Design of Polarization-Independent Reflective Metalens in the Ultraviolet–Visible Wavelength Region

nanomaterials

Article Design of Polarization-Independent Reﬂective Metalens in the Ultraviolet–Visible Wavelength Region

Huifang Guo 1,2, Song Yue 1,2,* , Ran Wang 1,2, Yu Hou 1, Man Li 1,2, Kunpeng Zhang 1 and Zichen Zhang 1,2,*

1 Microelectronics Instruments and Equipment R&D Center, Institute of Microelectronics, Chinese Academy of Sciences, 3 Beitucheng West Road, Beijing 100029, China; [email protected] (H.G.); [email protected] (R.W.); [email protected] (Y.H.); [email protected] (M.L.); [email protected] (K.Z.) 2 School of Microelectronics, University of Chinese Academy of Sciences, No. 19(A) Yuquan Road, Beijing 100049, China * Correspondence: [email protected] (S.Y.); [email protected] (Z.Z.)

Abstract: Flat lens or metalens, as one of the most important application branches of metasurfaces, has recently been attracting significant research interest. Various reflective and transmissive metalenses have been demonstrated in the terathertz, infrared and visible wavelength range. However, metalens operating in the ultraviolet (UV) wavelength range is rare. Moreover, the development of reflective UV metalens, the important counterpart of transmissive ones, falls far behind. In this work, with thorough investigation of material properties, we propose a reflective metalens based on

silicon dioxide (SiO2) and aluminum (Al) that operates in the vacuum ultraviolet (VUV) to visible wavelength region. Four reflective metalenses were designed and optimized for wavelengths of 193, 441, 532 and 633 nm, and prominent focusing capability was observed, especially for the VUV wavelength of 193 nm. Dispersion characteristics of the metalenses were also studied within ±50 nm of the design wavelength, and negative dispersion was found for all cases. In addition, the SiO + Al Citation: Guo, H.; Yue, S.; Wang, R.; 2 Hou, Y.; Li, M.; Zhang, K.; Zhang, Z. platform can be, in principle, extended to the mid-infrared (IR) wavelength range. The reflective VUV Design of Polarization-Independent metalens proposed in this work is expected to propel miniaturization and integration of UV optics. Reflective Metalens in the Ultraviolet–Visible Wavelength Keywords: metasurface; reflective metalens; ultraviolet; silicon dioxide; aluminum Region. Nanomaterials 2021, 11, 1243. https://doi.org/10.3390/nano11051243

Academic Editor: Arthur P. Baddorf 1. Introduction Miniaturization of optical systems plays an important role in modern information Received: 2 April 2021 technology, enabling plenty of applications such as AR/VR [1], endoscopy [2], camera Accepted: 6 May 2021 module of cell phones [3], miniaturized spectrometer [4], etc. Traditional optical systems Published: 8 May 2021 manipulate wavefronts of light through accumulation of gradual phase change with the propagation of light waves, rendering optical components bulky, expensive and inefficient. Publisher’s Note: MDPI stays neutral Metasurfaces [5,6], delicate arrays of subwavelength optical scatterers/resonators, can with regard to jurisdictional claims in generate abrupt local phase change at a 2D interface, providing a unique opportunity to published maps and institutional affil- planarize and miniaturize most traditional optical elements. Due to their great capability to iations. manipulate multiple degrees of freedom of light, including amplitude, phase, polarization and wave vector, metasurfaces are believed to be able to revolutionize traditional optical components such as flat lenses [7,8], beam deflectors [9–11], wave plates [12,13], meta- holograms [14,15], sensors [16], perfect absorbers [17–19], orbital angular momentum Copyright: © 2021 by the authors. generators [20–22], etc. Licensee MDPI, Basel, Switzerland. Among these, flat lens or metalens, as one of the most fundamental optical elements, This article is an open access article has attracted significant research interest in recent years. Hitherto, on the one hand, distributed under the terms and various reflective and transmissive metalenses have been demonstrated in the terahertz conditions of the Creative Commons Attribution (CC BY) license (https:// (THz) [23,24], IR [25–27] and visible [28–30] wavelength range. On the other hand, how- creativecommons.org/licenses/by/ ever, metalens operating in the UV wavelength range is rare—despite this, UV optics 4.0/). have plenteous applications in the fields of high-resolution photolithography [31], imag-

Nanomaterials 2021, 11, 1243. https://doi.org/10.3390/nano11051243 https://www.mdpi.com/journal/nanomaterials Nanomaterials 2021, 11, 1243 2 of 12

ing [32] and chemical/biological sensing [33]. Miniaturization of optical systems in the UV frequency range proved particularly challenging due to difficulties in material selection and fabrication of nanostructures with high aspect ratios for UV wavelengths. Metallic metasurfaces based on gold (Au) or silver (Ag) work well from THz to near-IR, but their performance deteriorates substantially in the visible to UV regions due to intrinsic Ohmic losses. Dielectric metalenses based on silicon (Si), titanium dioxide (TiO2), silicon nitride (Si3N4) and gallium nitride (GaN) have recently been demonstrated in the visible range. However, these devices suffer from the materials’ inter-band transitions (e.g., TiO2 at 3.2 eV and GaN at 3.4 eV), thus they could not cover the UV range. Very recently, Yao et al. demonstrated ultraviolet metasurfaces based on Si nanobars on quartz substrate working at a wavelength down to 290 nm [34]. Liu et al. demonstrated ultraviolet metasurfaces with ~80% efficiency based on Nb2O5 nanobricks on quartz substrate operating at the wavelength of 355 nm [35]. Zhang et al. achieved UV metalens operating at 325 nm and meta-hologram down to 266 nm wavelength, based on HfO2 metasurface on quartz substrate [36]. In the meantime, some theoretical works on UV metalens emerge as well, utilizing MgO [37] or Si3N4 [38] nanobricks on quartz (glass) substrates, respectively. Despite the recent progress in transmissive UV metalens, it is noticed that the development of reflective UV metalens, the important counterpart of transmissive ones, falls far behind. Actually, reflective metalenses do exist in infrared and visible wavelength ranges [39,40], based on metal–insulator–metal (MIM) [40] and hybrid metal–dielectric configurations [41]. However, the working wavelength of reflective metalens can hardly be extended to the UV range, due to the absorption loss of metals and dielectrics involved in these works. Considering the importance of reflective UV metalens in applications such as photolithography and spectroscopy, we propose and demonstrate numerically in this work a polarization insensitive UV metalens operating in reflection mode. With a thorough investigation of material properties, we choose silicon dioxide (SiO2) and aluminum (Al) as the constituent material. Through arranging SiO2 nanopillars on top of an Al film, we propose a reflective metalens that pushes the working wavelength down to vacuum ultraviolet (VUV) range, i.e., 193 nm. The material combination chosen here not only holds superior UV property due to its large-enough bandgap and high-enough plasma frequency but also is cheap, abundant, CMOS compatible and easy to fabricate. Moreover, the material combination allows us to build reflective metalenses in the visible and even mid-IR wavelength range as well. The reflective VUV metalens proposed in this work holds promise to miniaturize UV optics, opening new pathways for various potential applications such as lithography and imaging, as well as spectroscopy.

