Direct observation of unidirectional exciton polaritons in layered van der Waals semiconductors

doi:10.21203/rs.3.rs-3752149/v1

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Direct observation of unidirectional exciton polaritons in layered van der Waals semiconductors

https://doi.org/10.21203/rs.3.rs-3752149/v1

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Unidirectional excitation of highly confined guided modes is essential for nanoscale energy transport, photonic integrated devices, and quantum information processing. Among various feasible approaches, the mechanism based on optical spin-orbit coupling has been investigated for unidirectional routing of surface plasmons and valley exciton polaritons, without exploiting the complicate magneto-optical effects and parity symmetry breaking. So far, the direct nanoimaging of such exotic polaritonic modes in near fields has remained elusive. Here, we report the real-space nanoimaging of unidirectional exciton-polariton in van der Waals semiconductors. We couple photonic spins into the tip of a scattering-type scanning near-field optical microscopy for circular dipolar excitations of spin-orbit interactions, thus enabling the unidirectional exciton propagation (with remarkable ratio of unidirectionality R=3.44 for TM mode). Via switching to the opposite helicities, we observe the reversed opposite directions. Our work offers a promising avenue for detecting and processing spin information for future communication technology at the nanoscale.

Physical sciences/Optics and photonics/Optical physics/Nanophotonics and plasmonics

Physical sciences/Nanoscience and technology/Other nanotechnology

Spin-orbit coupling (SOC) is important in electronics, quantum mechanics and nanophotonics (1–4). For example, spin Hall effect as the relativistic SOC phenomena can allow the separation of charges of opposite spins in an electric bias without a magnetic field (5–7), enabling next-generation nanoelectronic devices such as spintronics (8). This breakthrough has been extended to optics and photonics in past two decades. Through the photonic SOC (9), the unidirectional excitation of optical guided modes via spin excitations is reported. Specifically, the circularly polarized dipolar emissions coupled to a guided mode can lead to robust one-to-one relation between the spin of dipolar source and the propagation direction of the mode (10, 11), without exploiting a magnetic field or the parity-symmetry breaking (12). These unidirectional excitation of guide modes provide opportunities for various on-chip optoelectronic technologies and spintronic devices.

Particularly, polaritons – hybrid photon and matter excitations – are one kind of typical modes with transverse spins and have shown great promise to control light at the nanoscale over spectral regions ranging from the visible to the terahertz (13–17). Recently, unidirectional excitation of plasmons through controlling photonic SOC was demonstrated in a metal film with a nano-slit (10). Via hybridization of such plasmonic mode to excitons from transition metal dichalcogenides (TMDs), the spatial separation of valley excitons was reported, allowing the probe of valley degree of freedoms (18–20). Through a nanoantenna (21) or grating coupler (10) at the end of the waveguide (or the edge of a metal film) to couple these polaritons to far field, one can experimentally measure the intensity contrast from different exits of modes, thus obtaining the signature of unidirectional propagations of polaritons. So far, there is no real-space direct experimental mapping of such unidirectional features. The major challenges include the simultaneous generations of SOC and the nanoscale imaging of the mode at the material’s interface.

Here, we report the near-field mapping of unidirectional exciton polaritons (EP) in layered TMD semiconductors induced by the SOC effect. The layered TMD semiconductors host strongly bound excitons (22–24) and the optical waveguide mode, where EPs are formed due to the strong coupling between excitons and waveguide photons. The waveguide EP can transport over long distance, promising future nanophotonic circuits (25–31). To probe and achieve unidirectional excitation of these waveguide EPs, we used a scattering-type scanning near-field optical microscopy (s-SNOM) that is illuminated by a circularly polarized laser. The laser is incident at 60° onto the sharp atomic force microscope (AFM) tip, inducing the generally elliptically polarized dipolar excitations of waveguide EPs and hence the SOC-enabled unidirectional propagations. Using the s-SNOM system, we visualize the wavefront profiles of unidirectional EPs in real space at the same time, along with our calibration method based on the symmetry of transverse electric (TE) mode. Our finding exemplifies a generalizable framework for real-space imaging and spin-controlled directional excitation of polaritons in many other van der Waals (vdW) materials and polar dielectrics (14, 16).

