Goos-Hanchen Research Articles

Optical quantum Hall Goos–Hänchen effect in graphene

Strong Goos–Hänchen (GH) effect at a prism-graphene interface in the quantum Hall effect (QHE) condition is reported. Based on the full quantum description of the temperature-dependent surface conductivity of graphene present in the unconventional quantum Hall regime, magnetically strong tunable QHE GH shifts emerge. Our approach is based on deriving the generalized Fresnel coefficients with antisymmetric conductivity tensor for the Kerr phase of the incident linearly polarized light. Moreover, it is demonstrated that at low temperatures, GH shifts map plateaus as the intensity of the magnetic field grows. This quantum modulation of the GH effect in graphene by an applied magnetostatic bias may open doors to new opportunities for optical devices and QHE sensing applications in 2D materials.

High-sensitivity Goos–Hänchen shift gas sensor based on subwavelength hyperbolic metamaterials

Optical gas sensors play an increasingly important role in many applications, particularly for the detection of toxic gases. A novel Goos–Hänchen (GH) shift optical gas sensing scheme based on subwavelength hyperbolic metamaterials (HMMs) is proposed. The GH shift intensity, direction and the critical wavelength characteristics were revealed. By virtue of the GH shift and subwavelength HMMs characteristics, we designed an ultra-sensitive gas sensor to detect helium (He), hydrogen (H2), carbon monoxide (CO) and methane (CH4). The study shows that the sensitivities of the gas sensor can reach as high as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. With proper surface chemical modification, this GH shift gas sensor would be a powerful tool for high-sensitive gas sensing applications.

Observation of Giant Angular Goos-Hanchen Shifts Enhanced by Surface Plasmon Resonance in Subwavelength Grating

The effect of the Goos-Hanchen (GH) angular shift for a visible light beam under the excitation of surface plasmon resonance (SPR) in a metal subwavelength grating has been investigated. Extremely large angular GH shifts have been demonstrated for a subwavelength grating with an optimal depth. The high sensitivity of the beam shape transformation and the GH shift to a change in the angle of incidence near the SPR has been shown by rigorous electromagnetic simulation and demonstrated experimentally. The focusing of the reflected beam near the subwavelength grating surface has been demonstrated.

Half-quantized helical hinge currents in axion insulators.

Fractional quantization can emerge in noncorrelated systems due to the parity anomaly, while its condensed matter realization is a challenging problem. We propose that in axion insulators (AIs), parity anomaly manifests a unique fractional boundary excitation: the half-quantized helical hinge currents. These helical hinge currents microscopically originate from the lateral Goos-Hänchen (GH) shift of massless side-surface Dirac electrons that are totally reflected from the hinges. Meanwhile, due to the presence of the massive top and bottom surfaces of the AI, the helical current induced by the GH shift is half-quantized. The semiclassical wave packet analysis uncovers that the hinge current has a topological origin and its half quantization is robust to parameter variations. Lastly, we propose an experimentally feasible six-terminal device to identify the half-quantized hinge channels by measuring the nonreciprocal conductances. Our results advance the realization of the half-quantization and topological magnetoelectric responses in AIs.

An Enhanced High Q-Factor Resonance of Quasi-Bound States in the Continuum With All-Dielectric Metasurface Based on Multilayer Film Structures

Confinement of light is very important to the field of optics, and it is theoretically possible to achieve the perfect confinement for optical modes located in the continuous domain radiation state. Achieving perfect confinement is possible for bound states in the continuum (BIC), which localize waves that lie in the continuous spectrum of the radiative state and remain in a perfect localized state. In this article, we propose a metasurface that consists of arrays of silicon nanoellipsoidal pairs and calculate its transmission spectra and energy bands. Based on an all-dielectric metasurface, a dielectric multilayer film is incorporated to improve the quality factor of the array composed of ellipsoidal table pairs by an order of magnitude. By breaking the symmetry of ellipsoidal table pairs, quasi-BIC resonance modes excited by electric quadrupole (EQ) and magnetic dipoles (MDs) are realized using asymmetric silicon nanoellipsoid surfaces, where the quasi-BIC modes have high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> -factors. In this article, the relationship between the structural asymmetry of Fano resonance controlled by symmetry-protect BICs and the radiation <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> -factor is analyzed and demonstrated theoretically. At the same time, we use quasi-BIC resonances in asymmetric silicon nanoellipsoidal pairs of metasurfaces to achieve a huge Goos–Hänchen (GH) shift enhancement, which exceeds the third-order wavelength and a very large group index to achieve excellent slow-light effects. Our work is centered on the design of simulations for the BIC metasurface. Meanwhile, based on the simulation design results, we propose to advance the application of optical communication devices, BIC sensing, optical switches, and optical modulators.