2. Material Choice and Design of Structural Unit Reflective metalens based on MIM configuration usually has lower efficiency [40], thus we choose the hybrid metal-dielectric configuration to build our reflective metalens. To achieve a highly efficient reflective metalens in the targeted VUV wavelength region, optical properties of the constituent material, represented by its complex refractive index, need to be examined carefully. Simply speaking, the dielectric material used should have a negligible absorption loss, and the metal constituent should demonstrate metallic property in the whole operation wavelength range. Adhering to the above criteria, we select SiO2 as the dielectric and Al as the metal constituent. Dielectric constants of thermally grown SiO2 thin films are adapted from [42] and displayed in Figure1a. Since the bandgap of thermally grown SiO2 thin film is quite large, i.e., 9.3 eV, corresponding to an interband transition wavelength of 133.3 nm, thermally grown SiO2 thin film is a good candidate for UV optics. Seen from Figure1a, the imaginary part of dielectric constant of thermally grown SiO 2 thin film is essentially zero down to 150 nm, covering the whole visible range and extending to the mid-IR (~8 µm). Meanwhile, compared to noble metals such as Au and Ag, Al has a higher plasma frequency and is a prominent plasmonic material in the UV range [43,44]. Seen from the dielectric constants of Al displayed in Figure1b, Al keeps metallic (real part of dielectric constant ε1 < 0) for the whole wavelength range displayed here (0.03~14 µm). Nanomaterials 2021, 11, 1243 3 of 12

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UV range [43,44]. Seen from the dielectric constants of Al displayed in Figure 1b, Al keeps metallic (real part of dielectric constant ε1 < 0) for the whole wavelength range displayed Based on the materialhere (0.03~14 properties, μm). Based we foresee on the thatmaterial the SiOproperties,2 + Al combination we foresee that is athe good SiO2 + Al combi- platform to constructnation reﬂective is a good metalensplatform thatto construct works well reflective from VUV metalens (193 nm)that allworks the waywell tofrom VUV (193 the mid-IR (~8 nm)µm) all wavelength the way to range. the mid-IR (~8 μm) wavelength range.

Figure 1. Real (Re(ε)) and imaginary (Im(ε)) part of dielectric constants of (a) SiO2 and (b) Al in the 0.03–1.5 µm range. Figure 1. Real (Re(ε)) and imaginary (Im(ε)) part of dielectric constants of (a) SiO2 and (b) Al in the Insets show0.03–1.5 their dielectricµm range. constants Insetsshow in the their 1.5–14 dielectric µm range. constants in the 1.5–14 µm range.

While the SiO2 + Al material combination has the potential to build reflective While the SiO2 + Al material combination has the potential to build reflective metalenses from VUVmetalenses to mid-IR from range, VUV we restrictto mid-IR ourselves range, we in thisrestrict work ourselves to the UV in andthis visiblework to the UV and wavelength range,visible with wavelength more attention range, devoted with more to the attention UV range. devoted The operation to the UV principle range. The operation and structural unitprinciple of the and reflective structural metalens unit of isthe schematically reflective metalens shown is in schematically Figure2a,b, respec-shown in Figure 2a,b, respectively. The structural unit is a SiO2 nanopillar on top of an Al film. Thickness of the tively. The structural unit is a SiO2 nanopillar on top of an Al film. Thickness of the Al film is set to a fixedAl film value is set of to 200 a fixed nm, value which of is 200 thick nm, enough which is to thick reflect enough all electromagnetic to reflect all electromagnetic waves in the wavelength range considered in this work. SiO2 nanopillar is used as the waves in the wavelength range considered in this work. SiO2 nanopillar is used as the phase shifter duephase to theshifter high due symmetry to the high of its symmetry geometric of shape,its geometric resulting shape, in polarization resulting in polarization insensitive focusinginsensitive behavior. focusing Figure behavior.2c is a side Figure view 2c of is the a side metalens view of unit, the metalens where H isunit, the where H is the height of the SiO2 nanopillar. Figure 2d is a top view of the metalens unit, where P and D height of the SiO2 nanopillar. Figure2d is a top view of the metalens unit, where P and D is the period andis the the period diameter and of the the diameter nanopillar, of the respectively. nanopillar, With respectively. plane wave With incidence plane wave incidence from above, thefrom phase above, of reflected the phase wave of reflected is controlled wave by is changingcontrolled theby diameterchanging Dthe and diameter D and height H of theheight nanopillars. H of the nanopillars. Numerical analysis of proposed metalenses was carried out using COMSOL Mul- tiphysics, a commercial software based on finite element method. Considering that the calculation of three-dimensional metalens model requires a large amount of memory, and the cylindrical structure has polarization-independent characteristics, we simplified our model to a two-dimensional (2D) case (see AppendixA for the details of simulation set- up). In the following, all the simulation results were obtained from 2D models, thus the corresponding reflective metalens discussed is a cylindrical lens, whereas discussions over working wavelength and focusing property can be easily extended to the 3D case. Figure3a–d show the simulated reflectance (R, black curves), transmittance (T, blue curves), absorptance (A, green curves) and reflection phase (red curves) of the structural units designed for typical wavelengths in the UV–visible range, i.e., λd = 193 nm, 441 nm, 532 nm and 633 nm, respectively. By optimizing geometric parameters of the SiO2 nanopillars at each design wavelength (see AppendixB for the details of optimization procedure), it is found that with the increase in diameter of the nanopillars, the unit cells can completely cover a phase change range of 0~2π while maintaining the reflectance close to 90%. The optimal period P of the unit cells and height H of SiO2 nanopillars for each design wavelength are labeled aside the insets in Figure3a–d.