As shown in Fig. 1a, WS₂ thin flakes are exfoliated onto standard SiO₂/Si wafers. We use the oblique illumination of the He-Ne laser with circular polarization (λ₀ = 632.8 nm), which is close to the low energy branch of EP in WS₂ waveguides we used in the following experiments (32). With SOC, we anticipate the unidirectional propagation of EPs, originating from the high-spatial-frequency radiations asymmetrically coupled into the waveguide modes.

For better understanding of SOC here, we examine the waveguide modes first. The dielectric WS₂ nanoflakes is uniaxial with the optic axis along z direction. The Air/WS₂/SiO₂ three-layer structure exhibits ordinary (TE) and extraordinary (transverse magnetic, TM) waveguide modes (28). The associated in-plane modal wavevectors are shown in Fig. 1b where the thickness of WS₂ nanoflake varies. For thin flakes (d < 30 nm), only the fundamental TE₀ mode is supported, while for thicker WS₂ flakes (d > 50 nm), more waveguide modes, particularly the extraordinary TM modes, can be observed with the increasing in-plane momentum as the thickness increases.

In our experiments to map the SOC, distinguishing those TE and TM modes from the viewpoint of the near-field modal symmetry is important, for both the calibration and the SOC feature extraction. For this purpose, we consider the elliptical dipolar excitations. As for a dipole (p_x,0,p_z) polarized perpendicularly to the dielectric slab, TM modes can be induced and the electric field distribution shows significant asymmetric spatial frequency, which drives the TM modes of the dielectric slab to propagate unidirectionally. By decomposing the electric field of dipole into TM modes with in-plane momentum (k_x,k_y) as E_z(x,y,z) = ∫${\stackrel{\sim}{E}}_{z}$(k_x,k_y,z)e^i(k_x^x+k_y^y)dk_xdk_y, the unidirectional property of the TM modes propagating along x axis (k_y = 0) is shown as:

$${\tilde {E}_z}({k_x},z)= - \frac{{ic}}{{8{\pi ^2}\omega \varepsilon }}\frac{{ \mp {k_x}{k_z}{p_x}+k_{x}^{2}{p_z}}}{{{k_z}}}{e^{i{k_z}|z - {z_{{\text{dipole}}}}|}}$$

where k_z = (k₀² - k_x²)^1/2 is the wavevector along z axis, ω is the angular frequency and k₀ = ω/c. Due to the vertical circularly polarized dipole is composed by two orthogonal dipole orientations p_x and p_z, the linear superposition of these two components results in an asymmetric distribution while the p_z component has even parity and the p_x component shows odd parity about k_x (see Supplementary Information, Section S1). For example, as illustrated in Fig. 1c and 1d, numerical simulations demonstrate that the TM₀ mode is allowed in a WS₂ slab with the thickness of 62 nm and it exhibits unidirectional propagation, which depends on the chirality of illumination.

Importantly, we should note that the WS₂ flake also support TE modes. Owing to the oblique illumination of the circularly polarized laser, the modulation from the apex of AFM deviates the circularly polarized dipole elliptically for both the horizontal and the vertical components. The horizontal components could generate an in-plane circular polarized dipole (p_x, p_y,0). When such an in-plane circular polarized dipole placed parallel to the dielectric nanoflake, TE modes can be excited and their magnitudes are independent to the circularly polarized state of the dipole. After similar process above, TE modes expansion can be expressed as E_y(x,y,z) = ∫${\stackrel{\sim}{E}}_{y}$(k_x,k_y,z)e^i(kxx+kyy)dk_xdk_y, where

$${\tilde {E}_y}({k_x},z)= - \frac{{ic}}{{8{\pi ^2}\omega \varepsilon }}\frac{{k_{x}^{2} \pm k_{z}^{2}}}{{{k_z}}}{p_y}{e^{i{k_z}|z - {z_{{\text{dipole}}}}|}}$$

The electric field shows symmetric spatial frequency distribution, and it results in the TE modes propagating in the dielectric flake only have a π/2 phase difference between opposite chirality. Corresponding numerical simulations are performed in a 10 nm-thick WS₂ slab, which only supports TE₀ mode and the symmetric field distributions of TE modes for opposite horizontal chirality component (p_x, p_y,0) are demonstrated in Fig. 1e and 1f.

