Out-of-plane trion emission in monolayer WSe2 revealed by whispering gallery modes of dielectric microresonators

The manipulation of light emitted by two-dimensional semiconductors grounds forthcoming technologies in the field of on-chip communications. However, these technologies require from the so elusive out-of-plane photon sources to achieve an efficient coupling of radiated light into planar devices. Here we propose a versatile spectroscopic method that enables the identification of the out-of-plane component of dipoles. The method is based on the selective coupling of light emitted by in-plane and out-of-plane dipoles to the whispering gallery modes of spherical dielectric microresonators, in close contact to them. We have applied this method to demonstrate the existence of dipoles with an out-of-plane orientation in monolayer WSe2 at room temperature. Micro-photoluminescent measurements, numerical simulations based on finite element methods, and ab-initio calculations have identified trions as the source responsible for this out-of-plane emission, opening new routes for realizing on-chip integrated systems with applications in information processing and quantum communications. Out-of-plane photon emission in 2D semiconductors is rare but crucial for efficient light manipulation in planar optoelectronic devices and photonic chips. Here, an out-of-plane dipolar component of trions in monolayer WSe2 is revealed by exciting the whispering gallery modes of SiO2 microspherical resonators.

T he race to develop high-performance photonic and optoelectronic devices which take advantage of the distinctive properties and versatility of two-dimensional (2D) semiconductors 1-3 has already given rise, for example, to high-speed and high-responsivity waveguide-integrated photodetectors 4 , plasmonic nanocavities [5][6][7] , and optical resonators with enhanced light-matter interactions [8][9][10] , as the basis to construct nanolasers operating at room temperature 11,12 . Most of the optoelectronic and photonic devices developed so far are based on 2D transition-metal dichalcogenide (TMD) semiconductors such as MoS 2 , MoSe 2 , WS 2 , and WSe 2 . Consequently, the characteristics of the performance of these devices strongly depend on the in-plane (IP) dipolar nature of the robust free excitons of the 2D TMDs [13][14][15] . Light from IP excitons can be easily extracted in stacked (vertical) devices. However, some emerging applications in the generation of radially polarized light in 2D TMDs 16 and integrated photonic chips can be efficiently enabled when out-of-plane (OP) excitons mediate light-matter interactions [17][18][19][20][21][22][23][24] . Although rare, OP excitons can be found in 2D semiconductors. For instance, atomically thin layers of Indium Selenide (InSe) have demonstrated, as 2D TMDs, potential applications for next generation electronics and optoelectronics [25][26][27] due to their highly tuneable bandgap [28][29][30] and high electron mobility 31 . Nevertheless, unlike 2D TMDs, 2D layers of InSe have revealed to sustain luminescent free excitons with an intrinsic OP orientation 14 . This panorama puts into evidence the necessity of identify, among the different excitonic complexes existing in 2D semiconductors, those with a suitable dipole orientation for their optimal application in the emerging field of integrated photonic circuits based on 2D materials [32][33][34][35][36][37] . This question is particularly relevant for the development of novel devices based on monolayer TMDs, since strong spin-orbit coupling makes these materials offer, apart from bright and longlived dark excitons 38,39 , high-order charge-complexes with unexplored dipolar characteristics, such as bound excitons, trions [40][41][42][43][44] , and biexcitons 45 . These complexes are technologically promising as they can manifest even at room temperature [46][47][48] , have an intrinsic charge and spin degrees of freedom that facilitate their manipulation by the application of an electric or a magnetic field 45,49 , possess a valley degree of freedom (as free excitons), permit new optical gain mechanisms at extremely low carrier densities 50 , and can be further used as entangled photon sources [51][52][53][54][55] .
Back focal plane imaging is usually considered the method-ofchoice to discern the orientation of the dipole responsible for the luminescent signal emitted 13,14,56 . However, it is challenging to use this technique to discriminate contributions from different sources to the luminescent signal that may eventually have a different dipolar orientation. To overcome this limitation, more sophisticated methods have been proposed, but their application is rather limited as they require an efficient excitation of surface plasmon polaritons 57 .
