1. INTRODUCTION

When a beam with a beam waist is reflected or refracted, the reflected and transmitted beams do not follow the exact geometrical optical evolution. Wavelength-scale beam displacements occur in both the longitudinal and transverse directions. The longitudinal displacement is called the Goos–Hänchen (GH) shift [1], and the transverse displacement is called the Imbert–Fedorov (IF) shift [2] and the spin Hall effect of light (SHEL) [3–5]. Currently, optical shifts are attracting rapidly growing attention due to the development of nano-optics employing light evolution at subwavelength scales. Accurate measurements of beam shifts in various structures can help us study the light–matter interaction and the conversion of photon spin angular momentum into orbital angular momentum [6–8]. However, these optical shifts are of nanoscale which makes the measurement a great challenge for contemporary available instruments. Thanks to the development of quantum weak measurement techniques [9,10], the beam shift effect has now been experimentally observed in a wide range of interfaces and material structures, including metallic thin films [11,12], metamaterials [13–15], two-dimensional (2D) materials [16–20], etc.

So far, all existing experimental research on optical shifts is focused on single wavelength measurements. Realizing the measurement of beam shift from a wide spectral range is required to characterize the optical properties of materials to better understand light–matter interaction based on beam shifts. Spectroscopic studies can resolve a wide range of microscopic and macroscopic properties such as the energy levels and geometry of atoms and molecules, the reaction rates of specific chemical processes, and the concentration distribution of a substance in a specific region of space. It has been theoretically analyzed that optical shift spectra can be used to characterize the moiré superlattice of twisted bilayer graphene [21,22], hyperbolic frequency-bands in hyperbolic crystals [23], etc. However, quantum weak measurement techniques are only applicable to beam shift measurements at a single wavelength, and it remains a great challenge to achieve spectral measurements, especially for 2D materials with absorption. Recently, optical beam shifts in graphene and anisotropic 2D materials have been successfully obtained using beam displacement amplification technique (BDAT) [24,25]. More importantly, this technique enables direct and micro-area measurements of beam displacement, showing its great potential in measuring optical shift spectrum. Transition metal dichalcogenides (TMDCs) have more complicated band structure, richer exciton forms, and their optical characteristics fluctuate more strongly with the spectrum than graphene. As a result, the implementation of optical shift spectroscopy is more beneficial for studying the physical properties of TMDCs.

Here, we combined BDATs with a supercontinuum light source to achieve the measurements of GH and IF shift spectra in mechanically exfoliated 2D materials. Experiment and calculation results show that beam shift spectra in 2D materials strongly depend on the intrinsic optical properties and the layered distribution structure of the material and can clearly reflect exciton effects. Both GH and IF shift spectra of graphene are in good agreement with the predicted results due to its simple dispersion relation, while the optical shift spectra of ${{\rm WS}_2}$ with complex exciton effects display more complicated spectral structures than the predicted results. In addition, the interface structure at the subnanometer scale has a stronger influence on the optical shift spectrum than the dispersion of the complex refractive index. The excitonic characteristics and dispersion of optical shift spectra in ${{\rm WS}_2}$ are significantly enhanced by stacking graphene on ${{\rm WS}_2}$ to form van der Waals heterostructures. The overall change trend of GH shift spectrum can reflect the change of refractive index more accurately and can be well applied to the detection of gas. Our results show that optical shift spectroscopy can provide an unprecedented toolset for studying the properties of 2D and other nanomaterials and will open up various unforeseen applications in nanophotonics.

