Exciton Enabled Meta-Optics in Two-Dimensional Transition Metal Dichalcogenides

Supplementary Information for Exciton Enabled Meta-Optics in Two-Dimensional Transition Metal Dichalcogenides Zeng Wang,, Guanghui Yuan,, Ming Yang, Jianwei Chai, Qing Yang Steve Wu, Tao Wang, Matej Sebek,, Dan Wang #, Lei Wang #, Shijie Wang, Dongzhi Chi, Giorgio Adamo, Cesare Soci, Handong Sun,, Kun Huang, *, Jinghua Teng, * Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*STAR), 2 Fusionopolis Way, #08-03, Innovis, Singapore 138634 Centre for Disruptive Photonic Technologies, The Photonic Institute, SPMS, Nanyang Technological University, Singapore 637371, Singapore Department of Physics and Astronomy, University College London, London, WC1E 6BT, United Kingdom # State Key Laboratory of integrated optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun, Jilin, China 130012. Department of Optics and Optical Engineering, University of Science and Technology of China, Hefei, Anhui, China 230026 Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore Z.W. and G.Y. contributed equally to this work. * To whom correspondence may be addressed. Email: huangk17@ustc.edu.cn or jhteng@imre.a-star.edu.sg 1

1. Growth of MoS 2 layers The MoS 2 layers were grown on the sapphire substrate using physical vapour deposition. The Mo metal target was used for the deposition in the vaporized sulfur ambient. During the growth, the sputtering power, argon pressure, and substrate temperature were fixed to 10 W, 3.2 10-5 mbar, and 710 C, respectively. The thickness of the MoS 2 layers is controlled by the deposition time, in which 10 nm MoS 2 layers ( ~ 15 layers) was obtained for a deposition time of 80 minutes. 2. Simulation In evaluating the transmission of the bare and patterned films, we utilize the finite-difference time-domain (FDTD) methods to carry out the numerical simulations. The basic configuration in our FDTD model is shown in Fig. S2. Considering that the period of the nanoholes in this work is 250nm in both x and y directions, we constrain the simulation area within 250nm 250nm 1300nm. The 12 perfect matching layers (PMLs) are employed along the directions to avoid the undesired reflection from the boundaries. The periodic conditions are used in x and y directions. Because the thickness (from hundreds of micrometers to several millimeters) of the real substrate is too large for the FDTD model, we just simulate the contacting part between the film and substrate by setting the light source in the substrate. Thus, our simulated transmission of the sample has ignored the reflection from the bottom surface of the substrate. So, our simulated transmission (e.g., Figs. 1c and 1d) is defined as the ratio of the transmitted power recorded by the detector to the total power of the incident light source. In our model, the detector is set 0.5μm away from the top surface of the substrate, so that no evanescent wave is involved in the calculated transmission. Due to the ultra-small thickness of the 2D-material films, we use a fine grid of 0.25nm along z direction within the films, so as to reduce the simulation error. In Fig. 1c, the perfect-electric-conductor (PEC) film is directly sitting on the top of substrate and the holes are etched through the PEC film. Since no light can transmit through the PEC film, the simulated transmission in this case comes from only the etched holes, which helps us to exclude the undesired background. However, if a realistic material is employed, the 2

