Optical Beam Shifts Research Articles

Optical shift spectroscopy in two-dimensional materials

Optical beam shifts, such as the Goos–Hänchen (GH) shift and the Imbert–Fedorov (IF) shift, are fundamental optical phenomena. However, because these shifts are so minute, direct measurement is challenging, and obtaining an optical shift spectrum is even more difficult. Here, we successfully obtained GH and IF shift spectra using a beam displacement amplification technique. The optical shift spectrum of graphene shows very good agreement with the predicted results. Meanwhile, we observed two distinct peaks in the optical shift spectrum of WS2, corresponding to the A- and B-exciton transitions at the K-point in the Brillouin zone. More importantly, when graphene is stacked on WS2 to form a van der Waals heterostructure, the A-exciton characteristic of WS2 increases by an order of magnitude, which is essentially different from absorption and fluorescence spectra. Furthermore, refractive index change can be precisely captured by GH shift spectroscopy, which proves the optical shift spectrum to be an ideal candidate for a highly sensitive biosensor. Optical shift spectroscopy could enable new applications for nanophotonic devices and provide a platform for the study of intrinsic properties of two-dimensional materials, especially for van der Waals heterostructure.

Weak measurement of the Goos–Hänchen shift for a Hermite–Gaussian laser beam

We report on an experimental investigation of the Goos–Hänchen (GH) optical beam shift in the vicinity of the critical angle of incidence at an air–glass interface using a weak value amplification (WVA) technique for two mutually orthogonal first order Hermite–Gaussian (HG) modes (HG10 and HG01) of a light beam at 633 nm generated by a phase-only reflective spatial light modulator. We have developed a mathematical approach to visualize the beam shaping due to the WVA scheme of beam shifts for the HG modes. The study reveals the angle of incidence dependency of the GH shift in the total internal reflection condition. For both modes, a detailed study of the horizontal and transverse beam shift values with varied post-selection angles is also reported. In addition, a comparison of the beam shift values for both of the selected modes with the fundamental mode (HG00) has been demonstrated. We found a significant enhancement (about two to three times) in the beam shifts for the first order HG10 and HG01 modes compared to the fundamental mode (HG00). Our results clearly demonstrate the advantages of the HG modes of the light beam-exploiting WVA technique and thus may contribute significantly to this field and open up important applications in photonic manipulation and future technologies.

Longitudinal and Transverse Optical Beam Shifts Show Non‐separability

AbstractUnder the introduction of any tilted interface in its trajectory, an optical beam experiences polarization‐dependent deflections in the longitudinal and transverse directions with respect to the plane of incidence. The physics of such optical beam shifts are connected to profound universal wave phenomena governed by the fine interference effects of wave packets and have opened up avenues toward metrological applications. Here, the inherent non‐separability of the longitudinal and transverse optical beam shifts is revealed by considering a rather simple case of a partially reflecting Gaussian laser beam from a dielectric interface. This non‐separability appears substantially at some particular regions in the corresponding experimental parameter space. This manifests as a position–position non‐separable state of classical light field. The tunability of the related experimental parameters offers control over the degree of non‐separability. These findings are expected to be a step forward in the exploration of optical beam shifts and a number of analogous universal phenomena. The initial observation also indicates its practical impact on metrology and generation of high‐quality tunable position–position non‐separable states of classical light fields.

On anomalous optical beam shifts at near-normal incidence

We develop the theory of optical beam shifts (both Goos–Hänchen and Imbert–Fedorov) for the case of near-normal incidence, when the incident angle becomes comparable with the angular beam divergence. The developed theory uncovers the unified origin of the anomalous beam shift enhancement via the geometric Berry phase singularity. Particularly, we predict the large Goos–Hänchen shift occurring for small incidence angles. We also propose a simple experimental scheme involving a quarter-wave q-plate that allows us to observe the giant transverse and longitudinal, spatial and angular beam shifts simultaneously. Finally, we analyze the relevant beam parameters, polarization structure, and intensity profiles of the shifted transmitted beam. Our results can find applications in spin–orbit photonics, polarization optics, sensing applications, and quantum 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.