2. METHODS

A micro-area optical shift spectroscopy technique is based on beam displacement amplification combined with a supercontinuum spectral light source. The BDAT [Fig. 1(c)] is based on traditional microscopy techniques and draws on the idea of “localization” in single molecule fluorescence detection. It is a direct measurement technique for optical shifts with a spatial resolution of up to 4 nm [24]. The position of the two light points is measured separately using a position-sensitive detector (PSD) to obtain the distance between the amplified light points, where the initial distance between the light spots can be determined by the pre-determined magnification. When using the BDAT, the same spot is regulated to emit light at different locations and times to locate two positions, respectively. The distance between the two positions is the beam shift. For fixed optical configurations, the BDAT has a fixed amplification factor that does not change with the sample, polarization detection configuration, and wavelengths, which means that the BDAT is a direct displacement measurement method. As comparison, for the quantum weak measurement technique, the amplification factor strongly changes with the sample, polarization configuration, and wavelength. In many cases, accurate amplification factors cannot even be obtained for the quantum weak measurement technique, preventing direct measurement of beam shifts. Therefore, the BDAT outperforms quantum weak measurement with respect to the spectral measurements of optical shifts after introducing a wide spectral light source.

 

Fig. 1. Schematic diagram of the optical shifts and the experimental setup. (a) Diagrams of GH shift (${\Delta ^{\rm{GH}}}$) and IF shift (${\Delta ^{\rm{IF}}}$). (b) Reflection in multilayer thin-film model. ${n_2} = 1$, ${n_0}$ is the refractive index of BK7 glass, ${n_1}$ is the refractive index of ${{\rm WS}_2}$. (c) Schematic diagram of the BDAT. The BDAT is based on an objective lens magnification system. Two points of light with a distance of a few nanometers L1 are collected and amplified by the objective lens, and the distance between them becomes several hundreds of nanometers L2. Points of light are projected onto the PSD to obtain their positions (${P_g}$ and ${P_r}$, respectively). (d) Schematic diagram of the experimental setup used to measure optical shift spectra. P, Glan–Taylor prism; QWP, quarter-wave plate; HWP, half-wave plate; BS, beam splitter; O1, O2, and O3, long working distance objective lenses; AOM, acousto-optic modulator; RF driver, radio frequency driver. Inset is the microscopic image of the sample, with the red dot representing the laser spot.

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As shown in Fig. 1(d), the displacement amplification technique works in conjunction with a supercontinuum spectral light source to produce laser light at various wavelengths sequentially by modulating the acousto-optic modulator (AOM) via radiofrequency (RF) driver. The automatic scanning measurement of the beam shift spectrum is accomplished using a position-sensitive detector for data capturing. The process is a program-controlled automatic scanning of variable wavelength. For GH shift measurement, the QWP is replaced by the HWP, which is rotated to produce $s\!$-polarized and $p$-polarized light. For IF shift measurement, the QWP is rotated to produce left circularly polarized (LCP) light and right circularly polarized (RCP) light. While changing the polarization state of the incident light, the BDAT is used to locate the reflected light separately. As the IF shift is a lateral shift, we need to rotate the PSD by 90° (see Supplement 1 for more details).

3. RESULTS AND DISCUSSION

A. GH and IF Shift Spectroscopy in Graphene

A schematic diagram of the GH shift in graphene is shown in Fig. 2(a). GH shift arises from the dispersion of the transmitted and reflected beams, where the incident light is superimposed by plane waves of different angular spectra.

 

Fig. 2. GH and IF shift spectra in graphene. (a) Schematic diagram of the GH shift in graphene. $s\!$- and $p$-polarized lights are in green and blue color, respectively. (b) Dependence of GH shift on the incident angle and wavelength in monolayer graphene. (c) GH shift spectrum of monolayer graphene. Calculation (red line) and experimental (blue dot) have a good consistency. The inset shows an optical image and a Raman spectrum of a single layer of graphene. (d) Schematic diagram of the IF shift in graphene. LCP (green spiral) and RCP (blue spiral) shift in opposite transverse directions, $\Delta -$ and $\Delta +$. (e) Dependence of IF shift on the incident angle and wavelength in monolayer graphene. The black dashed line represents an incident angle of 45°. (f) IF shift spectrum of monolayer graphene. Calculation (red line) and experimental (blue dot) have a good consistency.