transmitted light through the film will also be recorded by the detector so that it brings the inaccuracy in the simulated transmission. In addition, the refractive index of MoS 2 depends on the number of layers. So, in our simulation, all the MoS 2 materials have the experimental refractive indices, which can be found by addressing the layer number 1. The refractive indices (4.861+2.863i) for 15-layer MoS 2 are used in Figs. 1d and 1e. The wavelength is located at 450nm in Fig. 1c and Fig. 2e of main text. The broadband response in Fig. 1d is located between 400nm to 500nm with a step interval of 1nm. 3. Fabrication The 15-layer MoS 2 is firstly grown on a sapphire substrate at an elevated temperature of 710 C using physical vapor deposition (Syskey sputtering system). Then, a 50 nm-thickness gold layer is coated by using e-beam evaporation (Denton Electron Beam Evaporator) to improve the conductivity and milling precision during FIB lithography (FEI, Helios Nanolab 650). Both the gold and MoS 2 layer within the nanoholes are etched at a milling current of 7 pa. After the top gold layer is removed using chemical etching method, we obtain the pure MoS 2 based photon sieves, the morphology of which is characterized by using AFM (Dimension, Bruker). 4. Hologram design We design a photon nanosieve hologram of 60 μm 60 μm in size to reconstruct an image of NANO (as sketched in Fig. 1b) at the cut-plane of z = 200 μm under the illumination of 450 nm wavelength light, by using the modified genetic algorithm. 2 To maximize the efficiency, we use the 220 nm-diameter nanoholes in the pixel pitch of 250 nm 250 nm, which leads to the smallest gap of 30 nm between two neighboring holes. The designed hologram containing 15,798 nanoholes is shown in Fig. 2b and the simulated image is provided in Fig. 2c. 5. Experimental setup To characterize the fabricated hologram, a weakly focused laser beam is used to illuminate the sample and the transmitted light is collected by using an objective lens (40 ) that is fixed on a high-precision stage. The holographic image is then recorded by a CMOS camera located at the same stage, which allows us to easily tune the distance between the hologram and objective lens. 3

6. Efficiency measurement A two-step procedure is used to measure the efficiency (as illustrated in Fig. S2 of Supporting Information). Firstly, we move the square micro-hole to the center of incident beam and tune the distance between the collection objective lens and sample, so that light passing through the micro-hole is recorded with an edge-clear bright square in the camera. The square mirco-hole having the same size (i.e., 60μm 60 μm) with the hologram is also fabricated at the identical sample, see Fig. S3. The transmitted power encircled in the square of capture image is taken as the incident power I in. Secondly, the hologram located at the same sample is shifted to the center of incident beam and then the distance between the objective lens and sample is raised by 200 μm to project the holographic image onto the camera. Without introducing any measurement error, the saturation of optical signals is avoided during recording the holographic images. Only the intensity located within the area of the NANO pattern is taken as the output power I image. Thus, the experimental efficiency is calculated as the ratio of I image /I in. Considering the power I in is the transmitted power through the top surface of the sapphire substrate, it is reasonable to take the I in as the total power incident on the free-standing MoS 2 -based hologram. The experimental efficiency excludes the influence from the reflection of light at the interface between sapphire and MoS 2 film. So, the experimental efficiency is the absolute efficiency of the proposed hologram. To match it, we calculate the absolute efficiency throughout this work. 7. Efficiency enhancement caused by the transmission through the MoS 2 film In experiment, the MoS 2 film gets thinner than the original thickness of 10nm (see Fig. 2g) due to the fabrication processes, so that the light transmitted through the thinner MoS 2 film will propagate forwardly and interfere with the reconstructed holographic image. As a result, both the image and its surrounding background increase, hereby enhancing the absolute efficiency. To illustrate this issue in details, we carry out the simulations about the diffraction of light from both the holes and the MoS 2 film. Since both the simulated and experimental absolute transmission are around 0.8 (see Fig. S4d), we take the amplitude of light transmitted through the holes as sqrt(0.8) 0.9. Because the ratio of the transmitted power through the periodic holes (in a square of 1μm*1μm) to the power transmitted through the unpatterned film square of 1μm*1μm is around 4.7 in experiment (see Fig. S4b), we can derive the amplitude of light 4