Non-reciprocal spatial and quasi-reciprocal angular Goos-Hänchen shifts around double CPA-LPs in PT-symmetric Thue-Morse photonic crystals.

We theoretically investigate the Goos-Hänchen (GH) shifts of reflected light beams in Thue-Morse photonic crystals. The systems are constituted by two Thue-Morse dielectrics multilayers and satisfy parity-time (PT) symmetry. Double coherent perfect absorption laser points (CPA-LPs) are achieved in the parameter space composed of the incident angle and the gain-loss factor. Dramatic changes in the phase of reflection coefficient induce giant positive and negative spatial GH shifts at the CPA-LPs, while great angular GH shifts exist around the exceptional points (EPs). The spatial GH shifts present non-reciprocity for the forward and backward incident light waves near the double CPA-LPs, while the angular GH shifts are quasi-reciprocal. Increasing the Thue-Morse sequence number, these characteristics are approved around multiple CPA-LPs as well. Our work could pave the way to explore high-accuracy optical sensors.

Goos–Hänchen and Imbert–Fedorov shifts of the Airy beam in dirac metamaterials

We theoretically derive the expression for the Goos–Hänchen (GH) and Imbert–Fedorov (IF) shifts of the Airy beam in Dirac metamaterial. In this work, the large GH and IF shifts can be found when the Airy beam is reflected near the Dirac and Brewster angles. Compared to the Gaussian beam, the GH shifts of the Airy beam are more obvious in the vicinity of the Brewster angle. Interestingly, it is found that the ability to produce an Airy vortex beam at the Dirac point. In addition, the magnitude and the direction of the GH shifts can be controlled by the rotation angles of the Airy beam. We take advantage of this property to design a reflective optical switch based on the rotation angle-controlled GH shifts of the Dirac metamaterial. Our solutions provide the possibility to implement light-tuned optical switches. Moreover, our model can also be used to describe the GH and IF shifts generated by novel beams in other similar photonic systems.

Experimental proof on the effect of beam width and spatial coherence on Goos-Hänchen shift

We have experimentally investigated the effect of beam width and spatial coherence on Goos-Hänchen (GH) shift of light in a double-prism structure. The beam width and spatial coherence of the incident light are well controlled and measured. The experimental results show that the GH shift is affected by both the beam width and spatial coherence of light, and this is qualitatively consistent with the prediction of coherence theory of light. The result can promote the application of controlling GH shifts of partially coherent finite beams in optical devices and sensors.

Spatial shifts of reflected light beam on black phosphorus/hexagonal boron nitride structure

We examined Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts of the reflective beam from the hexagonal boron nitride (hBN) covered by black phosphorus (BP) layers, where the BP layers are rotated by an angle with respect to the incident plane. The interaction of phonon polaritons in hBN and plasmon polaritons in BP, as well as the structure surface and interface between the two media determines the two shifts. In the common frequency–response range of the BP and hBN, the GH- and IF-shifts can be very large in the vicinity of epsilon-near-zero (ENZ) for a linearly-polarized incidence. The GH-shift can be continuously tuned from positive to negative or even to zero at a fixed frequency by adjusting the electron density and anisotropic axis-orientation of the BP. Another fascinating phenomenon is that the IF-shift can be not only excited by the linearly-polarized incidence but also greatly improved, even up to -156λ0. These conclusions are applicable to the other 2D anisotropic materials, which will become a guidance of new polarization-dependent, anisotropic optoelectronics devices.

Enhancing the nonreciprocal Goos-Hänchen shift by the Fano resonance of coupled gyromagnetic chains at normal incidence.

We report a resonance-enhanced nonreciprocal Goos-Hänchen (GH) shift for the wave reflected from the coupled gyromagnetic chains. We demonstrate that the Fano resonance enhances the GH shift with high reflectivity at normal incidence, and the resonance results from the interference between the leaky guided modes of the coupled chains. Furthermore, we show that the GH shift can be controlled by the number of stacked chains. The Fano resonance-enhanced GH shift offers a new efficiently way to enhance and control the GH shift for reflected wave beam. Such coupled gyromagnetic chains provide an extremely compact way for the devices such as unidirectional couplers and other integration photonic components, paving the way for the applications of nonreciprocal GH shift.

Optical Goos-Hänchen effect in uniaxially strained graphene.