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UV range [43,44]. Seen from the dielectric constants of Al displayed in Figure 1b, Al keeps metallic (real part of dielectric constant ε1 < 0) for the whole wavelength range displayed here (0.03~14 μm). Based on the material properties, we foresee that the SiO2 + Al combination is a good platform to construct reflective metalens that works well from VUV (193 nm) all the way to the mid-IR (~8 μm) wavelength range.

Figure 1. Real (Re(ε)) and imaginary (Im(ε)) part of dielectric constants of (a) SiO2 and (b) Al in the 0.03–1.5 µm range. Insets show their dielectric constants in the 1.5–14 µm range.

While the SiO2 + Al material combination has the potential to build reflective metalenses from VUV to mid-IR range, we restrict ourselves in this work to the UV and visible wavelength range, with more attention devoted to the UV range. The operation principle and structural unit of the reflective metalens is schematically shown in Figure 2a,b, respectively. The structural unit is a SiO2 nanopillar on top of an Al film. Thickness of the Al film is set to a fixed value of 200 nm, which is thick enough to reflect all electromagnetic waves in the wavelength range considered in this work. SiO2 nanopillar is used as the phase shifter due to the high symmetry of its geometric shape, resulting in polarization insensitive focusing behavior. Figure 2c is a side view of the metalens unit, where H is the height of the SiO2 nanopillar. Figure 2d is a top view of the metalens unit, where P and D Nanomaterials 2021, 11, 1243 is the period and the diameter of the nanopillar, respectively. With plane wave incidence4 of 12 Nanomaterials 2021, 11, 1243 from above, the phase of reflected wave is controlled by changing the diameter4 Dof and12

height H of the nanopillars.

Figure 2. (a) Schematic of the reflective metalens. (b) Schematic of the unit cell: SiO2 nanopillar on Al film. (c,d) Side- and top-view of the unit cell showing the height H, diameter D and period P of SiO2 nanopillars.

Numerical analysis of proposed metalenses was carried out using COMSOL Mul- tiphysics, a commercial software based on finite element method. Considering that the calculation of three-dimensional metalens model requires a large amount of memory, and the cylindrical structure has polarization-independent characteristics, we simplified our model to a two-dimensional (2D) case (see Appendix A for the details of simulation set- up). In the following, all the simulation results were obtained from 2D models, thus the corresponding reflective metalens discussed is a cylindrical lens, whereas discussions over working wavelength and focusing property can be easily extended to the 3D case. Figure 3a–d show the simulated reflectance (R, black curves), transmittance (T, blue curves), absorptance (A, green curves) and reflection phase (red curves) of the structural units designed for typical wavelengths in the UV–visible range, i.e., λd = 193 nm, 441 nm, 532 nm and 633 nm, respectively. By optimizing geometric parameters of the SiO2 nanopillars at each design wavelength (see Appendix B for the details of optimization proce-

dure), it is found that with the increase in diameter of the nanopillars, the unit cells can

completelyFigure 2. (a) cover Schematic a phase of the change reﬂective range metalens. of 0~2 (πb )while Schematic maintaining of the unit the cell: reflectance SiO2 nanopillar close onto 90%.Al ﬁlm. The (c ,optimald) Side- andperiod top-view P of the of theunit unit cells cell and showing height the H of height SiO2 H, nanopillars diameter D for and each period design P of

wavelengthSiO2 nanopillars. are labeled aside the insets in Figure 3a–d.

FigureFigure 3. 3. SimulatedSimulated reflectance reﬂectance (R), (R), transmittance transmittance (T), (T),absorptance absorptance (A) and (A) reflection and reﬂection phase phase of of

structuralstructural unit unit at at respective respective design design wavelength. wavelength. (a) Design (a) Design wavelength wavelength λd = 193λd =nm, 193 optimal nm, optimal P = 170 nm and H = 190 nm. (b) λd = 441 nm, optimal P = 250 nm and H = 520 nm. (c) λd = 532 nm, opti- P = 170 nm and H = 190 nm. (b) λd = 441 nm, optimal P = 250 nm and H = 520 nm. (c) λd = 532 nm, mal P = 340 nm and H = 620 nm. (d) λd = 633 nm, optimal P = 370 nm and H = 740 nm. optimal P = 340 nm and H = 620 nm. (d) λd = 633 nm, optimal P = 370 nm and H = 740 nm. 3.3. Reflective Reﬂective Metalens Device UnitUnit cells obtained aboveabove cancan provideprovide local local phase phase change change at at each each position, position, and and focusing focus- ingfunctionality functionality can can be obtainedbe obtained by by arranging arranging unit unit cells cells according according to to the the phase phase proﬁle profile of of a alens. lens. The The phase phase distribution distributionϕ (𝜑(𝑥)x) of aof metalens a metalens should should satisfy satisfy the the following following formula: formula: 2π 𝜑(𝑥) = 𝑥 + 𝑓 − 𝑓 λ