transmitted through the film as 0.9/sqrt(4.7) 0.41. So, to mimic the experimental results, the amplitudes of light through the holes and the surrounding MoS 2 film in our simulations are taken as 0.9 and 0.41, respectively. Thus, the realistic transmitted light contains two parts: the nanohole mask and the background mask (see Fig. S6a). In our simulations, the diffraction of such the transmitted light is calculated by using the numerical Rayleigh-Sommerfeld integral based on the fast Fourier transform 3, with a ultra-fine sampling grid of 20nm 20nm along both x and y directions. The simulated holographic image in Fig. S6c has the great agreement with the experimental image in Fig. S6b. It indicates that the parameters used in our simulation approach tightly the real ones in experiment. Therefore, our simulation model could be used to investigate the efficiency enhancement that is caused by the transmission through the film. Figure S6d presents the simulated holographic image that is contributed by only the nanohole mask. In comparison, the background mask yields the diffraction pattern in Fig. S6e, which shows a darker NANO pattern than its surrounding background. The resulting NANO pattern in Fig. S6c is a coherent superposition of light located within two NANO patterns in Figs. S6d and S6e. Different from the non-coherent superposition, the total power of NANO in Fig. S6c is larger than the summation of both powers encircled in the NANO patterns in Figs S6d and S6e. If the power at the NANO regions in Fig. S6d and S6e are taken as P 1 = E 1 (x,y) 2 = a+ib 2 = (a 2 +b 2 ) (where a=re(e 1 ) and b=im(e 1 )) and P 2 = E 2 (x,y) 2 = c+id 2 = (c 2 +d 2 ) (where c=re(e 2 ) and d=re(e 2 )), respectively, the corresponding intensity profile in Fig. S6c is P t = E 1 +E 2 2 = (a 2 +b 2 +c 2 +d 2 +2ac+2bd)=P 1 +P 2 + (2ac+2bd). It means that the resulting power P t is still larger than the summation of P 1 and P 2. So, the efficiency enhancement originates from P 2 contributed by the background and (2ac+2bd) contributed by the coherent interaction between the background light from the MoS 2 film and the signal light from the nanoholes. To illustrate the efficiency enhancement clearly, both three figures (i.e., Figs. S6(c-e)) are plotted with the same colorbar. Fig. S6c exhibits the enhanced intensity at the image region of NANO, compared with Fig. S6d. Therefore, the diffracted light from the MoS 2 film can help to enhance the efficiency of the holographic image. Meanwhile it also increases the surrounding background of the holographic image, decreasing the contrast of image. 5

8. Lens design We use binary particle-swarm-optimization algorithm 4, 5 to construct the supercritical focusing at a predefined distance (z=f) and spot size in terms of FWHM as well as the longitudinal length of needle. The design procedure is shown as follows. Firstly, the radius of 40 µm is divided into 160 rings with equal width of 250 nm. Each ring has a binary complex transmittance of either 1 (FIB milling region) or 0.2 exp(0.18πi) (2D material region), at the wavelength of 450 nm. The merit function 4 in the focal region is defined as I(r,z) = [ 2J 1(ar) ar ] 2 exp[ (z f)2 b 2 ], where a=3.233/fwhm, b=0.6dof, and DOF is depth of focus of the optical needle. Then the diffraction field is calculated by scalar angular spectrum method which gives good approximation. Due to radial symmetry of the ring structures, the calculation is simplified to a 1D Hankel transform for saving memory and time. The final SCL design is achieved when the intensity variance between the calculated field and target merit function is minimized. 9. 2D-SCL scanning confocal microscopy Fig. 5a sketches our self-built microscopy, where the achieved hotspot by our 2D-SCL is employed to illuminate the objects. To realize the aberration-less illumination, the object is inverted with its supporting substrate located upwards. A 3-dimensional piezo-nano-stage is utilized to fix the object so that the distance between lens and objects can be tuned precisely. The transmitted light through the objects is collected by an objective lens (Nikon CFI TU Plan Fluor EPI 100X) and recorded by a photomultiplier (PMT) after the spatial filtering by a 50 μm-diameter confocal pinhole that is located at the focal plane of the tube lens. The correlation between the object and PMT signal for a scanning image is realized by a raster scan of the piezo-nano-stage via Labview programming. 6