We prove the existence of relatively large Goos-Hänchen (GH) shifts for graphene in the presence of an applied strain in different crystallographic directions for p and s polarized beams. It is shown that GH shifts are smoothly increased by stretching the graphene's lattice. Moreover, we investigate the GH effect for strained graphene as a function of Fermi energy, which can be controlled by external factors such as gate voltage. We show that applied strain along zigzag and armchair orientations gives different results for GH shifts, which could provide a proper tool for the detection of strain in graphene.

Positive and negative Goos–Hänchen shifts in anisotropic two-dimensional atomic crystals

In this paper, the positive and negative Goos–Hänchen (GH) shifts in anisotropic two-dimensional atomic crystals are systematically investigated. As an example, the GH shifts including the spatial GH shift and the angular GH shift in the black phosphorus-substrate are studied. It is found that the spatial GH shift and the angular GH shift are sensitive to the incident angle, photon energy, optical axis angle and doping concentration. Further studies have shown that the signs variations of the spatial GH shift stem from a phase mutation of the reflection coefficients, and the angular GH shift is proportional to the angular derivative of the modulus of the reflection coefficients. Based on the above results, a systematic method of positive and negative regulations of GH shifts is explored, and it is found that the positive and negative of spatial GH shift can be flexibly controlled by altering the photon energy or rotating the optical axis angle, and the signs of angular GH shift can be easily regulated by changing the incident angle. Finally, combined with weak measurement techniques, an application scheme for accurately sensing the optical axis angle of black phosphorus based on the amplified GH shifts is proposed. These results can be extensively extended to other anisotropic two-dimensional atomic crystals.

Coherent control of spatial and angular Goos-Hänchen shifts with spontaneously generated coherence and incoherent pumping.

We propose an efficient scheme to manipulate the Goos-Hänchen (GH) shift of a reflected beam from a metal-clad waveguide, where a coherent atomic medium with a Λ-type configuration is employed as the substrate. Using experimentally achievable parameters, we identify the conditions under which spontaneously generated coherence (SGC) allows us to enhance the spatial and angular GH shifts of the reflected beam. With the help of SGC, the relative phases of the probe and control fields can alter the absorption gain and refractive index of the atomic medium, thereby manipulating the magnitudes, signs, and positions of the spatial and angular shifts. Furthermore, the spatial and angular GH shifts can be coherently controlled via adjusting the incoherent pumping rate and the intensity of the control field. Our proposal provides an avenue for the manipulation of spatial and angular GH shifts and potential applications in optical switching and optical steering.

Sensitivity Enhanced Plasmonic Biosensor Using Bi2Se3-Graphene Heterostructures: A Theoretical Analysis.

This study provided a theoretical insight for designing novel plasmonic biosensors using bismuth selenide (Bi2Se3)-Graphene heterostructures. It was a van der Waals (vdWs) stacked configuration composed of gold (Au) film, few quintuple layer (QL) Bi2Se3 and few-layered graphene. In particular, the proposed biosensor was created by Goos-Hänchen (GH) shift rather than phase, resulting in a more sensitive biosensing response. Under the excitation of 632.8 nm, significant sensitivity enhancement performance was obtained via varying the thickness of Bi2Se3-Graphene heterostructures. The best configuration was 32 nm Au film-2-QL Bi2Se3-3-layer graphene, generating the largest GH shift, as high as -1.0202 × 104 µm. Moreover, the highest detection sensitivity was determined to be 8.5017 × 106 µm/RIU, responding to a tiny refractive index (RI) change of 0.0012 RIU (RIU, refractive index unit). More importantly, our proposed biosensor has shown a theoretical feasibility of monitoring virus samples. For example, there was an efficient linear detection range for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, 0~13.44 nanomole (nM)) and its Spike (S) glycoprotein (0~59.74 nM), respectively. It is expected that our proposed plasmonic biosensor has a potential application in performing sensitive detection of SARS-CoV-2.

Enhanced and tunable Goos-Hänchen shift of reflected light due to Tamm surface plasmons with Dirac semimetals

In this paper, enhanced and tunable Goos-Hänchen (GH) shift of reflected light beam at mid-infrared band can be theoretically achieved by using a multilayer structure where a bulk Dirac semimetal (BDS) layer is coated on a distributed bragg reflector (DBR) separated by a spacer layer. This enhanced GH phenomenon results from the local field enhancement owing to the excitation of Tamm surface plasmons at the interface between BDS layer and spacer layer. Numerical calculation shows that the GH shift can be switched from negative to positive by harnessing the bulk conductivity properties of BDS, and can also be actively tuned through the Fermi energy of BDS or by controlling the structural parameters. These enhanced and tunable GH shifts are promising for fabricating BDS-based infrared shift devices and other applications in nanophotonics.

