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Bound states in the continuum (BIC) have been widely researched and applied in optics due to their unique electromagnetic response. However, there are still difficulties in predicting and customizing BIC spectra. To address this issue, we design an efficient combined neural network for highly accurate prediction of quasi-bound states in the continuum (q-BIC) spectrum, as well as for the inverse design of the polarization independent enhancement of the Goos-Hänchen (GH) shift. Firstly, we propose a C4 symmetric metasurface for achieving q-BIC spectrum and providing the condition of enhanced GH shift. By employing a combined neural network, the intensity, position, shape, and phase of q-BIC spectrum with ultra-narrow resonance can be accurately predicted and on-demand customized, even under a small dataset. Besides, we develop a screening algorithm for the q-BIC spectrum to quickly realize the polarization independent enhancement of GH shift. As an application, an ultra-high sensitivity refractive index sensor has been proposed, whose sensitivity can reach 2.31×107 µm/RIU for TM polarization and 1.03·106 µm/RIU for TE polarization. Therefore, this work brings new solutions for quick prediction of q-BIC spectrum and the development of flexible polarization photonic devices. [ABSTRACT FROM AUTHOR]

In this study, we investigate the electrically and magnetically tunable Goos–Hänchen (GH) shift of a reflected light beam at terahertz frequencies. Our study focuses on a photonic crystal heterostructure incorporating a monolayer anisotropic graphene. We observe a tunable and enhanced GH shift facilitated by a drastic change in the reflected phase at the resonance angle owing to the excitation of the topological edge state. Considering the quantum response of graphene, we demonstrate the ability to switch positive and negative GH shifts through the manipulation of graphene's conductivity properties. Moreover, we show that the GH shift can be actively tuned by the external electric field and magnetic field, as well as by controlling the structural parameters of the system. We believe that this tunable and enhanced GH shift scheme offers excellent potential for preparing terahertz shift devices. [ABSTRACT FROM AUTHOR]

We analyze the Goos–Hänchen (GH) shift and longitudinal spin splitting (LSS) at a planar interface between two optical media in the spin representation. While these optical effects have been studied previously, we examine the direct and cross-reflected light fields, and their interference from the spin representation to reveal the physical mechanism of the GH shift and establish a quantitative relationship between it and LSS. Furthermore, we show that angular asymmetric spin splitting occurs under the spin representation when linearly polarized light with a phase difference of 180° and an amplitude ratio angle deviating from 45° impinges on the air–glass interface at Brewster's angle. Finally, we reveal that the spin component field of the reflected light field for the total reflection case is different from that of the Brewster angle reflection, the most typical manifestation is that the intensity of the two spin component fields is not equal. [ABSTRACT FROM AUTHOR]

The study of a Gaussian laser beam interacting with an optical prism, both through reflection and transmission, provides a technical tool to examine deviations from the optical path as dictated by geometric optics principles. These deviations encompass alterations in the reflection and refraction angles, as predicted by the reflection and Snell laws, along with lateral displacements in the case of total internal reflection. The analysis of the angular distributions of both the reflected and transmitted beams allows us to understand the underlying causes of these deviations and displacements, and it aids in formulating analytic expressions that are capable of characterizing these optical phenomena. The study also extends to the examination of transverse symmetry breaking, which is a phenomenon observed in the laser beam as it traverses the oblique interface of the prism. It is essential to underscore that this analytical overview does not strive to function as an exhaustive literature review of these optical phenomena. Instead, its primary objective is to provide a comprehensive and self-referential treatment, as well as give universal analytical formulas intended to facilitate experimental validations or applications in various technological contexts. [ABSTRACT FROM AUTHOR]

Exceptional points are investigated in two different one-dimensional photonic crystals. Both periodic structures are parity-time-symmetric (PT) and have a three-layer unit-cell containing gain and loss medium in which a dielectric film is sandwiched between them. However, the unit-cell of one structure is not parity-time-symmetric solely, and the system has low symmetry. The introduction of a graphene layer leads to the appearance of new exceptional points, which their properties are strongly dependent on the chemical potential of graphene. Coherent perfect absorbing lasing (CPAL) points, their spectra, and Goos-Hänchen (GH) shifts are considered with the gain–loss factor and also with the chemical potential of graphene. In the low symmetry structure, to obtain maximum values of spectra, the small gain–loss factor is needed. Results of GH calculations show that both structures depict GH shifts at two different angles with small shift values. By increasing the chemical potential of graphene, GH shifts get high values, where, the angle dependency of GH shifts in the symmetric structures is considerable. [ABSTRACT FROM AUTHOR]