To quantitively characterize the directionality of the modes, based on Eq. (1) and Eq. (2), the ratio of unidirectionality is defined as R = |${\stackrel{\sim}{E}}_{{{\sigma }}^{-}}$(k_x)/${\stackrel{\sim}{E}}_{{{\sigma }}^{+}}$(k_x)|, where ${{\sigma }}^{-}$ denotes the left circular polarized (LCP) state and ${{\sigma }}^{+}$ represents the right circular polarized (RCP) state. As illustrated in Fig. 1g, unidirectionality exhibits negative correlation (k_x>k₀) with the in-plane momentum k_x, where an elliptical polarized dipole with (p_x, p_y, p_z) = (1, 0, -0.3i) is chosen as the illumination based on the experimental condition. For instance, R = 2.23 for TM₀ mode in a 62 nm-thick WS₂ slab, whereas R = 1 for the TE₀ mode in a 10 nm-thick WS₂ slab, showing strong signatures of SOC in EPs. Besides, this distinguished feature can allow us to use the TE mode to calibrate our system, which will be discussed later.

The schematic of the near-field imaging mechanism under circularly polarized illumination is depicted in Fig. 2a. With a circularly polarized incident laser beam, the vertical component of the circular polarization at the tip apex is coupled to the transverse electromagnetic field, resulting in unidirectional propagation of TM waveguide modes. Tip-launched waveguide modes propagate along the WS₂ sample, get scattered to the free space as the edge scattering, and then interfere with field which is directly scattered by the tip, forming the interference fringes. Note that the EPs in our measurement are the result of strong coupling between excitons in WS₂ and waveguide photons confined in Air/WS₂/SiO₂ three-layer structure. Under the RCP illumination and due to SOC, TM₀ EP mode will strongly propagate to x direction while weakly to -x direction (Fig. 2c); however, the TE₀ waveguide mode will be symmetrically launched and independent to RCP or LCP excitation (Fig. 2b). In this manner, if the edge of the WS₂ flake is located along y direction, the detected fringes interfered by the weak stream induced by RCP will be darker than that by the mainstream induced by LCP illumination. This is the first important factor of our experimental near-field observation of polaritonic SOCs in this work.

Besides, to prove the unidirectional propagation of TM₀ EP mode in experiments, we must exclude signal strength difference induced by experimental setup. It is known that the near-field intensity and fringe spacing (in-plane wavevector) of EPs are affected by the incident angle of laser beam as well as the scanning angle (26–28, 31). Under the same experimental conditions, a calibration value ${\delta }_{cv}$ thus can be used to substitute the term of incident angle and scanning angle in calculation ${k}_{\text{E}\text{P}}/{k}_{0}=k/{k}_{0}+{\delta }_{cv}$, where ${k}_{\text{E}\text{P}}$ refers to the theoretical wavevector of exciton polaritons and $k$ is the wavevector obtained by Fourier transforming of experimental near-field signals. The incident angle is $\alpha$= 60° and the angle between the incident laser beam and the sample edge is $\beta$=10°, which remain the same hereinafter. After concentrating the illuminating chiral field to a nanoscale spot at AFM apex, the excited opposite circularly polarized dipoles may have a certain degree of deviation in intensity. According to above theory, near-field signals in TE mode are independent on the circularly polarization state of incident laser. Thus, we can use the TE mode to directly make a calibration, which is the second important factors for our reports here. In following experimental results, a normalized factor R₀ = |${\stackrel{\sim}{E}}_{{{\sigma }}^{-}}$(k_TE)/${\stackrel{\sim}{E}}_{{{\sigma }}^{+}}$(k_TE)| is utilized to rectify the inevitable variations, where ${\stackrel{\sim}{E}}_{{{\sigma }}^{-}}$(k_TE) and ${\stackrel{\sim}{E}}_{{{\sigma }}^{+}}$(k_TE) are spectral amplitude for TE modes under LCP and RCP incidence, respectively.

