab and directly observe the beam shift, which is ~5 times the wavelength and approaches the waist radius. Based on periodic structures and only requiring simple manipulation of symmetry, our proposed method is an important step towards practical applications of beam shifting effects.

Control of Imbert-Fedorov shifts by the optical properties of rotating elliptical Gaussian vortex beams.

Based on the angular spectrum of rotating elliptical Gaussian vortex beams (REGVBs), the Imbert Fedorov (IF) shift of REGVBs with the topological charge m = 1 is calculated analytically and numerically. The effects of the topological charge and the vortex position on the IF shift of REGVBs are discussed. By comparing the IF shifts of Gaussian beams, Airy beams with finite energy and REGVBs, we find that REGVBs have unique advantages in the control of the IF shift, that is, the IF shift of REGVBs is similar to the odd symmetry near the Brewster angle, and the rotation parameters can specially control the magnitude and the direction of the IF shift at the same time. Our discovery breaks the previous thinking barrier, that is, most of the control of the IF shift direction is based on materials, and provides a new perspective for controlling the IF shift based on the properties of beams.

Magnetic field and Fermi energy modulated quantized Imbert–Fedorov shifts in graphene

We theoretically investigate the spatial Imbert–Fedorov (SIF) shifts of a light beam reflected from a graphene–substrate system in the presence of an externally applied magnetic field. We impinge a monochromatic light beam of finite width on the surface of a graphene–substrate system and investigate the reflection and transmission coefficients of the beam. We find that the Fermi energy modulated quantized transverse shifts can be achieved in the graphene–substrate system for incident angles in the vicinity of the Brewster angle and frequencies in the terahertz regime. In the case of partial reflection of the light beam, IF shifts acquire moderate magnitudes, while for the case of total internal reflection in the quantum Hall regime, our results show giant negative and positive SIF shifts. Furthermore, we demonstrate that the Brewster angle changes with changing magnetic field and Fermi energy. Our findings are important from the point of view of tuning the IF shifts with magnetic field and Fermi energy conveniently and effectively, which is required to develop new tunable photonic devices in the terahertz regime.

Goos–Hänchen and Imbert–Fedorov shifts of reflected rotating elliptical Gaussian beams from surfaces coated with cross-anisotropic metasurfaces

In this paper, we use the rotating elliptical Gaussian beams (REGBs) to impinge the surfaces coated with cross-anisotropic metasurfaces (CMs) to investigate the Goos–Hänchen (GH) and Imbert–Fedorov (IF) shifts. The effect of the CM coating on the reflection coefficient in this system is considered. In particular, we will show that the angle of incidence and the relative permittivity of the weakly absorbing medium have an influence on the GH and the IF shifts. A comparison with the case of surfaces without the CM is also discussed.

Adjustable spin Hall effect of light in surface plasmon resonance structure with consideration of angular Imbert–Fedorov shift

For a horizontally polarized Gaussian beam incident on surface plasmon resonance structure composed of prism, silver film, and absorptive liquid, the left- and right-handed circularly polarized components of the reflected beam undergo spin-dependent spatial and angular Imbert–Fedorov (IF) shift. We investigate spin Hall effect of light (SHEL) after the reflected beam travels a distance of Rayleigh range. It is shown that the maximum total transverse shift (TTS) of one spin component at Rayleigh range is always larger than the maximum spatial IF shift, and TTS is more sensitive to variations in the parameters of the structure than spatial IF shift. Furthermore, this SHEL is adjustable by changing the complex refractive index of the absorptive liquid. This research provides a simple way to enhance SHEL and may have potential application of improving the accuracy of sensors based on SHEL.

Studying the Imbert-Fedorov shift for a non-integer dimensional chiral-chiral planar interface

Using Yasumoto and Oishi's energy flux method, Imbert-Fedorov shift for a planar interface of ordinary dielectric/non-integer dimensional-dielectric/chiral chiral/non-integer dimensional chiral media is theoretically investigated. In the case of non-integer dimensional-chiral chiral interface, the behavior of Imbert-Fedorov shift is noted for both co and cross components of the reflected field. It is noted that variation of chirality parameter impacts the Imbert-Fedorov shift; both positive and negative shifts can be obtained. Furthermore, varying the value of the non-integer dimensional parameter and the value of permittivity also affects the shift.

Large spatial shifts of reflective beam at the surface of graphene/hBN metamaterials.

We theoretically studied the Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts of reflective beam at the surface of graphene/hBN metamaterials. The results show that the GH-shift is significantly enhanced and also possesses the large reflectivity when the light beam is incident at the critical angle near the Brewster angle. We found that the IF-shift is the largest when the reflective beam is a special polarized-beam or the reflective coefficients satisfy the conditions |rs | = |rp | and φs - φp = 2jπ (j is an integer). By changing the chemical potential, filling ratio and tilted angle, the position and width of frequency windows obtaining the maximum values of shifts can be effectively adjusted. The large and tunable GH- and IF-shifts with the higher reflectivity provide an alternative scheme to develop new nano-optical devices.

Photonic spin Hall effect in guided-wave resonance structure with consideration of beam propagation

We present a unified formalism about spatial and angular Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts. When a horizontally polarized Gaussian beam is reflected from guided-wave resonance structure, the photonic spin Hall effect (PSHE) caused by both spatial and angular IF shifts is theoretically investigated with consideration of beam propagation. When PSHE is observed at Rayleigh range of the reflected beam, the maximum total IF shift is larger than the maximum spatial IF shift. Meanwhile, total IF shift varies faster with the incident angle than the spatial IF shift. The formalism also shows that the spatial and angular IF shifts increase with the increase of the width of the resonant absorption dip. Theoretical predictions agree well with numerical calculations. Those results provide a new way to improve PSHE and have potential application of improving the accuracy of sensors based on PSHE of this structure.