This investigation focuses on the Goos–Hänchen (GH) and Imbert–Fedorov (IF) shifts on the surface of the uniaxial hyperbolic material hexagonal boron nitride (hBN) based on the biaxial hyperbolic material alpha-molybdenum (α-MoO3) trioxide structure, where the anisotropic axis of hBN is rotated by an angle with respect to the incident plane. The surface with the highest degree of anisotropy among the two crystals is selected in order to analyze and calculate the GH- and IF-shifts of the system, and obtain the complex beam-shift spectra. The addition of α-MoO3 substrate significantly amplified the GH shift on the system's surface, as compared to silica substrate. With the p-polarization light incident, the GH shift can reach 381.76λ0 at about 759.82 cm−1, with the s-polarization light incident, the GH shift can reach 288.84λ0 at about 906.88 cm−1, and with the c-polarization light incident, the IF shift can reach 3.76λ0 at about 751.94 cm−1. The adjustment of the IF shift, both positive and negative, as well as its asymmetric nature, can be achieved by manipulating the left and right circular polarization light and torsion angle. The aforementioned intriguing phenomena offer novel insights for the advancement of sensor technology and optical encoder design. [ABSTRACT FROM AUTHOR]

We conduct a theoretical analysis of the massive and tunable Goos–Hänchen (GH) shift on a polar crystal covered with periodical black phosphorus (BP)-patches in the THz range. The surface plasmon phonon polaritons (SPPPs), which are coupled by the surface phonon polaritons (SPhPs) and surface plasmon polaritons (SPPs), can greatly increase GH shifts. Based on the in-plane anisotropy of BP, two typical metasurface models are designed and investigated. An enormous GH shift of about −7565.58 λ 0 is achieved by adjusting the physical parameters of the BP-patches. In the designed metasurface structure, the maximum sensitivity accompanying large GH shifts can reach about 6.43 × 108 λ 0/RIU, which is extremely sensitive to the size, carrier density, and layer number of BP. Compared with a traditional surface plasmon resonance sensor, the sensitivity is increased by at least two orders of magnitude. We believe that investigating metasurface-based SPPPs sensors could lead to high-sensitivity biochemical detection applications. [ABSTRACT FROM AUTHOR]

Amidst the escalating issue of drug abuse, an urgent need for effective illicit drug detection methods has arisen. This paper introduces a novel optical approach utilizing the Goos–Hänchen Shift (GHS) to explore the possibility of on-site rapid detection of illicit drugs. Delving into the mechanisms, light absorption and attenuation in biological samples are considered through absorption and attenuation coefficients, establishing connections between complex refractive indices, complex dielectric constants, and GHS. A self-assembled GHS detection system measured GHS values across various samples: ultrapure water, serum, methamphetamine, serum–methamphetamine, heroin, and serum–heroin. These experiments unveiled substantial GHS variations among the samples. Refractive indices for serum, serum–methamphetamine, and serum–heroin samples were computed using GHS values and sample extinction coefficients, highlighting GHS's remarkable sensitivity to refractive index variations as a high-sensitivity refractive index sensing technology. The correlation between the dielectric constant and GHS was explored, yielding refractive indices for pure solutes—serum, methamphetamine, and heroin—of 1.66300, 1.51300, and 1.62300, respectively. Notably, the dielectric constants for these solutes were 2.76557, 2.28917, and 2.63413, emphasizing the dielectric constant's discriminative potential in identifying illicit drugs. In conclusion, these findings suggest that GHS holds promise for distinguishing various illicit drug types, charting an innovative path for illicit drug detection. [ABSTRACT FROM AUTHOR]

The study of a Gaussian laser beam interacting with an optical prism, both through reflection and transmission, provides a technical tool to examine deviations from the optical path as dictated by geometric optics principles. These deviations encompass alterations in the reflection and refraction angles, as predicted by the reflection and Snell laws, along with lateral displacements in the case of total internal reflection. The analysis of the angular distributions of both the reflected and transmitted beams allows us to understand the underlying causes of these deviations and displacements, and it aids in formulating analytic expressions that are capable of characterizing these optical phenomena. The study also extends to the examination of transverse symmetry breaking, which is a phenomenon observed in the laser beam as it traverses the oblique interface of the prism. It is essential to underscore that this analytical overview does not strive to function as an exhaustive literature review of these optical phenomena. Instead, its primary objective is to provide a comprehensive and self-referential treatment, as well as give universal analytical formulas intended to facilitate experimental validations or applications in various technological contexts.