In this work, we propose a versatile and simple method to spectroscopically elucidate the existence of an OP component in the photoluminescent response of a dipole which, at the same time, puts into evidence its feasibility to promote light coupling to a planar device. The proposed method relies on the different selective ability of IP and OP dipolar emission to excite whispering gallery modes of SiO 2 microspheres deposited on top of the emitting layers. We have applied this method to study the orientation of dipoles related to the different light contributions observed in monolayer WSe 2 at room temperature, these from trions and excitons. By microphotoluminescence (μ-PL) measurements, numerical simulations based on the finite element method (FEM), and ab initio calculations of the excitonic states we have found a non-negligible OP dipolar component of trions in monolayer WSe 2 , which contrasts to the well-established IP nature of its free bright excitons. These results establish that exciton complexes are excellent candidates for light manipulation in planar optoelectronic devices and photonic chips.

Results and discussion
Light-coupling effects in 2D-semiconductor/microsphere systems. Figure 1 puts into evidence pronounced lensing and strong light-coupling effects when, as is illustrated in Fig. 1a, dielectric microspheres are deposited on top of 2D semiconductors. Figure 1b shows μ-PL spectra acquired in a bulklike (16 nm thick) InSe nanosheet deposited on a SiO 2 /Si substrate and partly covered with SiO 2 microspheres (see optical image at the inset of Fig. 1b). The μ-PL spectrum measured in a bare region of the InSe nanosheet shows an emission peak located at 1.24 eV, corresponding to the radiative free-exciton recombination processes occurring at energies reported for bulk InSe 14,30 . Although it is almost negligible in this spectrum, it is worth mentioning that a weak broad emission is detected at energies higher than 1.45 eV, which stems from the amorphous SiO 2 substrate. Compared to the μ-PL spectrum measured in the bare InSe nanosheet, the one acquired in a point of sample covered with SiO 2 microspheres shows a strong enhancement of the signal intensity (see Fig. 1b and the μ-PL map in its inset) that makes visible even the weak luminescence coming from the SiO 2 substrate. This lensing effect, promoted by the microspheres, is not restricted to bulklike InSe nanosheets. In fact, the use of dielectric microspheres seems to provide for a tool to enhance the usually low-intensity PL signal of atomically thin InSe nanosheets without damaging the sample, as it has been demonstrated for a 2D InSe nanosheet 6.5-nmthick with an noticeable blueshift of its PL signal due to quantumconfinement effects (See Supplementary Fig. 1) 30 .
A similar lensing effect is observed in other 2D semiconductors. Figure 1c shows the μ-PL spectra acquired in a monolayer of WSe 2 deposited on a SiO 2 /Si substrate, on which a SiO 2 microsphere has been placed (see the optical image at the inset of Fig. 1c). In the bare region of the monolayer of WSe 2 , the PL spectrum shows a double-peak structure whose deconvolution has been performed by assuming gaussian-like components 48,58 . In this way, deconvolution processes have allowed to resolve a main PL peak centered at 1.666 eV, coming from optical recombination of the X 0 neutral exciton, and a second and broad PL peak centered at 1.640 eV. Such low-energy feature has been usually attributed to recombination of trions, whose observation is hard at room temperature but possible in doped samples (as those used in this work) due to the higher probability of forming charged excitons in these samples than in intrinsic ones 48,57,59,60 . In line with that observed for InSe nanosheets, the μ-PL spectrum measured in the region of the WSe 2 nanosheet under the SiO 2 microsphere (see also the PL map inserted in Fig. 1c) shows an enhanced intensity signal, compared to that of the bare monolayer.
Clearly, the lensing effect described above is promoted by the difference between air and the microsphere refractive index [61][62][63] , increasing the excitation power density on the sample (Fig. 2a, top panel) and consequently enhancing the global PL signal intensity. The lensing effect is not only restricted to the excitation process but extends also to the light-collection process (Fig. 2a, bottom panel). Importantly, this effect tends to enhance the collection of light within the numerical aperture of our optical objective that would be eventually lost in the absence of the microsphere, as the far-field emission from OP dipoles 38 .