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To calculate the reflection coefficients ${r^{s,p}}$ for $s\!$- and $p$-polarized light, we use the multilayer film reflection model [Fig. 1(b)] and the transmission matrix method (Supplement 1, Sec. 2) [26]:

Due to a linear dispersion relation at the ${K}$-points of the Brillouin zone, graphene exhibits constant refractive index and absorption in the visible and near-infrared regions (NIR). Therefore, the variation of GH shift over the optical wavelength is also a simple linear relationship in graphene. We calculated the GH shift of graphene at different incident angles and wavelengths, as shown in Fig. 2(b). For the convenience of the experiment, the angle of incidence used in the measurement of the GH shift spectrum is 45°. As shown in Fig. 2(c), the experimental result of the optical shift spectrum in monolayer graphene is in excellent agreement with the calculated result (Supplement 1, Sec. 4), indicating that our measurement of GH shift spectrum is reliable.

The IF shift is attributed to the geometrical Berry phase and the conservation of angular momentum [6,30]. There are two geometrical phases in optics: the spin redirection Rytov–Vladimirskii–Berry (RVB) phase [31,32], which is related to the evolution of the propagation direction of light, and the Pancharatnam–Berry phase [33], which is related to the polarization of light. In general, when light is reflected at an optical interface, the phase gradient of spin repositioning caused by spin–orbit coupling of light is small, and therefore the resulting spin splitting in position space is small and difficult to be directly observed. The eigenmodes of the IF shift are RCP and LCP circularly polarized waves, with the distributions representing spin-up and spin-down photons. A schematic diagram of the IF shift in graphene is shown in Fig. 2(d), with the blue and green spirals representing RCP and LCP light, respectively. IF shift can be written as [29]

It can be seen from the equation that the IF shift at the incidence of circularly polarized light is mainly determined by the differences in the amplitude and phase of the reflection coefficients between the $s\!$- and $p$-polarized lights.

From Eqs. (3) and (4), it can be seen that the IF shift is similar to the GH shift and also depends on the complex refractive index dispersion at the interface. Therefore, for graphene without dispersion, the change of IF shift with wavelength should be still a simple linear relationship. We calculated IF shifts of monolayer graphene at different incidence angles, as shown in Fig. 2(e). The IF shift experiments were carried out at an incidence angle of 45°. The experimental results of the IF shift spectrum for graphene are also in excellent consistency with the calculated results, as shown in Fig. 2(f). GH and IF shift spectra of graphene with different thicknesses are shown in Supplement 1, Sec. 4.

B. GH Shift Spectroscopy in ${{\rm WS}_2}$

A schematic diagram of the GH shift in ${{\rm WS}_2}$ is shown in Fig. 3(a). Due to the obvious bandgap and exciton effect, two-dimensional semiconductor materials (such as ${{\rm WS}_2}$, ${{\rm MoS}_2}$) exhibit strong dispersion in their complex refractive index in the visible to near-infrared region, indicating that the optical shift spectrum will also have a strong dispersion characteristic. Therefore, the optical shift spectra exhibit strong wavelength dependency and different spectral characteristic features associated to excitons and energy bands.

 

Fig. 3. GH shift spectra in ${{\rm WS}_2}$. (a) Schematic diagram of the GH shift in ${{\rm WS}_2}$. $s\!$- and $p$-polarized lights are in green and blue color, respectively. (b)–(d) Dependence of GH shift on the incident angle and wavelength in monolayer, 3 nm and 7.5 nm ${{\rm WS}_2}$. (e) Peak of A exciton in the extracted GH shift spectra. (f), (g) GH shift spectra of monolayer, 3 nm ${{\rm WS}_2}$. Theoretical calculation (red line) and experimental (blue dot) have a good consistency. Clear exciton signature exists in all the samples, and the A exciton matched the PL measurements (gray). (h) Experimental results of GH shift spectrum of 7.5 nm ${{\rm WS}_2}$, and calculated results using the refractive index of 3 nm thick (blue line) and the bulk (red line). Clear exciton signature exists in all the samples, and the A exciton matched the PL measurements (gray).