Tunable spatial Goos-Hänchen shift in periodic PT-symmetric photonic crystals with a central defect

The Goos-Hänchen (GH) effects are investigated for a transverse magnetic beam totally reflected by periodic PT-symmetric photonic crystals. A dielectric layer with a real refractive index situates as a defect in the center. Both positive and negative spatial GH shifts are induced around the defect mode. The GH shifts sensitively change with the refractive index of the defect layer. More importantly, giant negative GH shift effect with big reflectance could be found and modulated by increasing the gain-loss factor in PT-symmetric systems, which could improve the detecting sensitivity of the defect. Our study may be valuable in potential applications for highly sensitive sensors.

Polarization beam splitting in a Glan-Taylor prism based on dual effects of both birefringence and Goos-Hanchen shift

With the structure of biprism, polarization beam splitting in a Glan-Taylor polarizer was explored based on the birefringence and Goos-Hanchen shift. Due to the birefringence of the light in calcite crystal, the extraordinary light worked as the position calibration. As for the ordinary light, the propagated direction tilted noticeably due to the refraction as well as Goos-Hanchen effect at the prism-air interface of in the air gap. The Snell's law and stationary-phase approach were utilized for the calculation of the beam splitting between the two orthogonal polarization elements. By choosing appropriate incident angle and initial polarization, remarkable beam splitting was realized. With this configuration, the resolution with a magnitude of 10−5° and 10−3° was achieved for the response of the incident angle and polarization detection respectively.

Plasmonic Biosensing with Nano-Engineered Van der Waals Interfaces.

Observing a Goos-Hänchen (GH) shift of the incident light beam provides a simple and convenient method of detecting fast phase variations without the need for cumbersome direct phase measurements. Here, we show that few-monolayers-thick van der Waals structures (WS₂ , MoSe₂ and graphene) nano-engineered onto a plasmonic surface can enhance the phase variation sensitivity to analyte presence, leading to more than 3 orders of magnitude increase in the Goos-Hänchen shift (ca. 886 mm/RIU for a WS₂ /graphene/Au multilayer). The detection limit is evaluated to be as low as 0.1 aM (6.7 pg/mL) for bovine serum albumin protein with molecular weight of 67 kDa and 1 fM (24.4 ng/mL) for biotin (244 Da) molecules.

Correlation-enhanced Goos-Hänchen shift in Rydberg atomic gases

We present here a theoretical investigation on the Goos-H\"anchen (GH) lateral shift of a probe field as it is reflected or transmitted from a three-layer system with a Rydberg atomic gas sandwiched between two dielectric slabs. Driven by this weak probe field and a strong-coupling field, Rydberg atoms with dipole-dipole interactions are capable of producing a nonlocal Kerr effect whose strength could far exceed the corresponding local Kerr effect at a rather low atomic density. The resultant GH shift is distinct from that observed in an extremely diluted atomic gas with negligible Rydberg-Rydberg interactions and has been examined in two particular cases specified by different coupling frequencies for a fixed probe frequency. In both cases, the nonlocal Kerr effect is found to result in an obvious enhancement of the GH shift and more importantly provide an alternative way for controlling the GH shift by varying the atomic density in an appropriate range. Finally, we present a possible realization of a highly sensitive displacement sensor by exploiting an approximately linear relation between the displacement of one dielectric slab and the GH shift of the probe field.

Highly Sensitive Plasmonic Biosensors with Precise Phase Singularity Coupling on the Metastructures.

In this paper, we demonstrated the ability of a plasmonic metasensor to detect ultra-low refractive index changes (in the order of ∆n = 10−10 RIU), using an innovative phase-change material, vanadium dioxide (VO2), as the sensing layer. Different from current cumbersome plasmonic biosensing setups based on optical-phase-singularity measurement, our phase signal detection is based on the direct measurement of the phase-related lateral position shift (Goos–Hänchen) at the sensing interface. The high sensitivity (1.393 × 108 μm/RIU for ∆n = 10−10 RIU), based on the Goos–Hänchen lateral shift of the reflected wave, becomes significant when the sensor is excited at resonance, due to the near-zero reflectivity dip, which corresponds to the absolute dark point (lower than 10−6). GH shifts in the order of 2.997 × 103 μm were obtained using the optimal metasurface configuration. The surface plasmon resonance (SPR) curves (reflectivity, phase, GH) and electromagnetic simulations were derived using the MATLAB programming algorithm (by the transfer matrix method) and Comsol modeling (by finite element analysis), respectively. These results will provide a feasible way for the detection of cancer biomarkers.