Sensitivity of Whispering Gallery Modes to the orientation of radiating dipoles. Besides the lensing effect, the presence of the Fig. 1 Photoluminescence response of 2D nanosheets partly covered with SiO 2 microspheres. a Illustration of the measurement process of the PL response of nanosheets partly covered by dielectric microspheres. b Micro-PL spectra acquired in two points of the 16-nm-thick InSe nanosheet deposited on a SiO 2 /Si substrate, which is shown in the optical image in the inset. A certain number of microspheres can be observed in the optical image, as blurred spheres since the image was taking focusing on the nanosheet. The inset includes a PL map acquired in a region of the nanosheet delimited by the red dashed rectangle depicted on the optical image. The PL-signal integrated intensity of each point of the PL map follows the color-code indicated on the right side of the PL map, revealing a clear PL intensity enhancement in the region of the nanosheet covered with microspheres. The two μ-PL spectra shown in the main graph were acquired in each one of the two points marked in the PL map, one in a bare region of the nanosheet (A point) and the other in a point covered by a microsphere (B point). c Micro-PL spectra acquired in two points of a monolayer WSe 2 nanosheet deposited on a SiO 2 /Si substrate, which is shown in the optical image in the inset. In this case, a microsphere was purposely pushed on top of the WSe 2 nanosheet, which appears on the optical image as a burred bump. The inset includes a PL map acquired in a region of the nanosheet delimited by the red dashed rectangle depicted on the optical image. As before, the PL map reveals a clear PL intensity enhancement in the region of the nanosheet covered with the microsphere. The two μ-PL spectra shown in the main graph were acquired in each one of the two points marked in the PL map, one in a bare region of the nanosheet (C point) and the other on a point covered by a microsphere (D point). The μ-PL spectrum measured in the C point was deconvoluted into two gaussian components (shown on the graph), one attributed to the neutral exciton X 0 and the other to charged excitons X c . microspheres also promotes the appearance of strong resonances in the PL spectrum (see Fig. 1 and Supplementary Fig. 1) which reveal a strong coupling of emitted light from dipoles existing under the dielectric microspheres to modes of the spherical microresonator (Fig. 2b, c). The spectral response of these resonances, called whispering gallery modes (WGMs) [64][65][66] , mostly depends on the precise diameter of the microsphere (Supplementary Fig. 2), which may be used to fine-tune the relative weight of desired energy regions of the PL spectrum with respect to others. However, we would like to focus here on a photonic application of these microspheres on nanomaterials (See Supplementary Figs. 3 and 4), connected to the ability of WGMs of dielectric microspheres to provide for a tool to discriminate the OP component, from the IP one, of dipoles underneath (i.e., the luminescent dipoles of the 2D nanosheet), as illustrated in Fig. 2c. Figure 2d shows the μ-PL spectra measured in the SiO 2 /Si substrate, covering the 1.43-1.70 eV energy region where a weak emission from the amorphous SiO 2 overlayer has been detected (Fig. 1b). One of these spectra has been acquired in the bare SiO 2 / Si substrate (black continuous line), whereas the other has been recorded in a point of the substrate covered by a SiO 2 microsphere (red continuous line). In this second PL spectrum, the emitted light appears to couple to the WGMs of the microsphere on top, which gives rise to resonances that consist in relatively intense peaks separated to each other every 60-70 meV. Besides, the spectra reveal the additional presence of weak but clear resonances (see, for instance, the one at 1.675 eV) in between the more intense lines. To understand the origin of this pattern of alternating intense and weak resonances, we have calculated the spectral response of a dipolar emission when coupled to the WGMs of a spherical resonator of 4.66 μm in diameter, a value close to the nominal diameter of the microspheres (~5 μm, Methods section) that allows to nicely reproduce the experimental data. These numerical simulations are based on the treatment developed by Chew 67 , which disregards the effects of the substrate. See Supplementary Fig. 3 for further details about the effects of a realistic environment in the coupled emitterresonator, as obtained by FEM-based simulations. If we first consider that the dipole is oriented parallel to the z-axis -or OP- (Fig. 2c), its radiated field is expected to couple to a discrete set of transverse magnetic (TM) modes of the spherical resonator (Fig. 2d, orange curve), where the modal electric field is given in terms of the spherical vector wave functions N ð1Þ lm , with polar mode number l ¼ 1; 2; and azimuthal mode number m ¼ 0; ± 1; ; ± l. 68 . Note that the magnetic field of the vertical-dipole radiation is azimuthally oriented parallel toφ, allowing the electric field of the scattered signal set in terms of the spherical vector wave functions N ð3Þ lm 69 . Peak resonances of the scattered field, labeled as TM l;n in Fig. 2d (orange curve), are characterized by the solutions to the so-called modal equation and are classified by a radial mode number n ¼ 1; 2; . They are thus characteristic from each lth-order TM mode, taking into account a generalized 2l þ 1 mode degeneracy when varying the azimuthal index m 67 . Nevertheless, due to the location of the electric dipole set along the z-axis, the highly-symmetric scattered fields lead to excitation of only one azimuthal mode m ¼ 0 for each polar mode index. In addition, due to the relatively low Q factors associated with the dielectric microspheres, one can only observe peaks in Fig. 2d corresponding to the radial mode n ¼ 1 (those with l between 20 and 23).