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The GH shift spectra at different angles of incidence were calculated for ${{\rm WS}_2}$ film with different thicknesses based on the basic dispersion properties of ${{\rm WS}_2}$ (Supplement 1, Sec. 5), as shown in Figs. 3(b)–3(d). The data of complex refractive index for 1-3L ${{\rm WS}_2}$ are from the work of Hsu et al. [34]. We used the complex refractive index of the bulk ${{\rm WS}_2}$ for all calculations on ${{\rm WS}_2}$ samples with more than three layers. The GH shift spectrum experiment is carried out at an incident angle of 45°. Out of considerations for the stability and achievability of experimental setup, the 45° incident angle can ensure that there is no spot distortion (prisms must be isosceles right-angle prisms). And variations of the incident angle will only change the magnitude of the shifts without influencing the peak signatures linked to exciton properties in the optical shift spectrum. Of course, other angles of incidence can also be investigated. We also calculated IF and GH shifts over different incident angles over the range of 40°–50° for the 7.5 nm ${{\rm WS}_2}$ in the supplementary material (see Supplement 1, Sec. 5). The GH shift spectra for monolayer, 3 nm, and 7.5 nm ${{\rm WS}_2}$ exhibit the basic optical dispersion features of ${{\rm WS}_2}$ with A- and B-exciton effects, as shown in Figs. 3(f)–3(h). Two optical shift peaks, corresponding to the A- and B-exciton transitions at the ${ K}$-point in the Brillouin zone, are clearly visible in GH shift spectra for different thickness ${{\rm WS}_2}$. The A and B excitons located at around 620 and 520 nm, which are in good agreements the reported results in [35]. As a reference, we performed photoluminescence (PL) measurements [Figs. 3(f)–3(h) gray] and absorption spectra (see Supplement 1, Sec. 8) of ${{\rm WS}_2}$ with different thicknesses. It is found that peak positions of optical shift spectra are consistent with the A and B excitons in absorption and PL spectra. We observed the anticipated low redshift and matching peak width for the A exciton. The optical shift spectra for the various ${{\rm WS}_2}$ thicknesses display discrete peaks with positions and widths, which match the dominant exciton transitions in their absorption spectrum. This shows that the optical shift spectrum can identify the excitons of the TMDC material and are closely related to the material dispersion. GH shift spectra of ${{\rm WS}_2}$ with other thicknesses can be found in Supplement 1, Sec. 6.

Now, we concentrate on the location of the A exciton in optical shift spectra to examine the effect of thickness, as shown in Fig. 3(e). We discovered that at thin layers, the peak in the optical shift spectrum is redshifted as the layer thickness increase, which originates from the conversion from direct bandgap to indirect bandgap. And the measured A-exciton peak in the GH shift spectrum agrees with the theory if the thickness of ${{\rm WS}_2}$ is less than 3 nm, but for thicker ${{\rm WS}_2}$, deviation between experiment and theory is observed and increases as the thickness increases (for more details, see Supplement 1, Sec. 6). Currently, the refractive index with different wavelengths has been reported only for monolayer, two-layer, three-layer, and bulk ${{\rm WS}_2}$. There are no refractive index dispersion results for 7.5 nm ${{\rm WS}_2}$ yet. For the experimental results of optical shift of 7.5 nm ${{\rm WS}_2}$, we calculated the optical shift using the refractive index of 3 nm and bulk ${{\rm WS}_2}$, respectively. As shown in Fig. 3(h), the calculated optical shift results obtained using the refractive index of bulk and 3 nm ${{\rm WS}_2}$ are not in good agreement with the experimental results. Therefore, in order to make the calculation results more consistent, it is necessary to accurately obtain the refractive index dispersion relationship of 7.5 nm ${{\rm WS}_2}$.

The GH shift spectrum of ${{\rm WS}_2}$ excellently exhibits A-exciton and B-exciton effects, which are consistent with traditional absorption and fluorescence spectra. To ensure their reproducibility, we repeated the tests on several monolayers of ${{\rm WS}_2}$ and obtained equivalent findings (Supplement 1, Sec. 7). However, it can be seen that there is a significant difference between the GH shift spectrum and traditional absorption and fluorescence spectra. The optical shift spectrum is highly thickness-dependent, and changes of thickness can significantly affect the overall characteristics of the optical shift spectrum. As the thickness changes, the opening of the exciton peak in the GH shift spectrum changes from top to bottom (Supplement 1, Sec. 6), whereas the transmission spectrum (Supplement 1, Sec. 8) does not invert the overall shape of the spectrum, but only increases the value of the spectrum.

