Probing the optical near-field interaction of Mie nanoresonators with atomically thin semiconductors

Optical Mie resonators based on silicon nanostructures allow tuning of light-matter-interaction with advanced design concepts based on complementary metal – oxide – semiconductor (CMOS) compatible nanofabrication. Optically active materials such as transition-metal dichalcogenide (TMD) monolayers can be placed in the near-ﬁ eld region of such Mie resonators. Here, we experimentally demonstrate and verify by numerical simulations coupling between a MoSe 2 monolayer and the near-ﬁ eld of dielectric nanor-esonators. Through a comparison of dark-ﬁ eld (DF) scattering spectroscopy and photo-luminescence excitation experiments (PLE), we show that the MoSe 2 absorption can be enhanced via the near-ﬁ eld of a nanoresonator. We demonstrate spectral tuning of the absorption via the geometry of individual Mie resonators. We show that we indeed access the optical near-ﬁ eld of the nanoresonators, by measuring a spectral shift between the typical near-ﬁ eld resonances in PLE compared to the far-ﬁ eld resonances in DF scattering. Our results prove that using MoSe 2 as an active probe allows accessing the optical near-ﬁ eld above photonic nanostructures, providing complementary information to sophisticated near-ﬁ eld microscopy equipment.

Introduction.-Opticalresonators are essential in many applications such as laser systems and sensing.The physical size and properties of the resonator are adapted to the specific application and to the relevant part of the electromagnetic spectrum [1].Optical resonators that are capable of amplifying optical fields in very small nanoscopic volumes, for addressing individual nanocrystals or molecules in the near-field, are called nanoresonators [2][3][4][5][6][7][8][9][10][11][12][13].They can be fabricated by bottom-up techniques, such as growth of metallic nanoparticles, or top-down approaches, such as Si-nanoresonators on CMOS compatible substrates [14][15][16][17][18][19].Whereas the resonance energies of a resonator with macroscopic dimensions, such as a laser cavity, are directly accessible in a standard optical far-field measurement, the situation for nanoresonators is more challenging.It has been shown experimentally and in a substantial body of theory work that there is a shift between the optical resonance energy in the near-field compared to the measured resonance energies in the far-field.The exact nearfield resonance is key for applications for example in sensing of molecules directly placed in the near-field [20] and it has been accessed up to now either in sophisticated tip-enhanced experiments or through extrapolation from far-field data [21][22][23][24][25].
Here we show that by placing an atomically thin semiconductor directly in the near-field of individual dielectric nanoresonators, we have access to the near-field resonance energies without the use of complex near-field spectroscopy techniques.We compare the near-field resonance energies with far-field resonance energy measurements on the same resonators and observe a clear blue-shift of the near-field energies in our far-field results.We show tuning of the optical absorption of the atomically thin semiconductor MoSe 2 through the interaction with the nanoresonator near-field and our results are well reproduced by model calculations of the shift between near-and far-field resonances.
Results and Discussion.-Wefabricated two sets of Si/SiO 2 nanoresonator arrays on silicon-on-insulator (SOI) substrates.The nanoresonators are cylindrical pillars, arranged as close-packed heptamers as sketched in Fig. 1e and 1f.The diameters of the individual cylinders increase from 50 nm to 300 nm with steps of 50 nm.The gaps between neighbouring pillars are 50 nm, 100 nm or 300 nm.The structures are fabricated as arrays of seven discs to match approximately the size of a diffraction limited, focused laser beam, in order to maximize the experimental signal associated with the Si-NRs.On the final nanostructures, MoSe 2 monolayers are aligned and transferred on top of the nanoresonators using a micromanipulator system [26].A description of the fabrication process is given in the supporting information.
In figure 1a  DF spectra are collected using the same setup as the DF images.To this end, the signal is sent to a spectrometer instead of the imaging camera.The setup for taking dark-field images and spectra is depicted in the supplement Fig. 4. We will focus in the following on two selected nanoresonators, "NR1" (blue, Fig. 1e) and "NR2" (red, Fig. 1f).
These heptamers have respective diameters of 250 nm (NR1) and 300 nm (NR2), the gap between the pillars is identical for both Si-NRs (100 nm).We selected these two NRs because their main Mie resonances lie at different, well distinguishable energies.We measured the scattered light intensity before and after the monolayer transfer, shown in Fig. 1b, respectively 1d.We observed a small, global blue-shift on the order of 10 meV for the resonances when the MoSe 2 monolayer was on top of the nanoresonators, this small energy-shift is at the limit of our detection accuracy.Knowing the size of this shift is helpful for analyzing the spectral shift between measured near-field and far-field resonances discussed below.
Spectral shift between near-field and far-field.In a second step, we want to analyze the impact of the nanoresonators on the absorption of the MoSe 2 monolayer.We carry out photoluminescence excitation (PLE) experiments [27] where temperature, position, and optical power are kept constant and the excitation wavelength is varied from 450 nm to 650 nm (corresponding to 2.75 eV -1.90 eV).The optical power of the laser is set to 100 nW, after making sure that the MoSe 2 absorption is not saturated at this illumination power (see also supplemental figure S4).We avoid tuning the laser close to the MoSe 2 exciton emission peaks which occur around 745 nm (≈ 1.66 eV) [28][29][30], in order to remain in a non-resonant excitation regime.During the entire measurements, the sample is kept in a closed-loop cryostat at a temperature of 5 K. Typical PL spectra are shown in the supplemental Fig. 9, where we also provide a comparison with room temperature measurements (T = 300 K).
An illustration of the optical setup can also be found in the SI Fig. 5.