When tilting the dipole p from the OP configuration to have an IP dipolar component, excitation of transverse electric (TE) modes in the dielectric resonator starts to be allowed (see Supplementary Discussion 1). Now, the electric field in the resonator includes terms depending on the spherical vector wave functions M ð1Þ lm . As a result, a new set of natural frequencies associated with the peaks labeled as TE l;n will also appear in the spectrum of the scattered electric field accompanied by their corresponding TM l;n ones, involving the spherical vector wave functions M ð3Þ lm . The relative coupling strength of TM and TE modes depends on the tilting angle of the dipole. If the dipole is fully IP oriented (Fig. 2c), the coupling strength to TE l;n modes is significantly higher than to their corresponding TM l;n ones ( Fig. 2d, purple curve). However, in comparison with the TM modes excited by the OP dipoles, both TM and TE modes excited by IP ones are less intense (Fig. 2d). In this case, note that the excited azimuthal modes with TE and TM polarization are now m ¼ ± 1 exclusively 67,69 . On the contrary, the radial index n ¼ 1 of the observed peaks is maintained unaltered here.
The nice match observed between experimental and simulation results summarized in Fig. 2d reveals a clear preference of WGMs in dielectric microspheres to couple to light emitted from OP dipoles in detriment of that from IP ones. Naturally, this selective behavior of WGMs provides for an easy, fast, and powerful method to detect the presence of OP dipoles in an emitting 2D layer. Furthermore, the observation of WGMs at a particular energy of the PL spectrum can be considered as a fingerprint of the ability of the emitted photons to propagate along a planar structure, somehow represented by a dielectric microsphere. Since each kind of radiative excitonic complex (free-exciton, trion, biexciton, etc) can be identified by its transition energy, the spectral distribution of WGMs in the PL spectrum would allow to identify and select, among all excitonic complexes of a system, the optimal candidates to be implemented in optoelectronic devices designed to operate in a particular planar configuration.
Out-of-plane component of luminescent dipoles in InSe nanosheets and WSe 2 monolayers evidenced by and Whispering Gallery Modes. The method proposed above, to disentangle the OP component of radiative excitonic complexes and detect their potential ability to couple its light to horizontal devices, has been applied to 2D materials with promising applications in optoelectronics, photonics, and quantum communications. InSe and WSe 2 can be considered as paradigm systems which give rise to 2D semiconductors and devices with a completely different orientation of their respective free neutral excitons. Luminescent free excitons of 2D InSe have been recently demonstrated to be OP whereas those of monolayer WSe 2 are IP [13][14][15] . With the aim to emphasize the effects of the microspheres on the PL response of these kind of nanosheets, we show, in the middle panels of Fig. 3a, b, the ratio between the μ-PL spectra acquired in a point of the nanosheet under the microspheres and in another of the bare one, for the 16-nm-thick InSe nanosheet and the monolayer WSe 2 already described in Fig. 1, respectively. For the sake of clarity, top panels of Fig. 3a, b show again the original μ-PL spectra acquired in each one of these nanosheets and bottom panels display the spectral response calculated for IP and OP dipolar emission eventually coupling to the WGMs of a spherical resonator of 4.69 μm in diameter, within the energy range enclosed by the PL response of each nanosheet, respectively. Results summarized in Fig. 3 reveal a different behavior of the excitation of WGMs, depending on the nanosheet probed. The PL intensity ratio obtained for the 16-nm-thick InSe nanosheet (Fig. 3a, middle panel) shows an approximately constant enhancement factor of 4-5, in the energy range comprising the PL peak (1.20-1.35 eV), due to the lensing effect. Overlapped with this basement line, the spectrum shows clear and pronounced resonances at the energy positions expected for light coupling to the WGMs of the microspheres when the emitter is, precisely, an OP dipole (Fig. 3a, bottom panel). A similar behavior arises for thinner InSe nanosheets ( Supplementary Fig. 1), although the microsphere used in this experience was slightly bigger (of 4.80 μm in diameter). These results support previous works reporting the OP orientation of radiative free excitons in InSe 14 , and allow us to conclude, by the relatively simple