1. Introduction

Circularly or elliptically polarized light carries angular momentum in the form of spin or so-called optical spin. For structured light, the distribution and orientation of optical spin can be strongly modified from that of plane waves [1–5]. A striking feature is that the direction of optical spin can be perpendicular to the propagation direction of light, i.e., transverse optical spin [3–10]. In addition, optical spin can be transferred to the direction of the light, i.e. the optical Hall effect. When materials that have an anisotropic optical response to circularly polarized light, such as chiral molecules and spin-polarized/valley-polarized emitters, interact with transverse optical spin, the light–matter interaction is correlated with the direction of the light, which is referred to as chiral interaction [11]. This chiral light–matter interaction has been demonstrated in various systems, such as photonic crystals [12], topological edge states [13], evanescent fields [7,8,14–16], and chiral meta-surfaces [17,18].

Recently, the emergence of transition metal dichalcogenides (TMDs), which are 2D layered semiconductors, has stimulated new research interests in valleytronics [19–23]. Excitons of 2D TMD layers can carry valley pseudospin and interact selectively with circularly polarized light (thus, optical spin) depending on the valley index [22–26]. In contrast to spin states in a conventional semiconductor, two degenerate valley states are spatially separated at the edge of the hexagonal Brillouin zone, thus resulting in robust valley polarization even at room temperature without an external magnetic field [27–29]. For this reason, TMD materials have been widely used to demonstrate chiral valley–photon interactions. There have been successful experimental reports for directional exciton emissions, directional Raman scattering, near-field valley excitations, using various nanophotonic structures such as silver nanowires [16], metamaterials [17,18], and photonic crystals [12]. Chiral valley–photon interaction offers the possibility of the all-optical manipulation of valley pseudospin on a chip.

However, for this implementation, the chiral valley–photon interface should be developed further, especially in relation to valley-selective excitation [30], directional valley detection, and directional valley transport. In particular, for long-range valley transport using chiral interaction, simple structures are preferable to more complicated ones because of the potential fabrication issues for large-area devices. Plasmonic nanowires with transverse optical spin have been of interest due to their benefits of simple fabrication and easy accessibility for integration with TMD layers, but the propagation loss of plasmonic modes is severe, thereby limiting the long-range transport of valley information. Though a dielectric waveguide is expected to provide the same functions as a plasmonic waveguide, valley-dependent directional emission using a dielectric waveguide has yet to be demonstrated.

Here, we demonstrate the long-range directional transport of valley information via valley-dependent directional coupling to dielectric nano- and microwires. The evanescent fields of a dielectric wire have a very robust and homogenous transverse optical spin density and mediate the valley-dependent coupling. The spin-momentum locking of the transverse spin leads to valley-dependent directional coupling to the waveguide. We achieved directional emission of the excitons in a valley to the waveguide at room temperature, and the transferred valley information along the direction of the guided modes was transported over a distance of >10 µm along the waveguide. We also discuss the advantages and disadvantages of dielectric waveguides compared to plasmonic systems as a platform for chiral valley–photon interfaces. There is a clear trade-off between the coupling efficiency and propagation loss, but we confirmed that the proposed dielectric system provides better performance when the transport distance is larger than ∼10 µm. Therefore, the dielectric waveguide system has the potential to play an important role in long-range valley/spin–photon interfaces.

2. Proposed structure

For the experimental demonstration of the chiral valley–photon interaction, we utilized multilayered tungsten disulfide (WS₂) flakes because of their outstanding excitonic properties and robust valley polarization. Although the indirect transition is dominant for multilayers, a multilayered WS₂ also maintains direct bandgap transitions at the K and K’ valleys. The energy of the exciton transitions at the K and K’ valleys remains similar with changes in thickness (e.g. 2.02 eV for a monolayer and ∼1.98 eV for multilayers). Most importantly, the exciton transitions in multilayers exhibit more robust valley polarization compared to that in a monolayer. In multilayered WS₂, the interlayer hopping of excitons is strongly suppressed due to the layer-valley-spin locking effect [27–29]. Consequently, excitons maintain valley pseudospin even in bi- and multilayers. Furthermore, because exciton lifetimes are shorter in multilayers, valley polarization increases as a function of the thickness of the WS₂ layers [16]. Therefore, multilayered WS₂ allows for the robust investigation of the chiral valley–photon interaction at room temperature.