Wavelength and chemical potential dependence of optical beam shifts in graphene

We predict the spatial and angular Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts in partial (PR) and total internal reflection (TIR) conditions for fundamental Gaussian mode beams of a wide range of wavelength (400–1300 nm) impinging upon a graphene-coated dielectric surface. The GH and IF shifts turn out to be extremely dependent upon the chemical potential of graphene along with the wavelength of the incident light, thus enabling one to appropriately choose the operating wavelength and tune the chemical potential in the desired region to obtain maximum beam shifts in graphene. We also show that the typical features of the optical beam shifts are potentially linked with the optical conductivity of single-layer graphene. We expect the current study to be of fundamental significance in the field of optoelectronics and device industry based on graphene and other 2D materials.

Generic optical singularities in Brewster-reflected postparaxial beam fields

Brewster reflection of a postparaxial optical beam at a plane dielectric interface unravels fundamentally significant optical singularity dynamics. We express the simulated field-component profiles of a Brewster-reflected postparaxial beam field via empirical functions, using which we demonstrate optical beam-shifts and formation of phase singularities. These occurrences naturally reveal the presence and complex transitional dynamics of generic polarization singularities, which we observe via simulation and experiments. A single reflection being the core process, our method becomes a fundamentally appealing way to generate optical singularities and to study their dynamics.

Investigation of the optical beam shifts for monolayer MoS2 using polarimetric technique

The spatial and angular Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts are examined for fundamental Gaussian beam (633 nm) reflected from a monolayer of MoS2 using the ‘Stokes polarimetric’ technique. This technique enables us to promptly determine the magnitudes of the reflection coefficients and their relative phase differences which gives the optical beam shifts. The GH and IF shifts are measured with different polarization basis along with varying angle of incidence. This is a precision technique depending only upon the polarization components of the light beam and is quite independent of the fluctuations of the light intensity. The response of GH and IF shifts for MoS2 substrate is significant and thus may open up new possibilities in the optical applications of 2D materials.

Quantum weak measurement of Goos–Hänchen effect of light in total internal reflection using a Gaussian-mode laser beam

We report a detailed experimental demonstration of the Goos–Hänchen (GH) shift of light in total internal reflection condition for a Gaussian mode laser beam of 633 nm passing through an air-glass interface. The quantum weak measurement (QWM) technique has been exploited as a weak value amplification scheme to observe the amplified optical GH shift. The amplification of the GH shift depends on the angular deviation from the exact orthogonal position required for weak measurement. We have subsequently investigated the profiles of the beam pattern and their horizontal and vertical shifts in detail. We also show that the beam shift values obtained experimentally agree well with the theoretical results for a specific choice of angle of deviation from the orthogonal condition of weak measurement. Our results clearly demonstrate the advantages of the QWM technique for amplifying and detecting tiny optical beam shift effects and may provide important applications in precision metrology.

Optical beam shift as a vectorial pointer of curved-path geodesics: an evolution-operator perspective.

When set to travel along a curved path, e.g., in a bending-waveguide setting, an optical beam tends to re-adjust its position, shifting away from the center of path curvature. This shift is highly sensitive to the spatial profile of the refractive index, providing a vectorial pointer for curved-path geodesics and bending-induced optical tunneling. An evolution-operator analysis of this effect extends an analogy with a time-evolution-operator treatment of quantum dynamics and suggests the routes whereby the ability of an optical beam to sense curved-path geodesics can be understood in terms of the pertinent evolution operators, path integrals, and imaginary-time/path theorems.