method used here, that radiative recombination processes of OP free excitons conform the whole room-temperature PL spectrum of InSe nanosheets. The dominant OP orientation of dipoles responsible for the room-temperature PL signal of InSe contrasts to these observed for monolayer WSe 2 (Fig. 3b). Unlike InSe, the magnification of the PL signal promoted by the microspheres as well as the excitation of WGMs resonances tend to concentrate in the lowenergy side of the PL spectrum of monolayer WSe 2 (Fig. 3b, middle panel), being both effects strongly reduced at the energies of the main PL peak. In fact, the excitation of WGMs becomes particularly strong at light-emission energies as low as~1.50 eV (see inset at the top panel of Fig. 3b), far beyond the energy range usually observed for radiative recombination of free excitons in monolayer WSe 2 at room temperature (Fig. 1c). Therefore, as occurs for InSe, WGMs resonances in the WSe 2 monolayer appear to be excited by its OP dipoles (Fig. 3b, bottom panel). These results reflect that, as reported, luminescent free-excitons of monolayer WSe 2 are strongly IP [13][14][15] . However, light emitted from the recombination of trions, which notably contribute to the low-energy side of the PL spectrum of monolayer WSe 2 (Fig. 1c), has a relevant OP dipolar component that promotes its coupling to the WGMs of the microspheres.
Optical selection rules of in-plane and out-of-plane radiating dipoles. The electronic states at the bandgap of monolayer WSe 2 are majorly tungsten d-orbitals and the spin-orbit interaction is strong, resulting in optical selection rules with IP and OP emission dipoles of distinct intensities (see the Supplementary Discussion 3 for discussion of the optical selection rules) 38,55 . In order to quantify the luminescent dipoles in monolayer WSe 2 we have calculated the exciton states for IP and OP polarized light. Figure 4a, b show the band structure of monolayer WSe 2 calculated along the M-K-Γ high-symmetry directions, indicating the electronic transitions relevant for the absorption of IP and OP light and the optical absorption including excitonic effects, respectively. The dark X 0 z and bright X 0 exciton transition energies are marked with blue and red vertical lines, separated by 69 meV. In contrast to InSe, the optical selection rules have the origin in the spin-orbit interaction 70,71 . The strong effect of the spin-orbit interaction is evidenced by looking at the wave functions of excitons X 0 z and X 0 in Fig. 4d. The excitonic wave function depends on the electron and hole position. In these calculations, we fix the hole position near the W atom and the resulting electronic density is displayed, with the X 0 z excitonic configuration showing a higher electron density on the Se atoms that is responsible for its OP orientation component. Moreover, each exciton X 0 and X 0 z has an associated trion family (X c and X c z , respectively) that inherits the optical selection rules (see Fig. 4c) 72 , whose recombination results in a broad PL-band at the energy of the peak around 1.640 eV, as shown in Fig. 1c, due to the coupling of light to both to IP and OP dipoles. These facts arise trions as the main source of OP light able to excite WGMs of dielectric microspheres.

Conclusions
To summarize, we have demonstrated a spectroscopic method that enables the identification of the out-of-plane component of radiating dipoles. This would allow to identify, at any temperature, potential sources for radially polarized light in monolayer transition-metal dichalcogenides, which may have applications in imaging, phase modulation, and diffractive optics, due to the cylindrical symmetry of their light. Also, this method opens up new routes for the realization of planar devices efficiently exploiting the fundamental properties of atomically thin materials. The technique does not require magnetic fields and can be easily implemented, making it accessible, versatile, and technologically relevant. To evidence the effectiveness of this technique, we have performed a spectroscopical analysis of the luminescent  Fig. 1b, c, respectively. Middle panels: intensity ratio between the PL spectra shown in their respective top plots, which evidence the coupling of emitted light to the WGMs of dielectric microspheres. Bottom panels: spectral response calculated for a dipolar emission coupled to the WGMs of a spherical microresonator of 4.69 μm in diameter, when these emitting dipoles are IP (purple curve) or OP (orange curve) oriented. The TM or TE character of each WGMs has been indicated on each resonance peak.