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2π q ϕ(x) = x2 + f 2 − f λ where λ, x and f are the incident wavelength, horizontal position from the center of the metalens and focal length of designed metalens, respectively. According to the phase distribution formula, the phase required at each position can be determined. Taking 193 nm design wavelength as an example, with optimized period and height of SiO2 nanopillars, only the diameter D of the nanopillars needs to be varied to achieve required phases. A home-written code was employed to match the diameter of nanopillars and the required phase at each position, and a corresponding metalens layout file was obtained, which was then imported into COMSOL to build the corresponding metalens model. Simulated reflected energy flux at typical wavelengths of 193, 441, 532 and 633 nm in the UV–visible range are shown in Figure4a–d, respectively. As can be seen from Figure4 , all four reflective metalenses show a clear focal spot along the optical axis around 10 µm away from the Al surface, close to the design focal length of 10 µm. Due to the 2D model used in the simulations, the reflective metalenses demonstrated here are actually cylindrical lenses, and the focal spots are actually line focuses. However, the discussions over 2D reflective metalens can be easily extended to 3D cases. The designed focal length for all metalenses is 10 µm, and the actual focal length is 10.58, 11.28, 10.78 and 11.04 µm, respectively, as indicated by the dashed white lines in Figure4a–d. Although there are small deviations between the actual focal length and the targeted value, focusing behavior is clearly seen for all four reflective metalenses in the UV–visible range. The reason for the deviation in focal length could be that the phase profile generated by the metasurface is an approximation to the perfect hyperbolic phase distribution of a lens, due to the pixel-wise discretization of the phase profile by metasurface. At the focus, the full-width half-maximum (FWHM) of the focal spots is also extracted and shown in Figure4e–h. From extracted data, the FWHMs are 250 nm for operation wavelength of 193 nm, 406 nm for operation wavelength of 441 nm, 383 nm for operation wavelength of 532 nm and 510 nm for operation wavelength of 633 nm. Except for the case of VUV wavelength of 193 nm, all other three reflective metalenses realized sub-wavelength focusing. Although the VUV metalens does not achieve subwavelength focusing here, this is not inherent to the material choice. Instead, this is closely related to the numerical aperture (N.A.) of the metalenses. In principle, one can reduce the FWHM size for the VUV metalens through increasing its N.A., simply by designing VUV metalens with shorter focal lengths, i.e., with a higher N.A. (see AppendixC for more discussions). It makes sense to have a direct comparison between SiO2 + Al metalens and SiO2 + Au/Ag metalens to confirm the superiority of metal Al in the VUV wavelength range. To do this, we replace the Al mirror in the metalens designed for 193 nm with Au and Ag, while keeping all other parts unchanged. Simulated reflected power flow are displayed in Figure5a–c, which share the same color bar to the left. It is obvious that when the Al mirror is replaced by Au or Ag mirror, the focus, albeit still at the same position, becomes very dim. This denotes that the metalens device composed of Au or Ag mirror does not perform as well as that composed of Al mirror. This can be better seen if we plot a line-cut across the focus along x-direction, which is displayed in Figure5d. It is seen again that the SiO2 + Al metalens outperforms the other two in the sense of focusing efficiency. This is understandable if one checks the optical properties of the Au, Ag and Al. Specifically, Au and Ag has interband transition starting from 2.4 and 4.02 eV [45], corresponding to a wavelength of 516.7 and 308.4 nm, respectively. Since the 193 nm falls within the interband transition absorption range of Au and Ag, metalens with Au and Ag mirror demonstrate heavy damping for incident light, resulting in reduced efficiency. Al, on the contrary, does not have interband transition absorption in the VUV wavelength considered here and has a higher bulk plasma frequency than Au and Ag [43,44], rendering it a better choice for reflective VUV metalens. Nanomaterials 2021, 11, 1243 5 of 12

where λ, x and f are the incident wavelength, horizontal position from the center of the metalens and focal length of designed metalens, respectively. According to the phase distribution formula, the phase required at each position can be determined. Taking 193 nm design wavelength as an example, with optimized period and height of SiO2 nanopillars, only the diameter D of the nanopillars needs to be varied to achieve required phases. A home-written code was employed to match the diameter of nanopillars and the required phase at each position, and a corresponding metalens layout file was obtained, which was then imported into COMSOL to build the corresponding metalens model. Simulated reflected energy flux at typical wavelengths of 193, 441, 532 and 633 nm in the UV–visible range are shown in Figure 4a–d, respectively. As can be seen from Figure 4, all four reflective metalenses show a clear focal spot along the optical axis around 10 μm away from the Al surface, close to the design focal length of 10 μm. Due to the 2D model used in the simulations, the reflective metalenses demonstrated here are actually cylindrical lenses, and the focal spots are actually line focuses. However, the discussions over 2D reflective metalens can be easily extended to 3D cases. The designed focal length for all metalenses is 10 μm, and the actual focal length is 10.58, 11.28, 10.78 and 11.04 μm, respectively, as indicated by the dashed white lines in Figure 4a–d. Although there are small deviations between the actual focal length and the targeted value, focusing behavior is clearly seen for all four reflective metalenses in the UV–visible range. The reason for the deviation in focal length could be that the phase profile generated by the metasurface is an approximation to the perfect hyperbolic phase distribution of a lens, due to the pixel- wise discretization of the phase profile by metasurface. At the focus, the full-width half- maximum (FWHM) of the focal spots is also extracted and shown in Figure 4e–h. From extracted data, the FWHMs are 250 nm for operation wavelength of 193 nm, 406 nm for operation wavelength of 441 nm, 383 nm for operation wavelength of 532 nm and 510 nm for operation wavelength of 633 nm. Except for the case of VUV wavelength of 193 nm, all other three reflective metalenses realized sub-wavelength focusing. Although the VUV metalens does not achieve subwavelength focusing here, this is not inherent to the material choice. Instead, this is closely related to the numerical aperture (N.A.) of the metalenses. In principle, one can reduce the FWHM size for the VUV metalens through Nanomaterials 2021, 11, 1243 6 of 12 increasing its N.A., simply by designing VUV metalens with shorter focal lengths, i.e., with a higher N.A. (see Appendix C for more discussions).