Exosomes have shown great potential in serving as a cancer biomarker over these years since they carry crucial information of their parent cells. Therefore, detection of exosomes is of vital importance to the early-stage diagnostics of multiple major diseases. In this paper, we have proposed a real-time and label-free sensing technique based on 2D Ge2Sb2Te5 (GST) nanomaterial enhanced plasmonic substrate. We have achieved a detection limit down to 104 exosomes/mL based on Goos–Hänchen (GH) shift measurement, which is more than two orders of magnitude superior to conventional SPR sensing techniques. Moreover, the detection of unpurified exosomes directly in cell culture supernatant (CCS) has been successfully demonstrated with a significant experimental GH shift signal of more than 120 μm been detected. Multiple control experiments using exosome-free solutions and control antibody coated substrates have also been performed, which validates the specificity of our device. The proposed plasmonic sensing scheme with enhanced sensing performance has the capability of detecting exosomes at low concentration levels. It also possesses the ability of direct detection of exosomes in CCS, which offers a convenient and efficient platform for exosome detection and analysis. We envision that this technique can serve as a promising tool in early-stage clinical diagnostics and treatment.

In this paper, the magnetically tunable Goos–Hänchen (GH) shift of a reflected beam at terahertz frequencies is achieved by using a multilayer structure where three layers of anisotropic graphene are inserted. The enhanced GH shift phenomenon results from the local field enhancement owing to the excitation of graphene surface plasmon polaritons at the interface between two dielectric materials. By considering the quantum response of graphene, the GH shift can be switched from negative to positive by harnessing the anisotropic conductivity of graphene, and the GH shift can be actively tuned through the external magnetic field or by controlling the structural parameters. By setting appropriate magnetic field and structural parameters, we can obtain GH values of −140 microns to 220 microns in the terahertz band. This enhanced and tunable GH shift is promising for fabricating graphene-based terahertz shift devices and other applications in nanophotonics. [ABSTRACT FROM AUTHOR]

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 S He = 3. 0 6 × 1 0 6 μ m/RIU , S H 2 = 2. 8 6 × 1 0 6 μ m/RIU , S CO = 1. 8 1 × 1 0 6 μ m/RIU , and S C H 4 = 9. 5 8 × 1 0 5 μ m/RIU. With proper surface chemical modification, this GH shift gas sensor would be a powerful tool for high-sensitive gas sensing applications. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a cavity containing an intracavity medium of five-level double-ladder-type atoms with electromagnetically induced transparency to enhance Goos-Hänchen shifts of reflected and transmitted light beams. The dependence of the Goos-Hänchen shifts has been analyzed. It is shown that Goos-Hänchen shifts can be controlled by modifying the intensity and detuning of the coherent control field without changing material and the structure of the dielectric interface. This work has considerable potential for applications such as optical devices in information processing, flexible optical-beam steering and alignment, optical sensors and optical switches.

The pulse widening in fiber communications causes a significant restriction of bit rate. The intermodal dispersion occurs not only in grade-index multimode fibers but also in the two-core single-mode fiber. The Goos–Hänchen (GH) shift is not considered in the conventional analysis based on geometric optics. The GH shift is calculated in the step-index fiber in this paper. The analytic expression is derived for calculating the pulse widening from intermodal dispersion in the multimode fiber. The analytic and numerical results show that GH shift has an important effect on the intermodal dispersion. The positive GH shift can decrease the pulse widening. The maximum transmission distance of a multimode fiber can be greatly increased when light propagates near the maximum critical propagation angle. [ABSTRACT FROM AUTHOR]

A novel surface plasmon resonance (SPR) sensor with transition metal dichalcogenides (TMDCs) and polyaniline (PANI)/chitosan composite for detection of heavy metal ions in an aquatic environment is proposed and analyzed. A novel Goos-Hänchen (GH) shift sensing scheme based on TMDCs and PANI/chitosan structure is proposed. The theory shows that the GH shift can be significantly enhanced in the SPR structure silver (Ag), TMDCs, and PANI/chitosan heterostructures. The refractive index of Cu2+ ion is 1.3516, and the maximum GH shift of the hybrid structure of Ag-MoSe2-PANI/chitosan is−2067 λ at resonance angle 69.19° with MoSe2 4 layers and PANI/chitosan 123 nm. When different Cu2+ ion concentrations are added into the sample layer, the refractive index of the sample and GH shift of the SPR sensor will change. The maximum sensitivity of 2.425 × 106 λ/RIU is obtained by Ag-WSe2-PANI/chitosan structure, which is 463.42 times higher than the traditional SPR Ag film and 112.84 times higher than Ag-PANI/chitosan structure. Therefore, the configuration with GH shift provides a new development direction for the detection of heavy metal ions in an aquatic environment. [ABSTRACT FROM AUTHOR]