Fig. S1. Absorbance spectra of PVD grown MoS 2 samples. The absorption spectra of 15- layer MoS 2 grown by PVD. High absorption close to 80% is observed around 450 nm, which is due to the unique band nesting effect in 2D MoS 2. Fig. S2. Configuration in our FDTD simulations. The structures are etched on a film with the thickness of t. The perfect matching layers (PMLs) are employed along the z direction to 7

realize a reflection-less virtual medium in simulation, hereby mimicking the realistic physical system. Fig. S3. The Raman signals from the etched and un-etched parts in our fabricated devices. (a) The microscopy images of our fabricated devices in an identical sample. It contains three holograms (the top panel), a lens (the left-bottom panel) and an etched square of 60μm 60μm (the right-bottom panel). (b) The Raman signals at the etched holes (red curves at the position A) and the MoS 2 film (blue curves at the position B) in the hologram sample. (c) The Raman signals at the etched ring (red curves at the position C) and the un-etched MoS 2 film (blue curves at the position D) in the lens sample. (d) The Raman signals at the etched square (red curves at the position E) and the un-etched MoS 2 film (blue curves at the position F) in the square sample. All three measurements in (b), (c) and (d) are implemented in a reflective-mode confocal microscopy under the pumping 532nm-wavelength laser that is focused onto these labelled points (i.e., A, B, C, D, E and F) by using an objective lens of 0.9 NA. The focal spot of the pumping laser is around 300nm, which is larger than the 220nm diameter of the etched holes. So, we can observe the low Raman single at the etched holes (see red curve in (b)) due 8

to the large focal spot that covers the surrounding MoS 2 in experiment. If we move the focal spot to the large-size etched structures (such as ring in (c) and square in (d)), no Raman signal is observed, which means that all the holes and rings are etched through the 4nm-thick MoS 2 film (as sketched in Fig. 2g of main text). Fig. S4. Sketches of measuring the absolute transmission of the fabricated sample. (a) The designed hologram composed of the nanoholes. In the hologram, the periodic holes only exist in some limited regions, such as the areas encircled in the green rectangles labelled by 1, 2 and 3. Correspondingly, some pure film regions (without any holes) are also labelled by the cyan squares labelled by A, B and C. In experiment, we can measure the absolute transmission of holes at the periodic-hole regions (e.g., positions 1, 2 and 3), and the absolute transmission of film at the pure-film regions (e.g., positions A, B and C). (b) The experimental transmitted intensity at the surface of the fabricated hologram. (c) The experimental transmitted intensity at the surface of the etched square that has the same size (i.e., 60μm 60μm) with the hologram. The transmitted power through such a sapphire square could be taken as the incident power of 9

our pure-mos 2 hologram. (d) The experimental (asterisks) and simulated (solid curves) absolute transmission of the periodic holes made in a 3nm (blue curve) or 4nm (red curve)- thick MoS 2 film. In the simulation, the 3nm- and 4nm-thick MoS 2 films (the experimental refractive indices with 7 layers in Ref. S1 are used in (d), (e), and (f).) are employed due to the decreased thickness of film after the fabrication processes. The experimental absolute transmission of hole array is defined as the ratio of the power encircled in the green rectangle (i.e., positions 1, 2 and 3) in (b) to the power encircled in the corresponding green rectangle in (c). In the simulation, we define the absolute transmission of hole array as the ratio of the simulated transmission of hole array sitting on the sapphire substrate to the simulated transmission (~92% over the spectrum from 400nm to 500nm) of the bare sapphire substrate (without the film on the top). One can find that both the simulated and experimental absolute transmission of hole array agree well. It indicates that the thickness of MoS 2 film is located between 3 nm to 4 nm, which is greatly consistent with the AFM results in Fig. 2g of main text. (e) The experimental (curves) and simulated (asterisks) absolute transmission of the MoS 2 film after the fabrication. The experimental absolute transmission of MoS 2 film is defined as the ratio of the power encircle in the cyan square (i.e., positions A, B and C) in (b) to the power encircled in the cyan square in (c). Correspondingly, its simulated absolute transmission is defined as the simulated transmission of light through a MoS 2 film to the transmission (~92%) of light through a bare sapphire substrate. The experimental value is slight lower than the simulated ones. It might originate from the fact that the MoS 2 film at the unpatterned region (e.g., positions A, B and C) within the hologram is thicker that those (e.g., positions 1, 2 and 3) located at the region near the etched holes, due to less possibilities of being etched by the scattering ions. (f) The experimental (asterisks) and simulated (solid curves) absolute transmission of the entire hologram. The experimental absolute transmission of the hologram is calculated as the ratio of the total power encircled in the white-solid square in (b) to the total power encircle in the white-solid square in (c). The simulated absolute transmission is defined as the ratio of the simulated transmission of the entire hologram to the transmission (~92%) of light through a bare sapphire substrate. In our simulation, the simulated transmission of the entire hologram is calculated as f*t hole +(1-f)*T film, where f is the filling factor of nanoholes 10