In order to couple valley-polarized excitons in WS₂ layers to transverse optical spin, an optimal candidate for dielectric waveguide structure was investigated. Of the various types of dielectric material, we utilized zinc oxide (ZnO), which has a wide bandgap of ∼3.37 eV. Therefore, there is no band-to-band light absorption in a ZnO medium at the exciton transition wavelength (∼1.98 eV) of multilayered WS₂. High-quality ZnO nano- and microwires can be easily synthesized using chemical vapor disposition. The diameter of a synthesized ZnO wire can be large enough to support optical guided modes along the wire, and its length can also be much longer (∼few tens of µm) than other possible types of synthesized wire [31]. Therefore, without the need for complicated nanofabrication processes for the waveguide structure, valley-polarized excitons can be easily coupled to guided modes by deterministically placing a ZnO wire on top of WS₂ layers [Figs. 1(a)–1(b)].

 

Fig. 1. (a and b) Schematic images of the chiral valley–photon interaction. Excitons in multilayered WS₂ show directional emission along ZnO wire depending on the valley index. (c) The emission spectrum from bare multilayered WS₂. Exciton transition at a wavelength of ∼630 nm exhibits a high degree of valley polarization (∼0.7). (d) Optical microscope image of a fabricated sample. (e) Photoluminescence image of a coupled WS₂ layer–ZnO wire system under laser excitation in the middle of the wire. Scattered light at the ends of the wire is coupled emission from the WS₂ layers to the wire. (f) The spectrum of the guided light which was collected at the edge of the ZnO wire.

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3. Numerical simulation

We first conducted a numerical simulation of the chiral valley–photon interaction near a ZnO wire. Because most synthesized ZnO wires have a hexagonal cross-section due to the crystal structure of ZnO, we employed a hexagonal geometry for the wire in calculating the optical guided modes. Figure 2(a) presents a fundamental optical guided mode in a ZnO wire positioned on a glass substrate. The intensity of the mode is highest at the center of the wire and evanescently decays at the wire boundary. The WS₂ layers are positioned at the interface between the ZnO wire and the glass substrate. Because the valley magnetization of the excitons in WS₂ layers follow the ±z-direction for the K and K’ valley index, respectively, the optical spin that excitons couple with should also follow the ±z-direction. In other words, excitons in WS₂ layers emit circularly polarized light with a handedness of ${\sigma ^ + } = {E_x} + i{E_y}$ or ${\sigma ^ - } = {E_x} - i{E_y}$ depending on their valley index. Therefore, we investigated transverse optical spin helically oscillating in the x-y plane (i.e. the plane of the WS₂ layers) that has the same handedness as the excitons in WS₂.

 

Fig. 2. Numerical simulation for guided modes in a ZnO wire. (a) The intensity distribution of a fundamental guided mode in a cross-sectional view (Radius of a hexagonal ZnO wire = 400 nm, Wavelength = 630 nm) (b-e) Calculated transverse optical spin density (degree of circular polarization of Ex and Ey) for the mode propagating in + x (b,d) and –x (c,e) direction, respectively, plotted in the y-z plane or x-y plane. (f) Transverse optical spin density as a function of wavelength (g) Transverse optical spin density for varying diameter of a ZnO wire.