The enhancement of the Goos–Hänchen (GH) shift has become a research hotspot due to its promoted application of the GH effect in various fields. However, currently, the maximum GH shift is located at the reflectance dip, making it difficult to detect GH shift signals in practical applications. This paper proposes a new metasurface to achieve reflection-type bound states in the continuum (BIC). The GH shift can be significantly enhanced by the quasi-BIC with a high quality factor. The maximum GH shift can reach more than 400 times the resonant wavelength, and the maximum GH shift is located exactly at the reflection peak with unity reflectance, which can be applied to detect the GH shift signal. Finally, the metasurface is used to detect the variation in the refractive index, and the sensitivity can reach 3.58 × 106 μm/RIU (refractive index unit) according to the simulation's calculations. The findings provide a theoretical basis to prepare a metasurface with high refractive index sensitivity, a large GH shift, and high reflection. [ABSTRACT FROM AUTHOR]

In this manuscript, the Goos-Hänchen shift of the transmitted and reflected probe beam is controlled and modified. Topologically localized regions are reported in the G-H shift by introducing the position and orbital angular momentum dependency in the Rabi frequencies of the control fields. The system parameters along with the azimuthal quantum number are used to control and modify G-H shift as well as the topological regions. Crater and peak type topological regions are reported in the G-H shift of the reflected as well as transmitted beam. The number of localized regions are reported to strictly follow the general formula 2l2. The maximum shift in the reflected spectrum is reported to be Sr/λ=−140, where as in the transmitted spectrum it is only St/λ=−15. The modified results might have significant applications in optical waveguide switches and sensors.

In this letter, we demonstrate the existence of large transmitted optical positive and negative Goos–Hänchen shifts in photonic crystal slabs numerically and experimentally. The Goos–Hänchen shift we observed directly reaches ∼20 μm, which is 30 times the wavelength, approaching the radius of the beam waist. To explain this phenomenon, we measure the transmission phase through the phase measurement system and find there is an acute phase change near the resonance in photonic crystal slabs, which enhances the Goos–Hänchen shift. Our experimental results are consistent with simulation, and the work can be used to modulate the propagation of light in further research.

The transmission and lateral shift properties of the one-dimensional photonic crystals containing Dirac semimetal-based hyperbolic metamaterials and chiral material defects are theoretically investigated by using the transfer matrix method in terahertz. It is found that the angle-independent omnidirectional photonic bandgaps (PBGs) for p-polarization can be realized in the photonic crystals made of dielectric and the Dirac semimetal-based hyperbolic metamaterials. However, the PBGs are blue-shifted with the incident angle for s-polarized wave. The omnidirectional PBGs can be tunable with the Fermi energy of the Dirac semimetal, the thickness ratio of the constitute layers and the structural parameters. When one or two isotropic chiral material layers are introduced in the photonic crystals, double or four polarization-dependent defect modes are found in the bandgap under oblique incidence due to the coupling and conversion between different polarized waves in the chiral defects. The frequency interval of the defect modes changes with the chirality parameter and the incident angle. It is also found that when a light is incident on the defective photonic crystals, the giant positive and negative Goos-Hänchen shifts of co-polarization reflected waves can be induced around the defect modes, which are sensitive to the polarization, the incident angle, the incident frequency and the chirality. The special optical properties of the proposed defective multiplayers provide possibilities for practical applications in designing polarization sensitive optical devices, such as filter and sensor. • Tunable omnidirectional bandgap in 1DPCs containing Dirac semimetal-based HMMs is designed in THz. • Polarization-dependent defect modes are found in the 1DPCs with chiral material defects. • Giant positive and negative Goos-Hänchen shifts of co-polarization reflected waves appear around the defect modes. [ABSTRACT FROM AUTHOR]