signal of InSe nanosheets and monolayers of WSe 2 . This study evidences that excitonic complexes with binding energies larger than that of the room-temperature free-excitons by even 150 meV (such as trions) have an important out-of-plane dipolar orientation, which makes them suitable candidates for their incorporation into planar devices with potential applications for information processing and on-chip communications. Interestingly, the wide energy range observed here for optical transitions in monolayer WSe 2 at room temperature with an important outof-plane dipolar component also corresponds to the region where quantum emitters are usually observed at low temperature.
Results reported here suggest that quantum light from these emitters are expected to efficiently couple into photonic chips to develop optimal quantum devices based on two-dimensional semiconductors.

Methods
Sample Preparation. InSe and WSe 2 2D nanosheets have been micromechanically exfoliated using the well-known scotch-tape technique. InSe monocrystals used here to prepare the nanosheets were cleaved perpendicular to the (001) direction from an ingot grown by the Bridgman method from a nonstoichiometric In 1.05 Se 0.95 melt. To act as n-dopant, tin, in a content 0.01%, was introduced previously to growth. From these ingots, thin n-doped InSe samples were cleaved and used to prepare atomically thin InSe nanosheets. InSe samples have been then directly transferred onto Si substrates coated with 285 nm of SiO 2 , previously cleaned with acetone, ethanol and isopropanol in an ultrasound bath. p-doped bulk WSe 2 (from HQgraphene) has been used here to obtain WSe 2 nanosheets, which were obtained by a micromechanical exfoliation method to a polydimethylsiloxane (PDMS) stamp. Monolayers of WSe 2 were distinguished from thicker ones by means of their PL emission at room temperature and then transferred onto the Si/SiO 2 (285 nm) cleaned substrates through the all-dry viscoelastic technique. The samples have been identified via optical contrast using a Zeiss Axio Scope.a1 microscope with an Axiocam ERc 5s camera.
SiO 2 microspheres solved in H 2 O (from Sigma-Aldrich) have been used, with a nominal diameter of 5 μm (4.83 ± 0.19 μm). To have a sparse concentration of these microspheres in solution, different aliquots in ethanol were prepared, and dropped onto the exfoliated substrates via spin coating, after which high vacuum is applied to force evaporation and avoid H 2 O residues. In the case of monolayer WSe 2 nanosheets, microspheres in their surroundings were shoved until precisely placed on top of the nanosheets, by using a tip probe attached to the transfer setup micromanipulators.
Micro-Photoluminescence measurements. Micro-Photoluminescence measurements have been performed in a Horiba Scientific Xplora micro-Raman system using a 532-nm CW excitation laser, not exceeding 70 μW of power in 7 s acquisition time measurements in InSe and 10 μW in 1 s acquisition time measurements in WSe 2 to prevent overheating. The optical excitation and collection spots are typically around 1 μm 2 .
Numerical calculations. In order to calculate numerically the WGMs of the spherical microresonator, we used the COMSOL Multiphysics modeling software based on the FEM. A unit point dipole pointing to the center of the microsphere (OP dipole) or oriented perpendicularly (IP dipole) was introduced in our frequency-domain model through the RF module. To block troublesome reflections from outer boundaries of the computational domain, a perfectly matched layer of one-wavelength thickness surrounding the photonic structure was implemented. The power emitted by the electric point dipole in the presence of the sphere (P) and isolated dipole (P 0 ) were calculated by considering the power flux through a smallscale closed surface surrounding the emitter.
The optical absorption of monolayer WSe 2 has been computed within the framework of the Bethe-Salpeter Equation, as implemented in Yambo code 73 . The input of the BSE are the electronic states of WSe 2 , calculated using density functional theory within the local-density approximation with the code Quantum Espresso 74 . We use fully relativistic pseudopotentials with semicore electrons for W. The simulations of the excitonic states have been performed in a 15 × 15 × 1 kgrid including 2 valence and 2 conduction bands. The vacuum distance between two periodic images is 30 Bohr.