C. IF Shift Spectroscopy in ${{\rm WS}_2}$

Exciton effects enhance the interaction between light and matter, leading to the appearance of exciton peaks in the GH shift spectra of ${{\rm WS}_2}$. When the incident beam is confined within the vertical plane of incidence, other effects can occur, namely, the IF shift. Next, we investigate the effect of thicknesses of ${{\rm WS}_2}$ film in the IF shift spectrum and the influence of exciton effects on the spin and orbital angular momentum transitions of light.

A schematic diagram of the IF shift in ${{\rm WS}_2}$ is shown in Fig. 4(a). In order to perform IF shift spectroscopy experiments, an angle of incidence must be determined. We calculate IF shifts from the visible to the NIR for different thicknesses of ${{\rm WS}_2}$ at different incidence angles, as shown in Figs. 4(b)–4(d). The IF shift experiments were also carried out at an incidence angle of 45°. The IF shift spectra also exhibit the fundamental optical dispersion characteristics related to exciton effects. We repeated the experiments on multiple monolayer samples to ensure their reproducibility and to obtain comparable results (see Supplement 1, Sec. 7). Two optical shift peaks are clearly visible in all spectra, corresponding to the A and B excitons. The optical shift spectra of ${{\rm WS}_2}$ with varying thicknesses all exhibit identifiable peaks with positions and widths that correspond to the dominating exciton transitions in ${{\rm WS}_2}$ light absorption. This implies that the IF shift peaks originating from the exciton effect are sensitive to the factors that affect the excitons such as thickness, which facilitates light–matter interactions and spin–orbit angular momentum coupling. IF shift spectra of ${{\rm WS}_2}$ films with other thicknesses can be found in Supplement 1, Sec. 6.

 

Fig. 4. IF shift spectra in ${{\rm WS}_2}$. (a) Schematic diagram of the IF shift in ${{\rm WS}_2}$. LCP (green spiral) and RCP (blue spiral) shift in opposite transverse directions, $\Delta -$ and $\Delta +$. (b)–(d) Dependence of IF shift on the incident angle and wavelength in monolayer, 3 nm and 7.5 nm ${{\rm WS}_2}$. (e) Peak of A exciton in the extracted IF shift spectra. Yellow is the experimental result, and green is the theoretical result. (f)–(h) IF shift spectra of monolayer, 3 nm and 7.5 nm ${{\rm WS}_2}$. A clear exciton signature was observed for all three thickness samples, where the A exciton matched the PL measurements (gray).

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Fig. 5. GH shift spectra in van der Waals heterostructure of graphene-${{\rm WS}_2}$. (a) Diagram of GH shift in ${\rm Gr} \text{-} {{\rm WS}_2}$. (b) Optical image of ${\rm Gr} \text{-} {{\rm WS}_2}$ and atomic force microscopy (AFM) images of graphene. (c) The peak valley difference of optical shift ${\Delta _{{\rm GH}}}$ at the A-exciton position when the monolayer ${{\rm WS}_2}$ is covered with graphene of different thicknesses. ${\Delta _{{\rm GH}}}_0$ is the peak valley difference of optical shift at the A-exciton position of monolayer ${{\rm WS}_2}$. (d)–(f) Calculated GH shift spectra in ${\rm Gr} \text{-} {{\rm WS}_2}$ heterostructure with different thicknesses. (g)–(i) Measured GH shift spectra in ${\rm Gr} \text{-} {{\rm WS}_2}$ heterostructure with different thicknesses. The lines are theoretical calculations, and the dots are experimental data.