To experimentally demonstrate the concept, we first imaged a thin WS₂ platelet with a thickness of 7 nm on a SiO₂ substrate, the topography of which is shown in Fig. 2d. In this sample, only TE₀ mode waveguide EPs can be excited (Fig. 1b). With a circularly polarized laser beam illuminating the tip, the launched EPs will propagate away from the tip (Supplementary Information, Section S2). In Figs. 2f and 2h, near-field images of EPs illustrate bright fringes parallel to the edge, showing a typical pattern for waveguide modes. These fringes exhibit similar amplitudes with a phase shift, confirming the theory we provide in Eq. (2).

We further verify the SOC induced unidirectional EP with a WS₂ flake with thickness around 62 nm (Fig. 2e), where lowest-order TM₀ is allowed (Fig. 1b). By illuminating LCP light, from the directional asymmetry calculation in Fig. 1g (R = |${\stackrel{\sim}{E}}_{{{\sigma }}^{-}}$(k_TM)/${\stackrel{\sim}{E}}_{{{\sigma }}^{+}}$(k_TM)| =2.23), the EPs propagating toward -x will be predominately excited than that propagating to the + x direction. Therefore, the amplitude of edge scattering is much greater than the one with RCP incidence, resulting in brighter fringes after interfering with the tip scattering signals. Figures 2g and 2i show the measured near-field amplitude images of EPs under right and left circularly polarized illumination, respectively. Notably, the interference fringe amplitude exhibits an enhancement with the LCP incidence, which verifies the unidirectional excitation of EPs. Such enhancement can be more pronounced in momentum space. As shown in Fig. 3a, we perform Fourier Transform (FT) of real-space signals of Fig. 2f and 2h to resolve the momentum-space EPs excitations. The wavevector of the TE₀ mode is determined to be 1.59k₀ and the FT peak of LCP equals to that of RCP. For a 62 nm-thick WS₂ flake, the corresponding FTs of the near-field image (Fig. 2g, 2i) are shown in Fig. 3b, a fundamental extraordinary mode (TM₀ mode) is observed at k = 1.62k₀. Specifically, the spectral amplitude of TM₀ mode excited by LCP beam is larger than that by RCP incidence with an unidirectionality R = 2.26.

According to the theoretical prediction in Fig. 1g, the unidirectionality R largely depend on the in-plane wavevector of TM EP modes (and hence the thickness of the WS₂). Figure 4a shows simulated thickness-dependent electric field distribution (E_z) of the EPs excited by an RCP dipole placed at 20 nm above the uppermost surface of the WS₂ sample, where counterpropagating waveguide modes are supported. However, owing to the unidirectional excitation, brighter fringes are observed towards + x direction. Figure 4b shows the corresponding FT analysis of the results in Fig. 4a, where the large thickness corresponds to larger wavevector. Here in the simulation, we blocked the uncoupled free-space components of the dipole excitation. Thus, the unidirectionality, i.e. the contrast of those TM EP modes propagating towards + x and -x direction, increases as the thickness of WS₂ increases (see Fig. S1 for circular polarized incidence).

Further, higher-order waveguide mode (TM₁) can be supported when the thickness continues increasing to approximately 110 nm. Here, we perform more experiments on a 125 nm-thick WS₂ flake. These self-hybridized EPs work in the strong coupling regime (33), with Rabi splitting energies (ħΩ) of 101 meV at room temperature (Supplementary Information, Section S8, Fig. S9). For instance, Fig. 4c shows the dispersion color map of an Air/125 nm WS₂/SiO₂ waveguide, where energy-momentum relation of the waveguide modes is constructed. Figures 4e and 4f show the real-space near-field image with LCP and RCP incidence, respectively. As expected, EPs are predominantly excited by LCP incidence (Fig. 4e), whereas weak fringes excited by the RCP incidence is observed (Fig. 4f). As shown in Fig. 4g, the FT peaks correspond to the wavevectors k_TM1 and k_TM0 are 1.56k₀ and 2.26k₀, respectively. The unidirectionality of TM₀ mode is R = 2, while the unidirectionality for TM₁ mode is R = 3.44. This can be explained by the wavevector of TM₀ mode (2.26k₀) is larger than that of TM₁ mode (1.56k₀) at the thickness of 125 nm (Fig. 1c), thus the unidirectionality of TM₀ mode is smaller according to the calculation in Fig. 1g. Furthermore, owing to the factor that the coupling efficiency with the s-SNOM tip apex for TM₁ mode is higher than for TM₁ mode (Supplementary Information, Section S6), the TM₁ mode retains predominate in the measured near-field signal. Our work established a self-consistent method to observe and image the in-plane unidirectional polariton modes in vdW materials.