and 0.272 in this work, T hole is the transmission (the ratio of the recorded power by the dector to the power of light source as sketched in Fig. S2) of light through the periodic (250nm-period) 220nm-diameter nanoholes in the MoS 2 film. T film is the transmission of light through the MoS 2 film on the sapphire substrate (see Fig. S2). Both the simulation and experiment agree well with each other. It indicates that the MoS 2 film after the fabrication process has the thickness of 4 nm, which doubly confirms the 4nm thickness illustrated in Fig. 2g of main text. Fig. S5. Sketches of measuring the total efficiency of the 2D nanosieve hologram. Before the measurement, we fabricated a square hole of 60 μm 60 μm through the MoS 2 film at the same sample of nanosieves so that light passing through the square hole is taken as the incidence of hologram. This square hole was moved to the center of incident beam and light passing through the hole was projected by an objective lens (40 ) onto the CCD, see the sketch in (a). d 1 is the working distance of the objective. The captured image by CCD is shown in (b), and the power encircled within an edge-clear square (red dashed square) is taken as the incidence I in of hologram. Then, we moved the nanosieves to the center of incident beam and lifted up the objective lens and CCD together by 200 μm (c) so that the holographic image (d) is projected on the CCD. To avoid any error, we just calculated the power encircled within the area of NANO as the power I image of image, where the edges of these letters are realized with the help of Photoshop software. Finally, the experimental efficiency is calculated to the ratio of I image to I in. 11

Fig. S6. Background effects caused by transmitted light from the unpatterned film in hologram. (a) The light pattern after considering the background. It is realized by adding the original mask multiplied by an amplitude factor of 0.9 (derived from the optical transmission (~0.8 in experiment) of nanohole array) and the reverse mask multiplied by an amplitude factor of 0.41 (0.9/sqrt(4.7), derived from the experimental transmission of nanohole array, and the ratio (4.7 in experiment) of experimental transmission of nanohole array and MoS 2 film). (b-c) The experimental (b) and simulated (c) holographic images at the target plane for the combined mask in (a). (d) Simulated holographic image for light passing through only the nanohole mask (left in (a)). (e) Simulated intensity profile at the target plane for light through the reversed mask (middle in (a)). 12

Table S1. The dimension of designed SCL. Ring No. R inner (μm) R outer (μm) Ring No. R inner (μm) R outer (μm) 1 0 0.75 24 23.5 23.75 2 2 2.25 25 24 24.25 3 3.25 3.5 26 24.75 25 4 3.75 4.5 27 25.25 25.5 5 4.75 6.25 28 25.75 26 6 6.5 6.75 29 26.25 26.75 7 7.25 7.75 30 27 27.25 8 8 8.25 31 27.5 27.75 9 8.5 8.75 32 28 28.25 10 9 10 33 28.5 28.75 11 10.25 10.5 34 29.25 29.5 12 11.5 11.75 35 29.75 30 13 12.75 13.75 36 30.25 30.5 14 14.5 15 37 30.75 31 15 15.75 16 38 31.25 31.5 16 17.25 17.5 39 31.75 33.75 17 18.25 18.75 40 34 34.75 18 19.25 19.5 41 35 35.25 19 20.5 20.75 42 36 37.25 20 21 21.25 43 37.5 37.75 21 21.75 22 44 38 38.25 22 22.25 22.5 45 38.5 39 23 23 23.25 46 39.75 40 13

Fig. S7. Simulated SCL intensity profiles at the x-z plane. The intensity profiles when the lens is illuminated by plane (a), convergent (b) and divergent (c) waves. The simulated results show that, the homogeneous needle is generated by using the illumination of plane wave. The convergent and divergent waves will lead to the intensity decrement at the right and left ends of the needle, respectively. In experiment, it is challenging to obtain a rigorous plane wave. After the comparison between our experimental and simulated needles, we can find that the inhomogeneous needle in Figures 4 (d and e) is caused by the illumination of a slightly convergent wave. 14