When reflection takes place off the surface of antiferromagnets, surface resonances, considered as an extension of surface polariton dispersion curves into the reflection region, can enhance the lateral shift of the reflected beam in the presence of an external magnetic field. The effect was earlier studied for both the applied field and the antiferromagnet easy axis perpendicular to the plane of incidence in the case of a small applied field. Here, using MnF 2 as the antiferromagnet, we extend the work to look at how increasing the field and changing the antiferromagnet orientation affects the results, which always display nonreciprocity. We find that, when the antiferromagnet easy axis is parallel to the surface within the plane of incidence, leading to spin canting, enhanced shifts in the reflection region occur in much the same way as when the easy axis is along the applied field direction, but an applied field an order of magnitude higher is needed. However, when the easy axis is perpendicular to the surface even higher fields are necessary, and it is difficult to achieve such enhanced shifts. • Enhanced Goos–Hänchen shifts are possible on reflection off antiferromagnets. • Enhancements are associated with surface resonance excitations. • The size of the shift and the required field depends on the antiferromagnet orientation. • Smaller shifts are obtained in spin canting orientations. • Larger applied fields are necessary in spin canting orientations. [ABSTRACT FROM AUTHOR]

The intrinsic connection between the transverse photonic spin Hall effect (PSHE) and the Imbert–Fedorov shift has been well characterized. However, physical insights into the longitudinal photonic spin splitting associated with the Goos-Hänchen (GH) shift remain elusive. This paper aims to expand the theory of the PSHE generation mechanism from the transverse to the longitudinal case by examining the reflection of each spin component from an arbitrarily linearly polarized incident Gaussian beam on the air-dielectric interface. Unlike the transverse case, both spin-maintained and spin-flipped modes exhibit non-zero longitudinal displacements, with the latter being affected by the second-order expansion term of the Fresnel reflection coefficient with respect to the in-plane wave-vector component. Meanwhile, the polarization angle plays a crucial role in determining the longitudinal PSHE since each reflected total spin component is a coherent superposition of these two corresponding modes. Remarkably, the imaginary part of the relative permittivity of the dielectric significantly affects the symmetry of the longitudinal PSHE. Furthermore, the GH shift results from a superposition of individual spin states’ longitudinal displacements, taking into account their energy weights. By incorporating the corresponding extrinsic orbital angular momentum, we explore the generation mechanism of the symmetric/asymmetric longitudinal PSHE. The unified physical framework elucidating the longitudinal photonic spin splitting and GH shift provides a comprehensive understanding of the fundamental origin of the PSHE and beam shifts, paving the way for potential applications in spin-controlled nanophotonics.

Amidst the escalating issue of drug abuse, an urgent need for effective illicit drug detection methods has arisen. This paper introduces a novel optical approach utilizing the Goos–Hänchen Shift (GHS) to explore the possibility of on-site rapid detection of illicit drugs. Delving into the mechanisms, light absorption and attenuation in biological samples are considered through absorption and attenuation coefficients, establishing connections between complex refractive indices, complex dielectric constants, and GHS. A self-assembled GHS detection system measured GHS values across various samples: ultrapure water, serum, methamphetamine, serum–methamphetamine, heroin, and serum–heroin. These experiments unveiled substantial GHS variations among the samples. Refractive indices for serum, serum–methamphetamine, and serum–heroin samples were computed using GHS values and sample extinction coefficients, highlighting GHS’s remarkable sensitivity to refractive index variations as a high-sensitivity refractive index sensing technology. The correlation between the dielectric constant and GHS was explored, yielding refractive indices for pure solutes—serum, methamphetamine, and heroin—of 1.66300, 1.51300, and 1.62300, respectively. Notably, the dielectric constants for these solutes were 2.76557, 2.28917, and 2.63413, emphasizing the dielectric constant’s discriminative potential in identifying illicit drugs. In conclusion, these findings suggest that GHS holds promise for distinguishing various illicit drug types, charting an innovative path for illicit drug detection.

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.

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. [ABSTRACT FROM AUTHOR]

For optical beams transmitted by a right-angle prism, the Goos–Hänchen shift can never be seen as a pure effect. Indeed, the lateral displacement, caused by the total internal reflection, will always be accompanied by angular deviations generated by the transmission through the incoming and outgoing interfaces. This combined effect can be analyzed by using the Taylor expansion of the Fresnel coefficients. The analytic expression found for the transmitted beam allows us to determine the beam parameters, the incidence angles, and the axial distance for which lateral displacements are compensated by angular deviations. Proposals to optimize experimental implementations are also briefly discussed. [ABSTRACT FROM AUTHOR]