In summary, we report the direct experimental observation of unidirectional EP modes in TMD semiconductors based on the s-SNOM technique. The observed unidirectional EPs are excited by a mimicked elliptically polarized dipole, which addresses the long-stranding challenges that optical Spin-Hall phenomena only observed via far-field imaging (18, 34). Furthermore, we foresee that based on the ultrafast pump-probe near-field imaging, our technique may open up possibilities of direct visualizing real-space dynamics of optical SOC (30). Our work provides an alternative but more direct approach to uncover the underlying physics of optical SOC as well as the EPs in TMD semiconductors, with possible application in optical switching, nanoscale light manipulation and polarization-based optical information process.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 62375039, 12174047 and 62205049), the Sichuan Province Science and Technology Support Program (Nos. 2020JDRC0006, 2022YFH0082 and 2022YFSY0023), and the National Key Research & Development Program (2021YFE0194200 and 2020YFA0309200). Q.Z. acknowledges the support from the start-up funding of University of Electronic Science and Technology of China. G.H. acknowledges the Nanyang Assistant Professorship Start-up Grant, Ministry of Education (Singapore) under AcRF TIER1 (RG61/23), and National Research Foundation of Singapore through the Competitive Research Program (CRP22-2019-0064).

Author contributions

Y.B., J.Y., and Q.Z., contributed equally to this work. Q.Z., G. H. and J.Y. conceived the idea. J.Y. and Y.B. performed the numerical calculations and full-wave simulations. Y.Z. fabricated the samples, Y.B. and J.Y. designed the experiments and performed near-field optical measurements. All authors have analyzed and discussed the results. Y.B., J.Y., G. H. and Q.Z. co-wrote the paper with the input of all authors. G. H. and Y. Y. supervised the project.

Competing interests

The authors declare no competing interests.

Data Availability

All data supporting the findings of this study are available in the main text, Methods or Supplementary Information. The data are also available from the corresponding authors upon reasonable request.

Numerical simulations

The numerical simulations in this work were performed with finite difference time domain method. The dielectric constant of SiO₂ is set as 1.45. For WS₂ at the illuminating wavelength of 632.8 nm, the x and y components of the real part of permittivity is 26.94, the corresponding z component is 6.58. Perfectly matched layers are set as the boundary conditions along x, y and z directions.

Sample fabrication

The chemical-vapor-deposition-grown WS₂ crystals were exfoliated onto heavily doped silicon substrates with a 285 nm SiO₂ layer on top. The WS₂ of various thickness were exfoliated from bulk samples and were measured by AFM.

Near-field nanoimaging

The near-field measurements were performed by using the commercial Bruker s-SNOM, which consists of an AFM setup operated in tapping mode. The resonance frequency and amplitude of the AFM are 277 kHz and 50 nm, respectively. The AFM tips are metal coated (PR-EX-SNM-A). A He-Ne laser with wavelength of 632.8 nm was used as the excitation source. A polarizer and a 1/4 waveplate were used to vary the polarization state of the incidence. The electric field localized around the apex of AFM tip is elliptically polarized by illuminating a circularly polarized light. The near-field signal on WS₂ is scattered by the edge and interferes with tip scattering signal, forming the interference bright fringes. The contribution owing to far-field background scattering is eliminated by modulating signals.

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Direct observation of unidirectional exciton polaritons in layered van der Waals semiconductors

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