Controlling photonic spin Hall effect via exceptional points

The photonic spin Hall effect (SHE), featured by a spin-dependent transverse shift of an impinging optical beam driven by its polarization handedness, has many applications including precise metrology and spin-based nanophotonic devices. It is highly desirable to control and enhance the photonic SHE. However, such a goal remains elusive, due to the weak spin-orbit interaction of light, especially for systems with optical loss. Here we reveal a flexible way to modulate the photonic SHE via exceptional points, by exploiting the transverse shift in a parity-time (PT) symmetric system with balanced gain and loss. The underlying physics is associated with the near-zero value and abrupt phase jump of the reflection coefficients at exceptional points. We find that the transverse shift is zero at exceptional points, but it is largely enhanced in their vicinity. In addition, the transverse shift switches its sign across the exceptional point, resulting from spontaneous PT-symmetry breaking. Due to the sensitivity of transverse shift at exceptional points, our work also indicates that the photonic SHE can enable a precise way to probe the location of exceptional point in photonic systems.

Weak measurement of the Goos–Hänchen shift of partially coherent light beams

Optical beam shifts are very small and challenging phenomena to measure. Weak measurement techniques have been developed to amplify and more easily measure the shifts of spatially coherent beams. We here investigate theoretically a weak measurement technique for measuring the Goos–Hanchen shift of partially spatially coherent beams. We show that the amplification factor of the technique depends on the global coherence degree of the field and on the size of the Goos–Hanchen shift experienced by the beam. Large amplification factors can be obtained for low shifts, even for very incoherent beams. But, for higher beam shifts, such as those occurring near critical incidence, the amplification factors are modest to low for beams of low coherence.

Tunable Goos–Hänchen and Imbert–Fedorov shifts

Abstract The optical beam shift is a spatial displacement of an optical beam in geometrical optics that particularly occurs when a laser beam reflects from an interface. In this paper, the dependence of the Goos–Hanchen (GH) and Imbert–Fedorov (IF) shifts from the interface of quartz and garnet on the external direct current voltage (EDCV) are investigated by a Thorlabs BP209-IR slit beam profiler. The optical properties of the circularly polarized and linearly polarized laser beams are measured using a Thorlabs PAX 5710IR3 polarimeters. The results show that the change trend of the GH and IF shifts are the same, whereas the initial and terminal voltages are different. The maximum value of the GH and IF shifts are 20 . 9 μ m and 33 . 4 μ m when the EDCVs are at about 3.2 V and 2.0 V, respectively

Large lateral shift in complex dielectric multilayers with nearly parity–time symmetry

We investigate the lateral shift of optical beam in complex dielectric multilayers with nearly parity–time (PT) symmetry. The gain and loss of dielectrics are modulated to achieve nearly PT symmetry. As light impinges on the multilayers, a laser point (LP) and exceptional points (EPs) appear in the parameter space composed of the incident angle and refractive index. The phase of reflection dislocates at the LP and EPs, inducing large lateral shift around these points. The shift can be positive and negative, and the polarities of the lateral shift convert at the LP and EPs. The shift, which is sensitive to the incident angle and refractive index of dielectrics, could be tuned flexibly. The study may find potential applications in highly sensitive sensors.

Upper-limited angular Goos-Hänchen shifts of Laguerre-Gaussian beams.

The angular Goos-Hänchen shift of vortex beam is investigated theoretically when a Laguerre-Gaussian (LG) beam is reflected by an air-metamaterial interface. The upper limit of the angular GH shift is found to be half of the divergence angle of the incident beam, i.e., |Θup| = (|ℓ| + 1)1/2/k0w0, with ℓ, k0, and w0 being the vortex charge, wavenumber in vacuum, and beam waist, respectively. Interestingly, the upper limited angular GH shift is accompanied by the upper-limited spatial IF shift. A parameter F is introduced to compare the total beam shift with the beam size. F varies with the vortex charge ℓ and the propagation distance zr. The values of F at zr = ∞ plane can approach 0.5, which are always larger than those at zr = 0 plane. These findings provide a deeper insight into optical beam shifts, and they may have potential application in precision metrology.