Fig. S8. A comparison between the simulated and experimental results for these microscopies (BF, SCM and 2D-lens SCM) under the coherent illumination. The simulations for coherent bright-field (BF) microscopy are implemented by using the imaging formula of an objective lens 6 : I(x,y)= t(x,y) h(x,y) 2, where t is the transmission of the objects and defined as a binary-amplitude mask without considering the interaction between the object and light throughout the entire paper, h=j 1 (v)/v is the coherent point spread function of an objective lens, v=krna, k=2π/λ, NA is the numerical aperture of objective lens and NA=0.9 in our case, λ is the wavelength, and r=(x 2 +y 2 ) 1/2. On the other hand, the imaging theory of scanning confocal microscopy 3, 7, 8 is employed to simulate the imaging results for traditional SCM and our 2D-lens SCM. The complex amplitude at the pinhole plane is U(x,y;x s,y s )= h 1 (x 0,y 0 ) t(x s -x 0,y s -y 0 ) h 2 (x/m-x 0,y/M-y 0 )dx 0 dy 0, where h 1 is the point spread function of the focusing lens, t is the transmission of objects, h 2 =J 1 (v)/v is the point spread function of the collection objective lens with a magnification of M, x s and y s are the scanning position of objects, x 0 and y 0 are the spatial coordinates at the object plane, x and y are the spatial coordinates at the pinhole plane. In our simulations, h 1 = J 1 (v)/v for the case of traditional 15

SCM, while for our 2D-lens SCM, its h 1 is the electric field at the focal plane of our lens, which is calculated by using angular spectrum method. If the pinhole has a transmission function of P(x,y) that is taken as a binary-amplitude circular function, the final image recorded by a detector is I(x s, y s )= U(x,y;x s,y s ) 2 P(x,y)dxdy, which gives all the scanning images in this figure. In our real experimental setup, the pinhole is substituted by a 50μm-diameter multimode fiber that has smaller detection area than its diameter 9. So, the pinhole size in our simulations is set to be 40μm in diameter for both SCMs. All the simulations are implemented by using our self-made codes in MATLAB software. One can find that our simulations have the good agreement with the experimental results. The coherent BF microscopy cannot resolve any double slit with the center-to-center distance varying from 180nm to 320nm, which is caused by the coherent superposition of the point spread functions. The traditional coherent SCM shows an imaging resolution of 260nm, which agrees well with the FWHM size (0.515λ/NA=257nm) of the point spread function of the employed objectives. Our 2D-lens SCM gives an imaging resolution slightly larger than 200nm, which relies on the illuminating spot created by our 2D lens. Therefore, for both coherent SCMs, their imaging resolution has strong dependence on the size of the illuminating spot, which means that our 2D-lens SCM works better than traditional SCM due to the smaller spot. Fig. S9. The imaging results by using incoherent bright-field microscopy. The images are taken by using an objective lens with its NA=0.9 and a bandpass (100nm-bandwidth) filter centered at 450nm is employed to yield the incoherent imaging. The imaging resolution of an 16

incoherent BF microscopy is determined by the Rayleigh criterion of 0.515λ/NA(FWHM), which behaves better than coherent BF microscopy. In the captured images, the noise is caused by the weak power of our incoherent source due to the bandpass filter. The original images are taken in a reflective mode of incoherent BF microscopy, which leads to the bright background and the dark objects. In order to compare with other microscopies, the imaging results in Figures (a) and (b) are inverted by using its maximum intensity of the original images to subtract the intensity of every pixel. Fig. S10. A comparison between the simulated and experimental results for these microscopies (BF, SCM and 2D-lens SCM) under the incoherent conditions. For this case, the incoherent point spread function is employed in our numerical simulations. The incoherent BF microscopy has the image I(x,y)=t(x,y) h(x,y) 2, which offers a imaging resolution of 0.515λ/NA(FWHM). The incoherent scanning confocal microscopy has the image I(x s, y s )= I(x,y;x s,y s ) P(x,y)dxdy, where I(x,y;x s,y s )= h 1 (x 0,y 0 ) 2 t(x s -x 0,y s -y 0 ) h 2 (x/m-x 0,y/M-y 0 ) 2 dx 0 dy 0. The simulated results for the incoherent case are better than those for the coherent case in 17