Lateral Goos-Hänchen (GH) shifts at the Fano resonances are theoretically investigated in superconducting photonic crystals. The photonic system consists of superconductor layer pairs with embedded graphene and a dielectric layer. With an oblique incident light, multiple Fano resonances are realized in the transmission spectrum because of the embedded graphene. Large GH shifts of the reflected light, including positive (Δ p) and negative (Δ n) GH shifts, are obtained around the Fano resonances. The GH shifts almost keep stable for different chemical potentials of graphene. By decreasing hydrostatic pressure or incident angle, larger Δ p and | Δ n | are achieved and the corresponding frequency has a redshift. By increasing the ambient temperature, Δ p and | Δ n | first increase smoothly and then decrease sharply. Overall, Δ p is more sensitive than Δ n , while the reflectance corresponding to Δ n is much larger than that corresponding to Δ p. Large and tunable GH shifts in our study may have great potential for optical detectors and transducers. [ABSTRACT FROM AUTHOR]

Two-dimensional surface polaritons (2DSPs), such as graphene plasmons, exhibit various unusual properties, including electrical tunability and strong spatial confinement with high Q-factor, which can enable tunable photonic devices for deep subwavelength light manipulations. Reflection of plasmons at the graphene's edge plays a critical role in the manipulation of 2DSP and enables their direct visualization in near-field infrared microscopy. However, a quantitative understanding of the edge-reflections, including reflection phases and diffraction effects, has remained elusive. Here, we show theoretically and experimentally that edge-reflection of 2DSP exhibits unusual behaviors due to the presence of the evanescent waves, including an anomalous Goos-Hänchen phase shift as in total internal reflections and an unexpected even-odd peak amplitude oscillation from the wave diffraction at the edge. Our theory is not only valid for plasmons in graphene but also for other 2D polaritons, such as phonon polaritons in ultrathin boron nitride flakes and exciton polariton in two-dimensional semiconductors.

The enhancement of the Goos–Hänchen (GH) shift has become a research hotspot due to its promoted application of the GH effect in various fields. However, currently, the maximum GH shift is located at the reflectance dip, making it difficult to detect GH shift signals in practical applications. This paper proposes a new metasurface to achieve reflection-type bound states in the continuum (BIC). The GH shift can be significantly enhanced by the quasi-BIC with a high quality factor. The maximum GH shift can reach more than 400 times the resonant wavelength, and the maximum GH shift is located exactly at the reflection peak with unity reflectance, which can be applied to detect the GH shift signal. Finally, the metasurface is used to detect the variation in the refractive index, and the sensitivity can reach 3.58 × 106 μm/RIU (refractive index unit) according to the simulation’s calculations. The findings provide a theoretical basis to prepare a metasurface with high refractive index sensitivity, a large GH shift, and high reflection.

Goos-Hänchen shift provides a way to manipulate the transverse shift of an optical beam with sub-wavelength accuracy. Among various enhancement schemes, millimeter-scale shift at near-infrared range has been realized by a simple symmetrical metal-cladding waveguide structure owing to its unique ultrahigh-order modes. However, the interpretation of the shift depends crucially on its definition. This paper shows that the shift of a Gaussian beam is discrete if we follow the light peak based on the stationary phase approach, where the M-lines are fixed to specific directions and the beam profile is separated near resonance. On the contrary, continuous shift can be obtained if the waveguide is illuminated by a vortex beam, and the physical cause can be attributed to the position-dependent phase-match condition of the ultrahigh-order modes due to the spatial phase distribution. [ABSTRACT FROM AUTHOR]

A multilayer structure based on Dirac semimetals is investigated, where long-range surface plasmon resonance (LRSPR) of a dielectric layer/Dirac semimetal/dielectric layer are coupled with surface plasmon polaritons (SPPs) on graphene to substantially improve the Goos–Hänchen (GH) shift of Dirac semimetals in the mid-infrared band. This has important implications for the study of mid-infrared sensors. We studied the reflection coefficient and phase of this multilayer structure using a generalized transport matrix. We established that subtle changes in the refractive index of the sensing medium and the Fermi energy of the Dirac semimetal significantly affected the GH shift. Our numerical simulations show that the sensitivity of the coupling structure is more than 2.7 × 10 7   λ / R I U , which can be used as a potential new sensor application. The novelty of this work is the design of a tunable, highly sensitive, and simple structured mid-infrared sensor that takes advantage of the excellent properties of Dirac semimetals. [ABSTRACT FROM AUTHOR]