Optical beam shift induced by direct current

Optical beam shift is related to external conditions. Here, optical spot position and the polarization properties of the totally polarized, P‐polarized, and S‐polarized laser beams reflected from an aluminum film as a function of the external direct current (DC) voltage are measured by a Slit Beam Profiler and a polarimeter. The results show that the optical beam shift of the totally polarized laser beam and the S‐polarized laser beam jumps from 500 to 590 µm, and −10 to 70 µm, respectively, at different critical pressures, when the external DC value changes from 0 to 2.5 V, while the optical beam shift of the P‐polarized laser beam is small and has no jump. The degree of linear polarization of different polarized laser beams cannot change, while the degree of circular polarization of different polarized laser beams changes as a function of the external DC voltage value.

Controlling optical beam shifts upon reflection from a magneto-electric liquid-crystal-based system for applications to chemical vapor sensing

We investigate the tunability of the Goos–Hanchen shift experienced by a Gaussian light beam reflected from a multilayered heterostructure consisting of a nematic liquid-crystal cell sandwiched between electrodes and deposited on a magneto-electric/non-magnetic bilayer. Our calculations account for the optical anisotropy of the magnetic layer and of the liquid-crystal cell, as well as for the inhomogeneous refractive index distribution in the latter due to the reorientation of its molecules. We show that the Goos–Hanchen shift can be enhanced and controlled via the voltage applied to the liquid crystal cell and the magnetization direction of the magnetic film. We propose to exploit the voltage-induced tunability of the Goos–Hanchen shift in this system to design an optical sensor devoted to the detection of chemical vapors in the vicinity of the structure.

Optical beam shifts in graphene and single-layer boron-nitride.

Optical beam shifts from a freestanding 2D atomic crystal are investigated. In contrast with a 3D crystal, the magnitude of the Goos-Hänchen shift depends on the surface susceptibility of the crystal and not on the wavelength of the incident light beam. The surface conductivity of the atomically thin crystal is less important in this context because it enters in the expression of the shifts only as a second-order parameter. In analogy to a 3D crystal, the magnitudes of the Imbert-Fedorov shift and of the angular shifts depend, respectively, on the wavelength and on the square of the beam angular aperture.

Direct measurement of the Goos-Hänchen shift using a scanning quadrant detector and a polarization maintaining fiber.

High precision measurements of optical beam shifts are important in various fields including sensing, atomic force microscopy, and measuring beam shifts at interfaces. Sub-micron shifts are generally measured by indirect techniques such as weak measurements. We demonstrate a straightforward and robust measurement scheme for the shift, based on a scanning quadrant photodiode (QPD) that is biased using a low noise electronic circuit. The shift is measured with respect to a reference beam that is co-propagating with the signal beam. Thus, the shift of the signal beam is readout directly as the difference between the x-intercepts of the QPD scan plot of the signal and reference beams versus the position of the detector. To measure the beam shift, we use polarization multiplexing scheme where the p-polarized signal and s-polarized reference beams are modulated at two different frequencies and co-launched into a polarization-maintaining fiber. Both the signal and reference beam positions are readout by two lock-in amplifiers simultaneously. In order to demonstrate the utility of this method, we perform a direct measurement of Goos-Hänchen shift of a beam that is reflected from a plane gold surface. Accuracy of 150 nm is achieved using this technique.

Control of optical spin Hall shift in phase-discontinuity metasurface by weak value measurement post-selection.

Spin Hall effect of light is a spin-dependent transverse shift of optical beam propagating along a curved trajectory, where the refractive index gradient plays a role of the electric field in spin Hall effect of solid-state systems. In order to observe optical spin Hall shift in a refraction taking place at air-glass interface, an amplification technique was necessary such as quantum weak measurement. In phase-discontinuity metasurface (PMS) a rapid phase-change along metasurface takes place over subwavelength distance, which leads to a large refractive index gradient for refraction beam enabling a direct detection of optical spin Hall shift without amplification. Here, we identify that the relative optical spin Hall shift depends on incidence angle at PMS, and demonstrate a control of optical spin Hall shift by constructing weak value measurement with a variable phase retardance in the post-selection. Capability of optical spin Hall shift control permits a tunable precision metrology applicable to nanoscale photonics such as angular momentum transfer and sensing.