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It makes sense to have a direct comparison between SiO2 + Al metalens and SiO2 + Au/Ag metalens to confirm the superiority of metal Al in the VUV wavelength range. To do this, we replace the Al mirror in the metalens designed for 193 nm with Au and Ag, while keeping all other parts unchanged. Simulated reflected power flow are displayed in Figure 5a–c, which share the same color bar to the left. It is obvious that when the Al mirror is replaced by Au or Ag mirror, the focus, albeit still at the same position, becomes very dim. This denotes that the metalens device composed of Au or Ag mirror does not perform as well as that composed of Al mirror. This can be better seen if we plot a line- cut across the focus along x-direction, which is displayed in Figure 5d. It is seen again that the SiO2 + Al metalens outperforms the other two in the sense of focusing efficiency. This is understandable if one checks the optical properties of the Au, Ag and Al. Specifically, Au and Ag has interband transition starting from 2.4 and 4.02 eV [45], corresponding to a wavelength of 516.7 and 308.4 nm, respectively. Since the 193 nm falls within the interband transition absorption range of Au and Ag, metalens with Au and Ag mirror demonstrate heavy damping for incident light, resulting in reduced efficiency. Al, on the con- FigureFigure 4.4.Focusing Focusing performanceperformance ofof reflectivereflective metalensmetalens designeddesigned forfor representativerepresentative wavelengthswavelengths inin thethe UV–visibleUV–visible range.range. trary, does not have interband transition absorption in the VUV wavelength considered (a(a))λ λdd == 193 nm. nm. (b (b) )λλd d= =441 441 nm. nm. (c) (λc)d λ=d 532= 532nm. nm. (d) λ (d =) λ633d = nm. 633 Normalized nm. Normalized energy energy flux profiles flux profiles along the along white the dashed white dashedlines atlines wavelengthshere at wavelengths and hasof ( ea) higher193 of ( enm,) 193 bulk (f nm,) 441 plasma ( fnm,) 441 (g nm,frequency) 532 (g )nm 532 and nmthan ( andh) Au 633 (h )and nm. 633 Ag nm.FWHMs [43,44] FWHMs of, therendering of focal the focal spots it spots a arebetter arelabelled labelled on onthe theplots. plots. choice for reflective VUV metalens.

Figure 5. Focusing performance of reflective metalens designed for λd = 193 nm composed of (a) Figure 5. Focusing performance of reflective metalens designed for λ = 193 nm composed of (a) Au, (b) Ag and (c) Al Au, (b) Ag and (c) Al mirror. Except for the material of metald component, all other parts are the mirror. Except for the material of metal component, all other parts are the same for the three cases. (d) Line cuts along same for the three cases. (d) Line cuts along x-direction across the focus. x-direction across the focus. Dispersion characteristics of each metalens is also studied in the vicinity of ±50 nm Dispersion characteristics of each metalens is also studied in the vicinity of ±50 nm around the designed target wavelength. Taking the metalens designed for 193 nm as an around the designed target wavelength. Taking the metalens designed for 193 nm as an example, it canexample, be seen from it can Figure be seen 6a that from the Figure focusing6a that effect the of focusing the reflective effect ofmetalens the reflective is metalens obvious exceptis for obvious the wavelength except for of the 150 wavelength nm. Note that of 150all subplots nm. Note in that Figure all subplots6a share inthe Figure 6a share same color bar theon the same right. color A faint bar on focus the can right. be found A faint if focusone looks can beclosely found at ifthe one subplot looks closely at the of λ = 150 nm, whichsubplot indicates of λ = 150 the nm, lower which wavelength indicates limit the of lower the reflective wavelength metalens limit of opti- the reflective met- mized for 193 nm.alens On optimized the one hand, for 193 150 nm. nm Ondeviates the one a lot hand, from 150 the nmtargeted deviates wavelength a lot from the targeted of 193 nm; on thewavelength other hand, of 193 150 nm nm; onapproache the others hand,the absorption 150 nm approaches band-edge theof thermally absorption band-edge of grown SiO2 thin films, leading to reduced efficiency of the focusing device. With the in- thermally grown SiO2 thin films, leading to reduced efficiency of the focusing device. With crease in operationthe increasewavelength, in operation the focus wavelength, becomes more the focusobvious becomes and moves more continuously obvious and moves continu- downward alongously the downward optical axis, along meaning the optical that the axis, reflective meaning metalens that the is reflective negatively metalens dis- is negatively persive, in accordancedispersive, with in most accordance metasurface with mostdevices metasurface [39,40]. Figure devices 6b shows [39,40]. the Figure nor- 6b shows the malized reflectednormalized energy flux reflected along the energy optical flux axis along (x = the0) in optical the wavelength axis (x = 0) range in the of wavelength 150– range of 250 nm. By tracking150–250 the nm. peak By positions tracking of the the peak energy positions flux under of the energydifferent flux wavelengths under different in wavelengths Figure 6b, we obtainedin Figure and6b, we plott obtaineded positions and plotted of focus positions of the reflective of focus of metalens the reflective designed metalens designed for 193 nm underfor 193various nm underincident various wavelengths incident in wavelengths Figure 6c. It incan Figure be seen6c. Itthat can for be the seen that for the wavelength range of 150–250 nm, the actual focal position fluctuates within ±2 μm from the designed focal position and is negatively correlated with wavelength, demonstrating negative dispersion. Similar dispersion characteristics are observed for reflective metalenses designed for 441, 532 and 633 nm as well, as shown in Figure 6d–f, whereas