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  $\mu$ m/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. [ABSTRACT FROM AUTHOR]

We present a comprehensive analysis of the anomalous Goos–Hänchen (GH) displacement that occurs during the reflection of light beams at an interface between air and an anisotropic medium. This analysis also applies to the Imbert–Fedorov effect. Our study suggests that the anomalous GH displacement is primarily caused by polarization-dependent abnormal interference effects between the direct and cross-reflected light fields. Using the interface between air and a type II Weyl semimetal as an example, we provide a clear physical explanation for the relationship between spin-dependent abnormal interference effects and anomalous GH displacement. We demonstrate that spin-dependent constructive interference leads to a reduction in the GH displacement of the total reflected light field, while spin-dependent destructive interference results in an increase in the GH displacement of the total reflected light field.

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.

The birefringence characteristics of reflection and transmission of light pulse are explored in chiral medium driving by two probe electric and magnetic fields, while four control fields. The proposed medium shows significant birefringence behaviors in reflection/transmission and Goos-Hänchen (GH) shifted beams. The birefringent GH-reflected and GH-transmitted pulses show significant contribution in the space time gap creation for secure communication and invisibility. A space-time gap has been observed in the reflection, transmission and corresponding GH-shifted reflection and transmission birefringent beams. The theoretical results may be useful for noise free secure communication in radar technology. [ABSTRACT FROM AUTHOR]

A Goos–Hänchen shift (GHS) surface plasmon resonance (SPR) refractive index sensor with the employment of two-dimensional tin selenide (SnSe) is proposed. Both the magnitude and sign of GHS can be controlled with the number of SnSe layers. It is found that the magnitude of GHS can be significantly enhanced with the optimum configurations of α -SnSe and ɛ -SnSe integrated SPR structures, which is about 2.72 and 3.87 times higher than that of the optimized conventional SPR structure, respectively. A highly sensitive refractive index sensor based on the enhanced GHS is proposed, which provides a 6.4-fold improvement in sensitivity compared to the conventional SPR structure. These results offer a promising approach to achieve significantly enhanced GHS, and the designed GHS-SPR sensor could provide potential applications in chemical sensing and biosensing. • The effect of SnSe allotropes on the Goos–Hänchen shift enhancement is investigated. • The results offer a promising route to the significantly enhanced Goos–Hänchen shift. • A highly sensitive Goos–Hänchen shift surface plasmon resonance sensor is proposed. [ABSTRACT FROM AUTHOR]

Fano resonances are widely utilized in the design of low-power all-optical switches, optical sensors and nonlinear optical devices. Although various nanostructures support Fano resonances, the lack of mechanisms for linear tuning of Fano resonance has become a limitation. In this paper, we propose a heterostructure consisting of a single layer of Weyl semimetal (WSM) and a one-dimensional photonic crystal (1DPC). Owing to the interference between the discrete state supported by the single layer of WSM and the continuous states supported by the 1DPC, a Fano resonance occurs. Besides, both the position and the line shape of the Fano resonance can be tuned by the Fermi energy, the distance between two Wely cones, and the tilt parameter of the WSM, the number of periods of the 1DPC, and the incident angle. With the assistance of the Fano resonance, a large Goos-Hänchen shift can be achieved. This work may offer greater possibilities to explore the applications of Fano resonances, including high-performance sensors and narrowband filters. • The epsilon-near-zero response of the Weyl semimetal provides a discrete state. • Both the position and the line shape of the Fano resonance can be tuned. • Sharp Fano resonance assisted in obtaining large Goos-Hänchen shift. [ABSTRACT FROM AUTHOR]

We propose a two-dimensional grating waveguide structure based on guided-mode resonance (GMR) to greatly enhance the Goos-Hänchen (GH) shift due to the asymmetric Fano peak. In addition, the enhancement of the GH shift is located at the peak of the reflectivity, which enables a more accessible measurement compared to the conventional GH shift enhancement based on Brewster angle or transmission-type resonance. In particular, such structure supports four channels for the GH shift enhancements, with a maximum value of 4.8 × 10 4 λ 0 for the positive one and -6000 λ 0 for the negative one. Our results benefit the potential applications for optical sensors, optical filters, optical absorbers and surface plasmon resonators, etc. • We propose a structure supports four channels for enhancements of the Goos-Hänchen (GH) shift based on Guided-mode resonance. • The peak of the GH shift is located at the peak of the reflectivity. • The maximum positive GH shift reaches 48000 λ 0 and the maximum negative GH shift reaches − 6000 λ 0. [ABSTRACT FROM AUTHOR]

