# Routing valley exciton emission of a WS2 monolayer via delocalized Bloch modes of in-plane inversion-symmetry-broken photonic crystal slabs

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Aug 21, 2020

To demonstrate the existence of opposite circularly polarized states in momentum space, we designed an in-plane inversion-symmetry-broken PhC slab and studied the transmittance spectra in theory and experiment, as shown in Fig. 2. The slabs here are made of silicon nitride (Si3N4, refractive index 2) and silicon dioxide (SiO2, refractive index 1.5). The thickness of the Si3N4 layer is 150 nm. The thickness of the SiO2 layer is 500 microns, which could be considered infinite compared to the wavelength of visible light. Square lattices of holes with a period a = 390 nm are etched in the Si3N4 layer. To break the in-plane inversion symmetry, the shape of the etched hole in a unit cell is set as an isosceles triangle, with the height h and baseline length b of the triangle being equal (h = d = 250 nm), as shown in Fig. 2a. More details about the sample design can be found in Supplementary Material section 3.

We first simulated the angle-resolved transmittance spectra under σ+-polarized incidence by Rigorous Coupled Wave Analysis (RCWA), with the incidence plane along the Γ-X direction. The spectra are asymmetric, and there are some diminished regions on the photonic bands, indicated by blue arrows in Fig. 2b. These diminished regions correspond to the nonexcited states under σ+-polarized incidence. Hence, those states in the diminished regions are σ polarized. Changing the incident light to σ polarization, the diminished regions switch to the other side (Fig. S1b). To show this effect experimentally, we fabricated samples using electron-beam lithography and reactive ion etching (for more details, see Methods). By using a homemade polarization-resolved momentum-space imaging spectroscopy system (Fig. S4), angle-resolved transmittance spectra are measured (Fig. 2c), in accordance with the simulation. Both the simulated and experimentally measured results confirmed the appearance of optical modes with a high degree of circular polarization in our designed PhC slab. For comparison, we also researched the angle-resolved transmittance spectra of the PhC slab with in-plane inversion symmetry. Shown in Fig. 2d, the designed shape of the etched hole in the unit is a circle (diameter d = 210 nm). As expected, we did not observe asymmetric spectra under σ+-polarized incidence in either the simulation or experiment, as shown in Fig. 2e, f. When changing the incidence to σ polarization, the transmittance spectra are the same as those in the case of σ+ polarization (Fig. S1c). The results demonstrate that by breaking the in-plane inversion symmetry of PhC slabs, circularly polarized states emerge in photonic bands.

The large area of the WS2 monolayer is grown on a Si/SiO2 substrate by the CVD process and then transferred onto PhC slabs. Both PhC slabs and part of the unstructured flat Si3N4 substrate are covered (Fig. S10). To study the PL distribution in the far field, angle-resolved PL spectra are measured (Supplementary Material section 5), as shown in Fig. 3a–f. The detection plane is along the Γ-X direction, in accordance with the transmittance spectra measurement in Fig. 2. We selected σ+) PL by placing a quarter-wave plate and a linear polarizer in the detection path (Fig. S4). Figure 3e, f shows the asymmetric σ+) PL spectra of the WS2 monolayer on the PhC slab without in-plane inversion symmetry. The σ+) PL enhanced regions correspond to regions with a high degree of σ+) polarization in photonic bands. Figure 3a, b shows σ+) PL spectra of the WS2 monolayer on a flat substrate. Figure 3c, d shows σ+) PL spectra of the WS2 monolayer on the PhC slab with in-plane inversion symmetry. Different from those in Fig. 3e, f, all spectra in Fig. 3a–d are symmetric for both σ+ and σ detection. From the abovementioned experimental results, we can draw the conclusion that, as shown in the asymmetric spectra, valley photons emitted by the WS2 monolayer have been separated in the far field by PhC slabs without in-plane inversion symmetry. In addition, we performed time-resolved PL measurements at room temperature (Supplementary Material section 10). Compared with that for the WS2 monolayer on a flat substrate, the exciton radiative rate, namely, the reciprocal of radiative lifetime, is enhanced by 75% when the WS2 monolayer is on a PhC slab without in-plane inversion symmetry.

To further study the degree of separation in Fig. 3e, f, we plotted the angle-resolved σ+) PL spectra for a single wavelength, as shown in Fig. 3g, h. The dotted line refers to 615 nm, and the solid line refers to 628 nm, which are also marked in Fig. 3e, f. We observed that σ+ (red) and σ (blue) PL maximums separately appear at different angles. The σ+ and σ PL peaks are separated by nearly 6 degrees at 615 nm and 3 degrees at 628 nm. For comparison, PL spectra on a PhC with in-plane inversion symmetry for corresponding wavelengths are shown in Fig. S5, with the σ+ and σ PL maximums overlapping at the same angle. We also show that the photoluminescence of the WS2 monolayer on this PhC slab without in-plane inversion symmetry is highly directional. As shown in Fig. 3g, h, the full width at half maximum of the PL peaks (∆θ) is less than 3 degrees at 615 nm and 2 degrees at 628 nm. This result is due to the delocalized property of Bloch modes, leading to the long-distance spatial coherence property of the far-field emission by the WS2 monolayer on PhC slabs. According to the Fourier relation between momentum and position, a wide distribution in the real space means that the mode is localized inside a small area in the momentum space. This effect corresponds to the small angle distribution of the far-field emission, i.e., the directional emission, and will be further discussed later in this article. For this reason, although the separation of σ+ and σ PL peaks is small, the valley exciton emission could still be efficiently separated in the far field. Further, we quantify the degree of valley polarization by

$$Pleft( theta right) = frac{{I_ + left( theta right) – I_ – (theta )}}{{I_ + left( theta right) + I_ – (theta )}}$$

where I+ (I) refers to the PL intensity with σ+) polarization for a single wavelength, and θ is the radiation angle. The degree of valley polarization is plotted in Fig. S7, with the maximum degree of valley polarization calculated up to 84%. These results indicate that the PL of the WS2 monolayer on the PhC slab without in-plane inversion symmetry is highly directional and has a high degree of valley polarization.