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We also investigated the position of the A exciton in the IF shift spectra to examine the effect of thickness, as shown in Fig. 4(e). In thin layers, the peak positions of the optical shift spectrum progressively shift to longer wavelength range as the layer thickness increases, which corresponds to the transition from direct to indirect bandgap. In thick layers, the peak positions remain essentially constant. It can be seen that when the thickness of ${{\rm WS}_2}$ is less than 3 nm, the A-exciton peak of the IF shift spectrum agrees with the theory, but the difference between experiment and theory rapidly widens as the thickness increases (for more details, see Supplement 1, Sec. 6). We also observe that the IF and GH shift spectra of monolayer ${{\rm WS}_2}$ show not only peaks for A and B excitons, but also other peak structures that may be other excitons that maybe not detected in traditional spectroscopy. We now speculate that these additional exciton peaks may be related to the excited state of the A exciton corresponding to the 2s and 3s exciton resonance positions of the A exciton (Supplement 1, Sec. 7).

Although the PL peak and optical shift spectrum of ${{\rm WS}_2}$ are both related to excitons, they have different physical mechanisms. The PL peak mainly reflects the transition from the lowest excited state to the ground state, while the peak of the optical shift spectrum is closely related to the resonant frequency of the dielectric coefficient. Moreover, as the thickness changes, this situation becomes more complex. In some cases, there is a certain misalignment between the PL peak and the peak of the optical shift spectrum of ${{\rm WS}_2}$, as shown in Figs. 3(f)–3(h) and Figs. 4(f)–4(h).

The RVB phase is related to the direction of light propagation, an additional phase resulting from a change in propagation direction due to reflection of light at the ${{\rm WS}_2}$ dielectric partition interface. Due to the exciton effect, which facilitates the interaction of light with matter, and the conversion efficiency of spin and orbital angular momentum, a distinct peak and valley structure appears within the IF shift spectrum at the exciton position. Unlike the orbital angular momentum in classical mechanics, the orbital angular momentum of light is related to the spatial distribution of the light field, which is specifically classified into intrinsic orbital angular momentum (IOAM) and extrinsic orbital angular momentum (EOAM). The intrinsic orbital angular momentum of light has nothing to do with the choice of the coordinates of the spatial distribution of the light field and is only related to the helical phase wavefront. The extrinsic orbital angular momentum of light is related to the choice of the coordinate origin and is similar to the particle orbital angular momentum, which is equal to the position vector of the center of gravity of the light beam and the forked multiplication of the momentum, and the propagation path of the light is related. Therefore, what we call orbital angular momentum refers to the external orbital angular momentum of light, and the exciton effect affects the conversion efficiency of the external orbital angular momentum. From Figs. 4(b)–4(d) we can see more intuitively that the IF shifts vary significantly near the exciton position. The exciton nature and thickness of ${{\rm WS}_2}$ significantly affect the conversion of spin angular momentum to orbital angular momentum of photons, providing a new way to manipulate the RVB phase.

D. Optical Shift Spectroscopy in van der Waals Heterostructure

These optical shift phenomena can be highly dependent on the interfacial structure. Since the thickness of 2D materials is essentially smaller than the wavelength of light, complex interfacial structures can be formed by van der Waals interactions, and when ${{\rm WS}_2}$ is overlaid with different 2D materials [as depicted in Fig. 5(a)], its optical shift spectrum may undergo substantial changes. Therefore, we theorized how the air layer, graphene layer, and boron nitride layer affect the optical shift spectrum of ${{\rm WS}_2}$ (see Supplement 1, Sec. 9). Here we investigated the effect of graphene on the GH shift spectrum of ${{\rm WS}_2}$.

The optical image of graphene-${{\rm WS}_2}$ (${\rm Gr} \text{-} {{\rm WS}_2}$) and atomic force microscopy (AFM) images of graphene are shown in Fig. 5(b). The other optical images, Raman spectra, and AFM images of ${\rm Gr} \text{-} {{\rm WS}_2}$ are shown in Supplement 1, Sec. 10. From Figs. 5(d)–5(i), it is obvious that the dispersion of the optical shift spectra of the ${\rm Gr} \text{-} {{\rm WS}_2}$ van der Waals heterostructure is much improved as compared with the individual graphene and ${{\rm WS}_2}$. As the thickness of graphene increases, significant changes and enhancements in the optical shift spectral structure can be observed in the A-exciton region of ${{\rm WS}_2}$, especially for monolayer ${{\rm WS}_2}$. Figure 5(c) shows the peak valley difference of optical shift ${\Delta _{{\rm GH}}}$ at the A-exciton position when the monolayer ${{\rm WS}_2}$ is covered with graphene of different thicknesses. Both the simulation and experimental results show that when the thickness of graphene exceeds 10 nm, the optical shift spectral characteristics of exciton A are enhanced by more than an order of magnitude.