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wavelength range of 150–250 nm, the actual focal position fluctuates within ±2 µm from Nanomaterials 2021, 11, 1243 7 of 12 the designed focal position and is negatively correlated with wavelength, demonstrating negative dispersion. Similar dispersion characteristics are observed for reflective metalenses designed for 441, 532 and 633 nm as well, as shown in Figure6d–f, whereas the dispersionthe dispersion effect effect is weaker is weaker for these for these wavelengths wavelengths compared compared to the to case the of case193 nmof 193. Gener- nm. allyGenerally speaking, speaking, although although dispersion dispersion behavior behavi (chromatism)or (chromatism) exists forexists our for present our present reflective re- metalensflective metalens design, whichdesign, can which be eliminated can be eliminated by adapting by achromaticadapting achromatic metalens design metalens [46, 47de-], thesign reflective [46,47], the metalens reflective based metalens on the combinationbased on the of combination SiO2 nanopillars of SiO and2 nanopillars Al film proves and Al to workfilm proves from the to VUVwork tofrom the visiblethe VUV wavelength to the visible range. wavelength Considering range. the potentialConsidering of material the po- propertytential of ofmaterial SiO2 and property Al (see of Figure SiO2 1and), the Al SiO (see2 +Figure Al platform 1), the canSiO2 be + Al in principleplatform extendedcan be in toprinciple the mid-IR extended wavelength to the mid-IR range, wherewavelength one only range, needs where to optimize one only the needs metalens to optimize design the for themetalens corresponding design for wavelength. the corresponding For practical wavelength. application For practical of the reflective application metalenses, of the reflec- one possibletive metalenses, way could one be possible the off-axis way focusingcould bemethod, the off-axis i.e., focusing deflecting method, the beam i.e., off deflecting from the opticalthe beam axis off while from focusingthe optical it (seeaxis Appendixwhile focusingD for moreit (see details). Appendix D for more details).

Figure 6. DispersionDispersion characteristics characteristics of of reflective reflective metalenses. metalenses. (a) ( aDistribution) Distribution of ofreflected reflected energy energy flux flux for forthe themetalens metalens de- designedsigned for for 193 193 nm nm in in the the ±50±50 nm nm wavelength wavelength range. range. (b ()b Normalized) Normalized reflected reflected energy energy flux flux profiles profiles around around the focus alongalong thethe opticaloptical axisaxis inin thethe wavelengthwavelength rangerange ofof 150150 toto 250250 nm.nm. ((c)) Extracted focalfocal positionposition ofof metalensmetalens asas aa functionfunction ofof incidentincident wavelength for the design wavelength of 193 nm. (d–f), the same as (c), but for design wavelength of 441, 532 and 633 nm, wavelength for the design wavelength of 193 nm. (d–f), the same as (c), but for design wavelength of 441, 532 and 633 nm, respectively. respectively.

4. Conclusions

Through careful examination of the materialmaterial propertyproperty ofof thethe SiOSiO22 + Al combination, a reflectivereflective cylindrical metalens based on SiOSiO22 nanopillar on Al filmfilm waswas proposedproposed andand numerically demonstrated. Using Using COMSOL simulation and optimization, the diameter, height and period of unit cellscells ofof thethe SiOSiO22 cylinder werewere determined.determined. The optimizedoptimized unitunit cells realize reflectancereflectance closeclose toto 90% while completely coveringcovering aa 0~20~2π phase change. Four reflectivereflective metalenses were designed and optimized for wavelengthswavelengths of 193,193, 441,441, 532532 andand 633 nm, nm, and and prominent prominent focusing focusing capability capability was was observed observed for for all allreflective reflective metalenses, metalenses, es- especiallypecially for for the the VUV VUV wavelength wavelength of of 193 193 nm. nm. Dispersion Dispersion characteristics characteristics of the metalensmetalens were also studiedstudied withinwithin ±±5050 nm nm of of the the design design wavelength. It is found that the actual focal position of the metalensesmetalenses fluctuatesfluctuates withinwithin ±±22 μµmm of the designed focal length and isis negatively correlated with wavelengths, demonstratingdemonstrating negativenegative dispersion.dispersion. The material combination we used in this work not only allows us to build reflectivereflective metalensesmetalenses inin thethe UV to visible wavelength range but also holds the potential to be extended to the mid-IR. This makes the SiOSiO22 + Al combination a versatile platform to buildbuild miniaturizedminiaturized opticaloptical systems based based on on reflective reflective metasurface metasurface device devicess working working in the in theUV UVall the all way the wayto the to mid- the mid-IR,IR, enabling enabling a range a range of applications of applications in infiel fieldsds such such as as high-resol high-resolutionution photolithography, photolithography, chemical/biological sensing, sensing, imaging imaging and and spectroscopy, spectroscopy, etc.

Author Contributions: Conceptualization, H.G. and S.Y.; data curation, H.G. and M.L.; formal analysis, H.G., S.Y. and M.L.; funding acquisition, S.Y. and Z.Z.; project administration, Z.Z.; software, R.W., Y.H. and K.Z.; writing—original draft, H.G.; writing—review and editing, S.Y., R.W., Y.H. and Z.Z. All authors have read and agreed to the published version of the manuscript.