Based on the measured angle-resolved σ+) PL spectra of the WS2 monolayer on the PhC slab without in-plane inversion symmetry, we mapped the PL intensity distribution of a single wavelength in momentum space, as shown in Fig. 4a–d. The upper (lower) row corresponds to 615 (628) nm. The PL spectra along different directions in momentum space were measured by rotating the sample in-plane relative to the entrance slit of the imaging spectrometer. The projected momentum k is calculated by k = k0sinθ (k0 = 2π is the wavevector of light in the free space, θ is the emission angle relative to normal of the sample plane). The intensity distribution of σ+) PL in momentum space confirmed that the PhC slab without in-plane inversion symmetry leads to directional valley exciton emission.

Then, we used P(k) to qualify the degree of valley polarization in momentum space, which is similarly defined by (Pleft( k right) = frac{{I_ + left( k right) – I_ – (k)}}{{I_ + left( k right) + I_ – (k)}}), as shown in Fig. 4e, f. Here, I+ (I) refers to the PL intensity with σ+) polarization for a single wavelength. Experimentally, the maximum calculated P reaches 88%, as shown in Fig. 4f. Note that the maximum P did not appear along the Γ-X direction in momentum space. The result is as expected because the circular polarized states of the designed PhC slab without in-plane inversion symmetry are slightly shifted from the Γ-X direction in momentum space40. The sign of P(k) reverses at opposite sides of the momentum space, demonstrating the separation of valley exciton emission with different chiralities. In contrast, we also measured and calculated P(k) of the emission by a WS2 monolayer placed on a flat substrate, and P(k) was negligible (Fig. S12).

In addition to valley-related directional emission in momentum space, we expected the spatial coherence property of emission by the WS2 monolayer on the PhC slab without in-plane inversion symmetry. Young’s double-slit experiments were performed, as shown in Fig. 5. The experimental setup is illustrated in Fig. 5a, and the working principle is based on Fourier transformation. The double slit is mounted on the real image plane inside the optical measurement setup to select radiation fields from two different positions on the sample. The radiation fields from these two positions intersect with each other on Fourier image 2 at the entrance of the spectrometer. Therefore, the spatial coherence properties on the surface of the sample could be directly detected in the far field. Changing the etched depth of the PhC slab, we were able to overlap the measured photonic band with the PL spectra of the WS2 monolayer to obtain enough signal intensity. Interference fringes are observed in the angle-resolved PL spectra along the Γ-X direction, as shown in Fig. 5b. The red-marked line is further plotted in Fig. 5c, showing the interference intensity distribution at 621 nm. The fringe visibility V is calculated to be ~50%, defined by (V = frac{{I_{{mathrm{max}}} – I_{{mathrm{min}}}}}{{I_{{mathrm{max}}} + I_{{mathrm{min}}}}}), where Imax and Imin are the intensities of adjacent maximums and minimums49. In this measurement, the real double-slit distance d is 120 microns. The scanning electron microscopy image of the double slit is presented in Fig. S13. The magnification of the real image is 20, so the effective double-slit distance on the sample is 6 microns. The 6-micron effective double-slit distance is almost ten times the emission wavelength, demonstrating that the measured spatial coherence length is larger than 6 microns. Moreover, the spatial coherence length could be calculated by (frac{lambda }{{{Delta}theta }}) in theory, which is widely used in optical coherence theory50. Here, ∆θ is ~0.0215 (1.23 degrees) at 621 nm (Fig. S14), and the calculated spatial coherence length is ~29 microns. In comparison, no interference fringes are observed when the WS2 monolayer is placed on a flat substrate, as shown in Fig. 5b, c. This result means that the far-field emission of the WS2 monolayer on a flat substrate has no long-distance spatial coherence property. Hence, we reveal that the far-field emission by the WS2 monolayer on the PhC slab without in-plane inversion symmetry has a long-distance spatial coherence property. This property of the PhC slab extends the coherence control on the PL of the WS2 monolayer from temporal coherence to spatial coherence.

In summary, we proposed in-plane inversion-symmetry-broken all-dielectric photonic crystal slabs to route valley exciton emission of a WS2 monolayer in the far field at room temperature. By breaking the in-plane inversion symmetry of the PhC slab, we observed paired circularly polarized states with different chiralities emerge from vortex singularities. Via coupling with those delocalized Bloch modes, valley photons emitted by the WS2 monolayer were separated in momentum space, and the exciton radiative rate was significantly enhanced. In addition, both the directional emission and the long-distance spatial coherence property benefit the applications of in-plane inversion-symmetry-broken PhC slabs to route valley exciton emission. In addition, our method could be extended to manipulate valley exciton emission of other TMDC monolayers. The ability of these PhC slabs to transport valley information from the near field to the far field would help to develop photonic devices based on valleytronics.