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Figures 2(b) and 2(d) present the calculated transverse optical spin density, ${S_3}/{S_0} = 2Re ({E_x}E_y^\ast )/({|{{E_x}} |^2} + {|{{E_y}} |^2})$[16], for the guided mode propagating in the + x direction, plotted for the cross-section of the wire (the y-z plane) and the position of the WS₂ layers (the x-y plane), respectively. The direction of the transverse optical spin in the evanescent fields is governed by $\overrightarrow S = \overrightarrow k \times \overrightarrow \eta $, where $\overrightarrow k$ and $\overrightarrow \eta $ are the propagation direction and the decay direction of the evanescent fields, respectively. Because we are interested in the optical spin along the z-direction for light propagating in the x-direction, the decay direction of the evanescent fields along the y-axis would determine the handedness of the optical spin in this case. Due to the mirror symmetry of the system with respect to y=0, the evanescent fields on either side of the wire have opposing decaying directions, thus resulting in the opposite handedness of the transverse optical spin for y<0 and y>0. Figures 2(c) and 2(e) display the same simulation results but for the guided mode propagating in the opposite (-x) direction. The transverse optical spin has a one-to-one relationship with the propagation direction of the guided mode due to the time-reversal symmetry of spin. If the propagation direction of the guided mode is switched to the opposite direction, which is a similar situation to the time-reversal operation, the handedness of the transverse optical spin becomes the opposite. This is referred to as the spin-momentum locking of transverse optical spin. Therefore, the results in Figs. 2(c) and 2(e) display exactly the same amplitude but the opposite sign of the transverse spin when compared to the results in Figs. 2(b) and 2(d).

In addition to the handedness of the transverse optical spin, it is also important to note that the amplitude of the transverse optical spin density is very high and uniform near the boundary of the ZnO wire. The maximum transverse optical spin density is ∼0.9, which is comparable to that of a plasmonic nanowire (∼0.95). Figure 2(f) presents the maximum density of the transverse optical spin at the evanescent fields as a function of the wavelength. Although the confinement of the guided fields (or the effective refractive index of the guided mode) varies as a function of the wavelength, the high transverse optical spin density remains almost constant regardless of the wavelength. We also investigated the effect of the radius of the ZnO wire on the transverse spin density of the evanescent fields [Fig. 2(g)]. For a ZnO wire that supports multi-modes with a large diameter, the evanescent fields of all guided modes produce very high optical spin densities. Even though the transverse spin distribution inside the waveguide is sensitive to the mode numbers, the evanescent fields of guided-mode carry robust optical spin densities [30]. In summary, the optical spin density of the evanescent field is not sensitive to the different wavelengths for different waveguide sizes. Although a high value of local transverse optical spin density can be obtained in a various type of nanophotonic structures [12,32,33], the robustness and uniformity of the transverse optical spin for different size of the structure or different wavelength of light are great benefits of evanescent field-based optical spin.

We also directly simulated the radiation of valley-polarized excitons in the WS₂ layers near the ZnO wire. As discussed earlier, as a consequence of the valley-dependent optical selection rule, excitons in WS₂ layers can be considered as a circular dipole. Even for zero valley polarization, i.e. evenly populated excitons in K and K’ valleys, the excitons in each valley emit circularly polarized light. Thus, we positioned a circular dipole near the ZnO nanowire to mimic the emission of a valley-polarized exciton, and the radiation was collected at the ends of the wire to calculate the directional coupling efficiency. Directionality is defined by $({I_L} - {I_R})/({I_L} + {I_R})$, where I_L and ${I_R}$ are the transmitted intensities at the left and right edge of the wire, respectively. The total coupling efficiency, ${I_L} + {I_R}$, represents the coupling strength as a function of the dipole position, which is not related to the handedness of the dipole. The directionality and total coupling efficiency for circular dipoles with opposite handedness and a linear dipole, calculated as a function of its position along the y-direction, are shown in Fig. 3. Due to the time-reversal symmetry and mirror symmetry of transverse optical spin, the emissions of a circular dipole also exhibit mirror symmetry across the wire and the spin-momentum locking effect. The maximum amplitude of the directionality is ∼0.7 and the sign switches for a dipole at the opposite side of the wire. Note that a linearly polarized dipole represents a conventional light–matter interaction, which is characterized by nondirectional emissions.

 

Fig. 3. Numerically simulated directional emission from (a and b) circularly polarized dipole sources and (c) a linearly polarized dipole. The directionality $({I_L} - {I_R})/({I_L} + {I_R})$ of the guided emission at the ends of the ZnO wire is estimated by changing the position of the dipole along the y-direction. The total guided emission ${I_L} + {I_R}$ indicates the coupling efficiency of dipole emission to the ZnO wire.