Figure S8. By setting the object as an ideal point source in the incoherent SCM, one can find that the total point spread function of this incoherent SCM is h incoherent = h 1 2 h 2 2, which is obtained under the condition that the size of pinhole is infinitesimal, that is, P(x,y)=δ(x,y). For the traditional incoherent SCM with the same focusing and collection objective lens (i.e., h 1 =h 2 =J 1 (v)/v), the incoherent SCM has the total point spread function h incoherent =h 4, which yields the ideal imaging resolution of 0.515 λ 2 NA ( 182nm in this paper) for an incoherent traditional SCM. But, the pinhole size cannot be infinitesimal so that such a resolution is not achievable in experiment. As a result, our simulated results can only show a resolving power of 220nm, which is larger than the ideal resolution of ~182nm. If the pinhole size gets smaller, the resolving power will approach this ideal value, as confirmed by Figure S8. Due to the smaller illuminating spot, our incoherent 2D-SCL SCM shows a better resolution than the traditional incoherent SCM, as expected. Considering that the SCL has the focal spot approaching the zero-order Bessel function of J 0 (v), we can get the best imaging resolution of 0.81 0.515 λ, which is derived by using h incoherent = h 1 2 h 2 2 = J 0 (v) 2 J 1 (v)/v 2. 2 NA Therefore, our 2D-lens SCM has an enhanced theoretical resolution by a factor of 20%, compared with the traditional SCM. But, we should note that the smaller spot of 2D lens is obtained by tuning the interference of a high-coherence laser. So, if one wants to get the predicted resolution by using a 2D lens, the non-coherence manipulation of light must be addressed in a reasonable way, which, however, is a unexploited regime in the community of flat optics and therefore needs more continuous efforts. 18

Fig. S11. The size effect of pinhole in a traditional incoherent scanning confocal microscopy. For a better understanding of this effect on the pinhole size, we test double slits with the center-to-center distance of 190nm in Figure (a), which can be resolved theoretically by the ideal resolution of 0.515 λ 2 NA for the case of λ=450nm and NA=0.9. The simulated line- scanning intensity profiles are shown by addressing the diameter of pinhole in Figure (b). It clearly shows that the tested double slits are resolved when the diameter is smaller than 20 μm. But, the cost is the decreased power by the detector because of the small pinhole. References: (1) Yu, Y.; Yu, Y.; Cai, Y.; Li, W.; Gurarslan, A.; Peelaers, H.; Aspnes, D. E.; Van de Walle, C. G.; Nguyen, N. V.; Zhang, Y.-W. Exciton-dominated dielectric function of atomically thin MoS 2 films. Sci. Rep. 2015, 5, 16996. (2) Huang, K.; Liu, H.; Garcia-Vidal, F. J.; Hong, M.; Luk'yanchuk, B.; Teng, J.; Qiu, C.-W. Ultrahigh-capacity non-periodic photon sieves operating in visible light. Nat. Commun. 2015, 6, 7059. (3) Huang, K.; Qin, F.; Hong Liu; Ye, H.; Qiu, C. W.; Hong, M.; Luk'yanchuk, B.; Teng, J. Planar Diffractive Lenses: Fundamentals, Functionalities, and Applications. Adv. Mater. 2018, 30 (0), 1704556. (4) Yuan, G.; Rogers, E. T.; Roy, T.; Adamo, G.; Shen, Z.; Zheludev, N. I. Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths. Sci. Rep. 2014, 4, 6333. (5) Qin, F.; Huang, K.; Wu, J.; Jiao, J.; Luo, X.; Qiu, C.; Hong, M. Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light. Sci. Rep. 2015, 5, 09977. 19

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