Referring to Eq. (2), the GH shift depends on the partial differential of the phase $\varphi$ with respect to the incident angle ${\theta _0}$. We calculate the term related to the partial differentiation of the phase to incident angle ($\frac{{\partial {\varphi ^s}}}{{\partial {\theta _0}}} - \frac{{\partial {\varphi ^p}}}{{\partial {\theta _0}}}$) for different thicknesses of ${\rm Gr} \text{-} {{\rm WS}_2}$ (see Supplement 1, Sec. 11). As can be seen, the addition of graphene increased the partial differential of the phase with respect to the incident angle, which in turn increased the dispersion of optical shift.

 

Fig. 6. ${{\rm WS}_2}$ and ${h}$-BN van der Waals heterostructure GH shift spectroscopy sensing model platform. (a) Sensing model platform. (b) Characteristics of GH shift spectra with micro-variable refractive indices of gas molecules. (c) Characteristics of the response of GH shift spectra relative to the shift spectra of ${n_3} = 1.0005$ in gas with micro-variable refractive index. (d) Characteristics of the response of ${{\rm WS}_2}$ with a thickness of 5 nm and ${ h}$-BN with a thickness of 40 nm GH shift spectra relative to the shift spectra of ${n_3} = 1.0005$ in gas with micro-variable refractive index. (e) Sensor based on GH shift spectra.

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The ${\rm Gr} \text{-} {{\rm WS}_2}$ experiments also show that the GH shift peak with monolayer ${{\rm WS}_2}$ displayed a specific redshift in comparison to theory [Fig. 5(g)], and the redshift steadily decreased with the increase of ${{\rm WS}_2}$ thickness [Fig. 5(h)]. In the 3 nm thick ${{\rm WS}_2}$ [as depicted in Fig. 5(i)], the calculated and experimental peaks match well, and the multilayer ${{\rm WS}_2}$ experiment did not show any peak shift in comparison to theory. This is due to the calculation’s limited consideration of the two materials in films with differing properties, which ignores the impact of the electron band structures of TMDC materials on the dielectric screening effect of graphene. The observed small redshift in the optical shift spectrum $t$ could be the result of charge transfer from ${{\rm WS}_2}$ to graphene induced by the existence of graphene surface states. When ${{\rm WS}_2}$’s electron–hole pair complex is broken, the shift peak moves in the direction of lower energy. This impact becomes less noticeable as the ${{\rm WS}_2}$ thickness rises. The presented redshift is consistent with the reported redshifts in the PL and transmission spectra [36]. In 2D materials, Coulomb interactions between charge carriers can influence the bandgap and exciton binding energy. The electron bandgap and exciton binding energy are modified as a result of the dielectric environment changing when graphene reaches the thin film ${{\rm WS}_2}$ environment, which causes the observed redshift of the exciton peak.

For absorption and fluorescence spectra, when ${{\rm WS}_2}$ was covered by graphene, the spectral characteristics are obviously weakened (see Supplement 1, Sec. 12). This is also a distinguishing feature of optical shift spectroscopy, which differs from absorption and fluorescence spectroscopy. This feature makes optical shift spectroscopy more suitable for studying the exciton effect of van der Waals heterostructures. At the same time, the enhanced dispersion in the van der Waals heterostructure makes optical shifts more suitable for the applications in sensing and other fields.