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4. Experimental demonstration

For the experimental demonstration, chemically synthesized ZnO wires were placed on multilayered WS₂ flakes. The WS₂ flakes were mechanically exfoliated from bulk WS₂ (purchased from 2D Semiconductors) and transferred to a cover glass substrate. Using a circularly polarized laser with a wavelength of 594 nm, excitons were selectively excited in the K or K’ valley depending on the handedness of the excitation laser. The handedness-resolved spectrum for a bare WS₂ flake is shown in Fig. 1(c). The valley polarization of the bare WS₂ flake was about 0.8 at room temperature. A long ZnO wire was selectively stamped on the WS₂ flake using a dry transfer method. An oil immersion lens was utilized for both laser excitation and the efficient collection of scattered light at the ends of the wire. The excitation spot (size ∼1 µm) was scanned across the ZnO wire because transverse optical spin has the opposite handedness depending on its position in relation to the center of the wire. Fluorescence images at the exciton emission wavelength were then taken directly using a cooled CCD camera. In addition to the bright spot that represents the direct emission from the excitation spot, two other bright spots representing the scattered light at the ends of the wire were also visible [Fig. 1(e)]. Figure 1(f) shows the spectrum collected at the edge of the wire. It was confirmed that the guided light along the ZnO wire was mostly from the WS₂ layer. Given that the intensity of the scattered light at the ends is proportional to the intensity of the guided light propagating toward the ends, we estimated the directional emission of the excitons by comparing the intensity between the ends of the wire. Figures 4(a) and 4(b) present the estimated directionality $({I_L} - {I_R})/({I_L} + {I_R})$ plotted as a function of the laser position. They showed apparent anti-symmetric trends in directionality for the valley-selective excitation conditions, with antisymmetric behavior observed for results with opposite handedness or at the opposite side of the wire. The plus or minus sign for the directionality indicates that the emission coupled to the wire propagated mostly to the left or to the right, respectively. As a control experiment, a linearly polarized laser was focused on the WS₂ layer to excite both the K and K’ valleys at the same time. Non-polarized excitons exhibited a relatively constant directionality that was also independent of the laser position across the wire [Fig. 4(c)]. Furthermore, as shown in Figs. 4(d)–4(f), the indirect emission at a wavelength of ∼800 nm did not exhibit any directional characteristics because the indirect transition interacts with randomly polarized light. The non-directional emission for the indirect bandgap transition represents direct evidence that the directional emission that we measured for the valley-polarized excitons in Figs. 4(a)–4(d) was not caused by the directional coupling of the laser light but represented the directional emission of valley-polarized excitons themselves.

 

Fig. 4. Experimentally measured directional emission from WS₂ layers in a ZnO wire under various excitation conditions. (a and b) Directional emission from valley-polarized excitons under circularly polarized laser excitation. (c) Nondirectional emission from excitons excited by a linearly polarized laser. (d-f) Nondirectional emission from an indirect bandgap that does not have valley/spin-dependent optical-selection rules.

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For quantitative analysis, we fitted the experimental data with the simulated results. The main differences between the experimental data and the FDTD modeling presented in Fig. 3 are the finite valley polarization and the finite size of the excitation laser spot, rather than a perfect single circular dipole at a defined position. In order to consider the finite size of the excitation spot, the simulated directionality from a point circular dipole source was convoluted with a point-spread function (PSF) for the laser spot as follows [16]:

Here ${\kappa _{tot}}$, ${D_0}$, and $\rho$ are the overall coupling strength, directionality, and background noise, respectively. The effect of the finite valley polarization (P_V) of the excitons in the WS₂ flake was also included. As shown by the gray lines in Fig. 4, the convoluted results fit the experimental results well, indicating that the experimentally observed valley-photon directional coupling had a maximum directionality that was as high as ∼0.7 for a single exciton.

5. Discussion

As we experimentally confirmed, the valley information in WS₂ layers was transferred to the directional information of guided light. Note that, when valley-polarized excitons are coupled to the transverse optical spin of the waveguide, the guided emission along the wire loses the handedness of the light soon after but it still carries valley information via translational momentum. For this reason, the scattered light at the ends of the waveguide exhibits linear polarization. This can be understood in terms of the spin–orbit coupling of light; the spin momentum of transverse optical spin is transferred to the orbital momentum of light (i.e. the translational momentum with respect to the reference position, which is the position of the dipole).