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Author Contributions: Conceptualization, H.G. and S.Y.; data curation, H.G. and M.L.; formal analysis, H.G., S.Y. and M.L.; funding acquisition, S.Y. and Z.Z.; project administration, Z.Z.; software, Nanomaterials 2021, 11, 1243 8 of 12 R.W., Y.H. and K.Z.; writing—original draft, H.G.; writing—review and editing, S.Y., R.W., Y.H. and Z.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by National Natural Science Foundation of China, grant number 61905273,Funding: andThis Beijingresearch Nova was funded Program by of National Science Natural and Technology, Science Foundation grant number of China, Z191100001119058. grant number 61905273, and Beijing Nova Program of Science and Technology, grant number Z191100001119058. Acknowledgments: The authors appreciate useful discussions with Haiyan Shi. Acknowledgments: The authors appreciate useful discussions with Haiyan Shi. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Appendix A Details of Simulation Set-Up Details of Simulation Set-Up Numerical analysis of metalenses was carried out using COMSOL Multiphysics, a Numerical analysis of metalenses was carried out using COMSOL Multiphysics, a commercial software based on finite element method (FEM). Considering that calculation of commercial software based on finite element method (FEM). Considering that calculation three-dimensional metalens model requires a huge amount of memory, and the cylindrical of three-dimensional metalens model requires a huge amount of memory, and the cylin- structure has polarization-independent characteristics, we simplified our model to a two- drical structure has polarization-independent characteristics, we simplified our model to dimensional (2D) case. SiO2 and Al domains were assigned, as shown in Figure A1a, a two-dimensional (2D) case. SiO2 and Al domains were assigned, as shown in Figure A1a, and the rest of the simulation domain is filled with air. A perfectly matched layer (PML) and the rest of the simulation domain is filled with air. A perfectly matched layer (PML) was added on the top of the unit cell, which absorbs reflected light from the structure. was added on the top of the unit cell, which absorbs reflected light from the structure. Floquet-periodic boundary conditions were used on both sides of the unit cell to simulate Floquet-periodic boundary conditions were used on both sides of the unit cell to simulate an infinite 1D array (Figure A1b), which is a generally adapted method in metasurface an infinite 1D array (Figure A1b), which is a generally adapted method in metasurface design [48]. Since the thickness of the Al mirror is several times thicker than the penetration design [48]. Since the thickness of the Al mirror is several times thicker than the penetra- depth of electromagnetic waves at the wavelengths considered in this work, transmittance tion depth of electromagnetic waves at the wavelengths considered in this work, trans- of incident light is essentially zero. Thus, only one port is placed on the interior boundary mittance of incident light is essentially zero. Thus, only one port is placed on the interior of the PML, adjacent to the air domain (Figure A1c). This port serves as the launching boundary of the PML, adjacent to the air domain (Figure A1c). This port serves as the and listening port at the same time, which is used to calculate reflectance and reflection launching and listening port at the same time, which is used to calculate reflectance and phase of incident light through S-parameter calculations. Very fine mesh sizes were used, reflection phase of incident light through S-parameter calculations. Very fine mesh sizes and maximal mesh sizes of 10 nm, λ/n_SiO2/20 and λ/20 were assigned to Al, SiO2 and were used, and maximal mesh sizes of 10 nm, λ/n_SiO2/20 and λ/20 were assigned to Al, air domains, respectively, where λ stands for the corresponding wavelength. The PML SiO2 and air domains, respectively, where λ stands for the corresponding wavelength. The domain is meshed with a swept mesh method (Figure A1d). For the simulation of the PML domain is meshed with a swept mesh method (Figure A1d). For the simulation of whole metalens device, typical total number of mesh elements is around 4~7 × 105, which the whole metalens device, typical total number of mesh elements is around 4~7 × 105, requires roughly 10 GB of memory to run the simulation (Figure A1e). which requires roughly 10 GB of memory to run the simulation (Figure A1e).

Figure A1. Simulation set-up showing (a) the Al, SiO2, air and PML domains, (b) periodic bounda- Figure A1. Simulation set-up showing (a) the Al, SiO2, air and PML domains, (b) periodic boundaries ries in x-direction, (c) the periodic launching and listening port and (d) the meshes used in the in x-direction, (c) the periodic launching and listening port and (d) the meshes used in the simulations. simulations. (e) Simulation set-up showing the whole metalens device and meshes of correspond- (e) Simulation set-up showing the whole metalens device and meshes of corresponding Al, SiO2 and ing Al, SiO2 and air domains. air domains. Appendix B Optimization Procedure of the Unit Cells of Meta-Atoms Take the structure unit of metalens designed for 441 nm as an example. The main geometric parameters of the unit cell include period P, diameter D and height H of the SiO2 nanopillars. Thickness of the Al film is set to a fixed value of 200 nm, which is thick enough to reflect all electromagnetic waves in the wavelength range considered in this