The combination of optical sensors and two-dimensional materials demonstrates the advantages of high sensitivity and high performance that are not available with conventional sensors. Based on this, we propose shift spectroscopy for gas sensing detection due to the large specific surface area of 2D materials, their gas compatibility, and suitability for high level surface interactions with gas molecules. First, we constructed a gas sensing model platform using optical shift spectroscopy combined with ${{\rm WS}_2}$ and hexagonal boron nitride (${h}$-BN) to form a gas sensing model. The working principle is to detect the change of refractive index of gas molecules in the environment by using optical shift. As shown in Fig. 6(a), the gas sensor platform consists of a single layer of ${{\rm WS}_2}$ and a 40 nm thick ${ h}$-BN with an incident angle of 41°. We analyze the GH shift spectra by calculating the refractive index changes of gas molecules in the environment. In the simulations of refractive index sensing, we take into account the magnification of the optical shift spectroscopy device. When the refractive index change value of the gas is set to ${\sim}{0.001}$, the shift magnitude near the A exciton and the overall trend show a significant change [Fig. 6(b)]. In order to more clearly show the influence of the refractive index change on the shift spectroscopy, we took ${n_3} = 1.0005$ as the basis to calculate the shift spectroscopy change of other refractive indices (${\delta _{\rm{GH}}} = {\rm GH}\text{-}{\rm SHIFT}_{n3}- {\rm GH}\text{-}{\rm SHIFT}_{n3=1.0005}$) [Fig. 6(c)], so that the refractive index change of the gas can be more clearly reflected by the shift spectroscopy change. We focus on the sensitivity of three wavelengths near the A exciton, each of which has a different sensitivity. Compared with a single-wavelength shift sensor, the shift spectroscopy has more samples to analyze, and the overall change trend of the spectroscopy can more accurately reflect the change in refractive index. In order to improve the resolution of the sensor, the platform consists of ${{\rm WS}_2}$ with a thickness of 5 nm and ${ h}$-BN with a thickness of 40 nm, with an angle of incidence of 41°. As shown in Fig. 6(d), it is clear that changes in the shift spectrum can more clearly reflect changes in the refractive index of the gas. With a sensitivity of 4 nm, our optical shift spectroscopy measurement technology enables ultra-high resolution of $1.26 \times {10^{- 7}}\;{\rm RIU}$ [Fig. 6(e)], combined with easy modification and adsorption properties of two-dimensional material surfaces. It is well suited for the detection of gas and specific receptor proteins. The platform exhibits versatile applications in facilitating fast chemical reaction processes. Notably, numerous chemical reactions generate gases as byproducts. By detecting the type and concentration of these gases, sensors enable monitoring the reaction’s progress and direction. Additionally, certain chemical reactions induce variations in solution conductivity, subsequently altering the overall refractive index. Sensors can effectively capture this refractive index change, aiding in the determination of ion concentration fluctuations within the reaction. However, it is important to acknowledge certain limitations, such as extended measurement time, which may pose challenges in monitoring real-time dynamic changes in refractive index when conducting measurements at multiple wavelengths.

4. CONCLUSIONS

We present a platform for micro-area measurements of optical shift spectra of 2D materials. With the help of the optical shift platform, for the first time, we measured the GH and IF shift spectra of ${{\rm WS}_2}$ with different thicknesses. It can be found that there are distinct peaks and valleys in the optical shift spectra of ${{\rm WS}_2}$, which correspond to the excitonic effect of the material. More importantly, the characteristics of the optical shift spectrum can undergo strong changes through the coverage of the dielectric layer and changes in the dielectric environment. By stacking graphene, we found that the characteristic structure in the optical shift spectrum of ${{\rm WS}_2}$ was strongly enhanced. Furthermore, because of its physical nature, optical shift spectroscopy exhibits spectral characteristics closely related to the interface structure at the subnanometer scale, which is different from traditional spectroscopies such as absorption, reflection, and fluorescence. The enhanced dispersion in van der Waals heterostructure makes optical shifts suitable to the applications in sensing and other fields. Our analysis shows that the sensor based on the overall change trend of the spectroscopy can more accurately reflect the change in refractive index and can be well suited for the detection of specific receptor proteins. Optical shift spectroscopy may open up a new perspective for material structure research and the application in nanophotonics, especially for two-dimensional materials.