In this study, the general treatment to obtain negative/positive giant Goos-Hänchen shifts for a slab cavity is provided. We find that there are two main types of giant shifts: The first type (type I) is associated with near-zero reflection coefficient, and the second type (type II) is associated with extra-large reflection and transmission coefficients. An infinite number of modes for each type are found. The general equations for both types with the model's parameters are presented to exactly locate the modes. Type I appears with near-zero absorption/gaining, while Type II appears with a finite gaining with values depend on the modes. The real values of the modes' susceptibility are found to be almost the same. Both types can generate negative or positive lateral shifts when the susceptibility is slightly modified. We finally present a discussion about their physical explanation and potential applications.

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.

For optical beams transmitted by a right-angle prism, the Goos–Hänchen shift can never be seen as a pure effect. Indeed, the lateral displacement, caused by the total internal reflection, will always be accompanied by angular deviations generated by the transmission through the incoming and outgoing interfaces. This combined effect can be analyzed by using the Taylor expansion of the Fresnel coefficients. The analytic expression found for the transmitted beam allows us to determine the beam parameters, the incidence angles, and the axial distance for which lateral displacements are compensated by angular deviations. Proposals to optimize experimental implementations are also briefly discussed.

We theoretically investigate the temperature-dependent Goos-Hänchen (GH) shifts in a symmetrical graphene-cladding waveguide (SGCW). The GH shifts in SGCW present a quasi-periodic tendency near the resonance angle with the change of temperature, which can mainly be attributed to the temperature dependence of the guiding layer’s thickness, instead of the graphene intraband conductivity and guiding layer’s refractive index. Importantly, tiny temperature fluctuations can cause significant deviations in GH shifts, and the deviations can be efficiently improved by adjusting the Fermi energy. Therefore, we propose a high-sensitivity temperature sensing scheme based on GH shifts in the SGCW, and the maximum sensitivity can reach up to −2.2 × 105 μm/°C. These researches may open avenues for applications of optical temperature sensors.

We proposed an effective and flexible scheme to achieve tunable giant Goos-Hänchen (GH) shift of reflected light in the configuration of guided-wave surface plasmon resonance with Rydberg atoms. With the super atom model of Rydberg atom due to the dipole blocking effect, we investigated the influence of Rydberg state population on GH displacement. By adjusting the external driving field on Rydberg atoms without changing the structure geometry, not only can GH shift be enhanced significantly to the magnitude of millimeter, but also the transition between positive and negative GH shift can be controlled at the same resonant angles. Furthermore, the resonant angle position of the maximum GH shift is also tunable via detuning the field. Our scheme may offer promising prospects for the optical switches and nano-sensors with high precision.

Plasmon‐based sensing relies on the interaction of photons with nanostructured materials. Surface plasmon resonance (SPR) biological and chemical sensors offer unique advantages of real‐time and label‐free detection techniques and therefore, they have been around in the commercial market for many decades. The principle of the Goos–Hanchen (GH) shift, whereby linearly polarized light undergoes a small lateral shift upon total internal reflection at a dielectric surface, is highly sensitive to refractive index (RI) changes in the sensing medium and can thus be utilized for plasmonic sensing. 2D materials such as graphene can boost the plasmonic efficiency of these sensors because of their excellent optical properties. Herein, a customized GH shift–based SPR sensor is devised using graphene‐coated Au chips. With the help of experimental results, it is shown that graphene can enhance the sensitivity of the conventional Au‐only configuration 2.35 times. [ABSTRACT FROM AUTHOR]

In this paper, a novel kind of one-dimensional (1-D) photonic crystals (PCs) using two-dimensional (2-D) hyperbolic material black phosphorus (BP) is proposed, to generate a huge lateral shift which is also known as Goos-Hänchen (GH) shift. The reflected features of such 1-D PCs are mainly ascribed to the thickness ratio of the layer of Au and BP, and the carrier density, due to the characteristics of the permittivities of BP layers and alternating Au-BP layers. In our simulation, the proposed PCs not only can create giant negative and positive GH shifts but also can generate a few adjustable changes under the influences of thickness ratio and carrier density. The simulated results show that the normalized negative one can reach about 253 times of the wavelength, the positive shift can be up to about 279 times. Such 1-D PCs using 2-D hyperbolic material might provide us a new theoretical possibility to produce giant GH shifts. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]