The absorption and hence the PLE response of the bare MoSe 2 [27] is expected to vary with the excitation energy.This variation is a result of the material's band-structure, the presence of high energy excitonic states as well as coupling to phonons [30][31][32][33].Our goal is to spectra for each excitation laser wavelength are numerically integrated, by summation of the counts per second in the spectral range around the emission peaks, from 1.5 eV -1.7 eV (see SI for raw spectra) [34].Hence, each data point in Fig. 2 is a separate PL measurement for a specific laser excitation energy.The direct comparison of the PLE measurements from MoSe 2 with and without Si-NR (c.f.Fig. 2), already reveals clear differences.To better visualize the effect of the nanoresonators on the PLE signal, we divide the integrated PL intensities from MoSe 2 on the Si-NRs I P L,NR (blue squares and red triangles in Fig. 2) by the signal from the bare MoSe 2 I P L,MoSe 2 (on flat substrate, gray dotted line in Fig. 2): This ratio ρ gives an estimation of the absorption enhancement due to the presence of a Theoretical simulations : We compare the experimental PLE spectra to full-field simulations via the Green's dyadic method (GDM) using our own python implementation "pyGDM" [35,36].The GDM is a volume discretization approach to solve Maxwell's equations in the frequency domain [37].A nanostructure of arbitrary shape and material is discretized on a regular hexagonal compact grid.We use tabulated refractive indices from literature for both parts of the pillars, the first 95 nm consisting of silicon [38] while the 30 nm thick capping is made of SiO 2 [39].With according Green's tensors [40], we describe the layered substrate, where a bulk silicon substrate is followed by a SiO 2 spacer layer of 145 nm, on top of which the nano-structures are placed in air.We illuminate the system with a plane wave at normal incidence in the same wavelength range as used in the experiments and we incoherently average two orthogonal linear polarizations.We calculate the electric field intensity enhancement just above the SiO 2 capping on the Si pillars in an area An unambiguous proof that we do indeed probe the optical near-field with the PLE technique is provided by the observation of a systematic shift between near-field spectra (PLE) and far-field measurements (DF scattering).This shift is of the order of 50 meV (see also Table I) and is reproduced by our simulations (Fig. 3c and d).It corresponds to the widely studied resonance shift between far-field and near-field, where the near-field amplitude is shifted to lower energies, compared to the far-field response.To get an intuitive, qualitative understanding, this shift can be explained with a damped harmonic oscillator (HO) model.The HO amplitude is given by: where A drive is the driving amplitude, in our case corresponding the amplitude of the incident field.Solving Eq. ( 2) for its extrema, one finds easily that the damping term γ leads to a red-shift of the maximum resonator amplitude ω Amax with respect to the eigenfrequency ω 0 [24]: On the other hand, far-field observables like the scattering or extinction cross section are proportional to the oscillator's kinetic energy, whose time average can be shown to be maximum at the non-shifted eigenfrequency ω 0 [24].While the effect has first been discussed for lossy plasmonic nanoresonantors [21], it has been explicitly shown later that radiative damping, responsible for broadening of leaky Mie resonances like in our SiNRs, leads to an analogous near-field shift [24].The shift has been experimentally demonstrated on plasmonic structures via scanning near-field microscopy (SNOM) measurements [25].
Without complex SNOM equipment, here we experimentally observe a red-shift of the PLE spectra compared to the far-field scattering results.It is in the order of the shift predicted by our near-field enhancement simulations, and therefore a clear signature that we indeed probe the optical near-field of the silicon nanostructures.
These observations rely on a sufficient spectral resolution to observe the near-field redshift in the PLE data.Please note that our approach also works at room temperature, as shown in the SI Fig. 8.
In conclusion, we transferred monolayers of MoSe 2 on top of Mie resonant silicon nanostructure arrays and compared the far-field scattering of these scatterers, using DF spectroscopy, with spectrally resolved measurements of photoluminescence enhancement.The latter is probing the optical near-field at the location of the TMD monolayer, i.e. just above the silicon nanostructures.We found that the PLE spectra show the same resonant features as the far-field measurements.We also observe the typical near-to-far-field spectral shift between the two types of measurements, which unambiguously confirms that we have access to the optical near-field of the silicon nanostructures.All results are confirmed by numerical full-field simulations.Our results demonstrate that the absorption efficiency and consequently the emission of direct-bandgap monolayer semiconductors can be enhanced and spectrally tuned by placing optically resonant nano-structures in their vicinity.It furthermore proves that the PLE measurements provide access to the optical near-field in an extremely narrow vertical region in the order of a nanometer (thickness of the TMD monolayer).Our work offers important insights for the design of efficient TMD-based nano-devices for light detection and emission.
Methods.-The silicon pillars were fabricated in a top-down approach via electronbeam lithography (EBL) and subsequent anisotropic plasma etching [42,43].Monolayer MoSe 2 flakes are exfoliated from bulk 2H-MoSe 2 crystals on Nitto Denko tape [44] and then exfoliated again on a polydimethylsiloxane (PDMS) stamp placed on a glass slide for inspection under the optical microscope, see supplement for further details.The silicon pillars were fabricated in a top-down approach via electron-beam lithography (EBL) and subsequent anisotropic plasma etching [42,43].A negative-tone resist (hydrogen silsesquioxane, HSQ) was spin-coated as thin film (around 50nm) on a commercial silicon-oninsulator (SOI) substrate.The SOI consists of bulk silicon followed by a 145nm thick burried oxide layer made of SiO