We also note that a nonzero off-set in measured directionality, in other words, the nonzero directionality at the center of the nanowire, can originate from differences in propagation loss, propagation length, or scattering efficiency that guided emissions propagating in opposite directions might experience. We investigated directional emission as a function of the excitation position along the wire, as presented in Fig. 5(a). Differences in the position of excited excitons lead to an asymmetric propagation distance for the guided emissions propagating to the left and right, which changes the off-set value of directionality but the contrast in directionality (${D_{\max }} - {D_{\min }}$) and total intensity remain constant. We note that the non-zero offset value can originate not only from differences in propagation loss but also from differences in propagation length or scattering efficiency that guided emissions propagating in opposite directions might experience.

 

Fig. 5. (a) Measured directionality of valley polarized exciton for various excitation positions along the wire. Δx indicates a relative position from x=0. (b) Experimentally measured propagation length of ZnO waveguide modes. The estimated propagation length of the ZnO wire is ∼16 µm. (c) The simulated intensity of guided emission as a function of propagation distance along a ZnO wire or a silver wire. (d) Effect of length and scattering efficiency of a ZnO wire on the directionality of scattered light. The original directionality of a single circular dipole was set to be 0.9.

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There are several important advantages and disadvantages to the use of dielectric nanowires compared to plasmonic nanowires for chiral interaction. Transverse optical spin densities are high and very robust in both dielectric and plasmonic systems because transverse optical spin is generated due to the evanescent nature at the boundary of the structures. However, in a plasmonic system, the electric fields of a plasmonic guided mode are highest at the boundary of the metallic structure in which the highest transverse optical spin exists. This results in a very high valley directional coupling efficiency. For a dielectric waveguide, the intensity of the electric fields at the position of the transverse optical spin that we are interested in is not as high as in a plasmonic system. Therefore, the coupled light from the excitons in a WS2 layer to the dielectric waveguide is much lower compared to the plasmonic system. However, because of the ohmic losses of the plasmonic structure, a dielectric waveguide is essential for the long-range propagation of light.

To determine the propagation length of the ZnO-guided modes used in this study, we investigated the scattered intensity as a function of the propagation distance. As shown in Fig. 5(b), a propagation length of ∼16 µm was observed for the ZnO wire at the exciton transition wavelength. It is known that silver nanowires used for the previous valley–photon interactions have a very short propagation length of less than ∼2 µm. Thus, there is a clear trade-off between the coupling strength and propagation distance when selecting a waveguide material for a chiral valley–photon interface. In order to investigate the effect of this trade-off, we theoretically compared the power transmitted from the dipole source to the ends of both plasmonic and dielectric waveguides as a function of the propagation distance. As shown in Fig. 5(c), the low propagation loss of the dielectric waveguide starts to make up for the low coupling strength when the travel distance is larger than 10 µm. This suggests that a ZnO wire is more efficient than a silver wire for use as a long-range chiral valley–photon interface. It should be noted that a long propagation length for the guided modes also affects the measured directionality. A proportion of the light reflected at the edges of the waveguide will propagate in the opposite direction and disrupt the experimentally estimated directionality. We derived a simple formula for the final directionality after multiple reflections at the edges;

6. Conclusion

We demonstrated directional emission from valley polarized WS2 layers to a ZnO wire. Any size of ZnO wire accompanies robust spin-momentum locked transverse optical spin near the boundary. As a result of chiral interaction near a ZnO wire, the direction of emitted light from excitons refers to valley information in WS₂ layers. The directional emission is transmitted over a long distance of 10-15 µm along the wire. We confirmed that the use of a dielectric waveguide is certainly important for the long-range directional transport of valley information. Dielectric waveguide systems would be the simplest and practical platform for chiral valley-photon interface because of their robustness for transverse optical spin and a low propagation loss of guided modes. We also note that a dielectric waveguide should also be utilized for the spin polarized quantum emitter, to realize a long-range quantum spin-photon interface for quantum information science applications.