B. Power Dependence of PL intensity
To evaluate the enhancement we also carried out power dependent experiments.We keep temperature, position, and excitation wavelength fixed, and now we vary the optical power from 10 -500 nW (see SI Fig. S4).The enhancement we measure in emission (on the NRs as compared to next to them) is a lower bound for the enhancement in absorption as the generated excitons do not all recombine radiatively (i.e. by emitting a photon in our detection window) [45][46][47][48].

FIG. 1 :
FIG. 1: dark-field scattering images and spectra with and without MoSe 2 (a) dark-field microscope image of SiO 2 /Si nanoresonators, the 15 structures on the top part of the image are hexamers (six pilars) with diameters varying from D=100-300 nm from left to right and the gap between pillars varying G=50-100-300 nm from top to bottom.The 15 structures on the bottom are heptamers (seven pillars) with the same variation.(b) Dark-field Scattering intensity of the two nanoresonators highlighted.(c) dark-field microscope image with a MoSe 2 monolayer on top.Caution, automatic white-balance was used, colors do not directly compare to (a).(d) Dark-field Scattering intensity of the two nanoresonators after transfer of MoSe 2 monolayer.(e and f) Sketches of the two selected nanoresonators NR1 and NR2, respectively (top view -see supplement for side view).
figure 1c shows the same sample after transfer of an MoSe 2 monolayer flake.A bright-field microscope image of the nanoresonators after MoSe 2 deposition is shown in the supplement Fig. S3, where the MoSe 2 covered region is clearly visible.By varying the Si-NR gap and diameter, different colors appear in the DF images, which demonstrates the geometrydependent Mie resonance energy shifts of the individual resonators in the visible spectral range.

FIG. 2 :
FIG. 2: Photoluminescence excitation measurements.Accumulated counts of the photoluminescence (PL) spectra measured on bare MoSe 2 (gray circles) and MoSe 2 on top of each nanoresonator NR1 (blue squares) and NR2 (red triangles), excited with a continuum laser at 40 different energies and at T=5 K.

FIG. 3 :
FIG. 3: Tuning of resoncances and spectral shift.Results of measurements and calculations for NR1 and NR2 (a) The result of dividing PLE over NR1 (blue squares) and NR2 (red triangles) by PLE on bare MoSe 2 , where we plot the ratio ρ as defined in Eq. 1.(b) Dark-field scattering intensity, same data as Fig. 1b and (c) Calculated near-field intensity enhancement above the SiNRs, averaged in the plane of the TMD (d) calculated far-field intensity enhancement above the SiNRs, averaged in the plane of the TMD.

of 1 ×
1 µm 2 , corresponding approximately to the size of the focused Gaussian laser beam (≈ emission beam diameter).Sketches and more details about simulations and model geometry can be found in the SI.The simulated spectra of the average near-field enhancement above the top surface are shown in Fig.2cfor heptamers with pillar diameters of D = 250 nm (NR1, blue) and D = 300 nm (NR2, red), and the far-field scattered intensity for the same structures shown in Fig.2d.We observe a good agreement with the experimental data, the simulations reproduce in particular all major resonance features.Very importantly our simulations reproduce the red-shift of the resonances when the structure size increases from D = 250 nm to D = 300 nm and the near-to far-field shift.Please note that the systematic blue-shift of around 0.05 − 0.1 eV between the absolute values of the simulated resonances and the experiment can be explained by the rough discretization of the Si discs' circular cross-sections on a coarse, regular mesh.Also, inaccuracies of the fabricated sample dimensions may play a role, in fact, deviations in the order of 20-25 nm between design and actual sample would induce an according systematic shift[41].Discussion : The comparison of the far-field DF scattering spectra with the MoSe 2 PLE spectra clearly demonstrate, that the Mie resonances of high-index dielectric nanoresonators can be used to tailor the absorption of a TMD layer.Furthermore, our results show that the PLE measurements access the optical near-field and probe the local field intensity enhancement.In the lateral directions (parallel to the substrate plane) the measurements reflect the average near-field intensity in a large zone, corresponding approximately to the illuminated area.Perpendicular to the surface on the other hand, the local near-field is probed in an extremely narrow vertical region, because the TMD is atomically thin.
-structure fabrication and TMD exfoliation

FIG. 7 :FIG. 8 :FIG. 9 :FIG. 10 :
FIG.7: Study of power dependence of MoSe 2 on Heptamer D300 G50 (red) and without NR (gray).Fixed excitation energy at 2.25 eV (550 nm), varied the laser power from 5 to 500 nW, and calculated the linear regression.For the red line the slope is 0.509 and for the gray it is 0.414.

TABLE I :
Energy of measured resonances, where we compare near-field (PLE) with far-field (dark-field scattering) experiments.Resonance labels according to Fig. 3a.
[44]OX).On top of the BOX follows a 95nm high silicon overlayer, which serves as building material for the nano-structures.The nano-patterns were written in the HSQ resist using a RAITH 150 writer at an energy of 30 keV.After EBL exposure, the resist was developed in 25 % tetramethylammonium hydroxide (TMAH).Finally, the patterns were etched into the 95nm thick silicon overlayer via reactive ion etching (RIE) in a SF 6 /C 4 F 8 plasma.RIE was stopped once etching arrived at the BOX layer.After the processing, an additional SiO 2 layer of approximately 30nm height remains on top of the structured Si, which is the residual developped HSQ resist.Monolayer MoSe 2 flakes are exfoliated from bulk 2H-MoSe 2 crystals on Nitto Denko tape[44]and then exfoliated again on a polydimethylsiloxane (PDMS) stamp placed on a glass slide for inspection under the optical microscope.Prior to transfer of MoSe 2 monolayers, the substrate with the nanoresonators is wet-cleaned by 60 s ultrasonication in acetone and isopropanol and exposed to oxygen-assisted plasma.