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Appendix B Optimization Procedure of the Unit Cells of Meta-Atoms Nanomaterials 2021, 11, 1243 9 of 12 Take the structure unit of metalens designed for 441 nm as an example. The main geometric parameters of the unit cell include period P, diameter D and height H of the SiO2 nanopillars. Thickness of the Al film is set to a fixed value of 200 nm, which is thick enough towork. reflect We all generally electromagnetic started with waves a reasonable in the wavelength value of range period considered P and scan in thisthe parameter work. We generallyH. For the startedselection with of P, a reasonableon the one valuehand, ofthe period period P P and should scan be the smaller parameter than H.theFor design the selectionwavelength of P,to on avoid the onehigher-order hand, the perioddiffraction. P should On the be smallerother hand, than the the period design wavelengthP cannot be totoo avoid small, higher-order otherwise there diffraction. would not On be the enough other space hand, for the the period diameter P cannot D of SiO be too2 nanopil- small, otherwiselars to vary. there Thus, would for the not design be enough wavelength space for of the 441 diameter nm, P = D250 of nm SiO is2 nanopillarsa moderate tochoice. vary. Thus,Then, forwith the the design P value wavelength fixed, the ofheight 441 nm,H is P scanned. = 250 nm Under is a moderate each value choice. of parameter Then, with H, thewe Pvaried value the fixed, diameter the height D of Hthe is scanned.nanopillar Unders and eachobtained value one of parametercurve of reflectance H, we varied and thereflection diameter phase D of(see the Figure nanopillars A2a). To and facilita obtainedte the oneselection curve of of optimal reflectance P and and H values, reflection the phaseaverage (see reflectance Figure A2 ofa). one To curve facilitate is defined the selection as 𝑅, ofand optimal the range P and of Hphase values, shift the covered average is reflectancedefined as ∆ ofφ one(Figure curve A2a). isdefined We then as usedR, and 𝑅 and the ∆ rangeφ as the of phaseindicator shift to coveredseek for isoptimized defined asvalues∆ϕ (Figure of P and A2 H.a). The We thencriterion used isR thatand the∆ϕ phaseas the shift indicator ∆φ should to seek cover for optimized at least 0values to 2π, ofand P the and average H. The criterionreflectance is that𝑅 should the phase be asshift high∆ asϕ possible.should cover After at a leastseries 0 of to rough 2π, and scan, the averagethe range reflectance of height HR canshould be co benstrained as high as to possible. 470~570 nm. After From a series Figure of rough A2b, scan,it can thebe found range ofthat height when H H can is smaller be constrained than 520 to nm, 470~570 high nm. reflectance From Figure can be A2 achievedb, it can be but found the phase that when cov- Herage is smaller is less than 5202π. nm,When high H is reflectance greater than can 520 be achievednm, the phase but the coverage phase coverage is over 2 isπ lessbut thanthe reflectance 2π. When decreases. H is greater Moreover, than 520 nm,an increase the phase in coverage the height is overH of 2theπ but nanopillar the reflectance means decreases.increase in Moreover,the aspect anratio increase of the structure, in the height thereby H of theincreasing nanopillar the difficulty means increase of nano-fab- in the aspectrication. ratio Therefore, of the structure, an optima therebyl H value increasing of 520 nm the difficultycan be picked of nano-fabrication. up. Then, we fixed Therefore, the H anvalue optimal and scanned H value parameter of 520 nm P can within be picked the range up. Then,of ±50 we nm fixed around the Hits valueinitial and value. scanned From parameterFigure A2c, P withinit can be the found range that of ± 50when nm P around is less its than initial 250 value. nm, high From reflectance Figure A2c, can it can be beachieved found but that the when phase P is coverage less than is 250 less nm, than high 2π. reflectanceWhen P is greater can be achievedthan 250 nm, but thethe phasephase coverage is is over less than2π but 2π the. When reflectance P is greater decreases than obviousl 250 nm,y. the Thus, phase it is coverage finally determined is over 2π butthat theP =reflectance 250 nm and decreases H = 520 obviously.nm is the best Thus, parameter it is finally combination determined for that the P =design 250 nm wave- and Hlength = 520 of nm 441 is nm. the The best parameter parameter optimization combination and for theselection design procedure wavelength is similar of 441 for nm. other The parameterdesign wavelengths. optimization and selection procedure is similar for other design wavelengths.

Figure A2. a Parameter optimization procedure. ( ) Reflectance and reflection phase of structural unit designed for 441 nm. Define the average reflectance as R and the phase coverage as ∆ϕ, which will be used as the indicator for parameter optimization.Figure A2. Parameter (b) Selection optimization of optimal procedure. parameter (a) Reflectance H with a preselected and reflection reasonable phase of valuestructural of P. unit (c) designed Selection for of optimal441 nm. parameterDefine the Paverage with the reflectance optimal value as 𝑅 of and H selected the phase in thecoverage previous as step.∆𝜑, which will be used as the indicator for parameter optimization. (b) Selection of optimal parameter H with a preselected reasonable value of P. (c) Selection of optimal parameter P with the optimal Appendixvalue of H selected C in the previous step. Discussion over the FWHM Size of the Focus for the VUV Metalens Appendix C The FWHM of 250 nm for metalens designed for 193 nm seems discouraging; however, Discussion over the FWHM Size of the Focus for the VUV Metalens it is not inherent to the choice of materials. It is instead closely related to the numerical apertureThe (FWHMN.A.) of of the 250 metalens. nm for metalens Specifically, designed for the for design 193 nm wavelength seems discouraging; of 193 nm, a how- focal lengthever, it ofis not 10 µ inherentm results to in the a N.A.choiceof of roughly materials. 0.401 It is (through instead calculationclosely related of N.A. to the= numer-n·sin θ, nical= 1aperture for air, and(N.A. sin) ofθ thecan metalens. be calculated Specifically, with the for aperture the design size wavelength of the metalens of 193 and nm, the a focal length of 10 μm results in a N.A. of roughly 0.401 (through calculation of N.A. = n·sin θ, n = 1 for air, and sin θ can be calculated with the aperture size of the metalens and the focal length). The diffraction limit of such a metalens with N.A. = 0.401 can be calculated using d = λ/(2 N.A.), which is 240.6 nm. Thus, the simulated FWHM of 250 nm for the metalens with 10 μm focal length is close to the diffraction limit. One can, in principle,

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focal length). The diffraction limit of such a metalens with N.A. = 0.401 can be calculated using d = λ/(2 N.A.), which is 240.6 nm. Thus, the simulated FWHM of 250 nm for the metalens with 10 µm focal length is close to the diffraction limit. One can, in principle, reduce the FWHM size of the focus through using metalenses with higher N.A. As a demonstration, we performed some numerical simulations of metalenses designed for Nanomaterials 2021, 11, 1243 193 nm VUV wavelength, but with a focal length of 5, 2 and 1 µm instead (see Figure10 A3 of). 12

In these cases, the N.A. is 0.632, 0.898 and 0.971 for focal length of 5, 2 and 1 µm, and the FWHM value of the focus is 160, 112 and 105 nm, respectively. These values are smaller thanthan the the value value described described in in the the main main text text and and are are close close to to their their corresponding corresponding diffraction diffraction limit.limit. Thus, Thus, the the FWHM FWHM values values can can be be improved improved by by designing designing a a VUV VUV metalens metalens with with a a N.A. N.A. shortershorter focal focal length, length, i.e., i.e., with with a a higher higher N.A.When When N.A.is is large large enough, enough, the the VUV VUV metalens metalens can also achieve sub-wavelength focusing. can also achieve sub-wavelength focusing.

FigureFigure A3. A3.Simulated Simulated reflected reflected power power flow flow for for a a metalens metalens designed designed for for 193 193 nm nm wavelength wavelength with with aa focalfocal length length of of (a )(a 1,) 1, (b )(b 2,) (2,c )( 5c) and5 and (d )(d 10) 10µm, μm, respectively. respectively. Subplots Subplots (a– d(a)– shared) share the samethe same color color bar tobar to the lower left. (e) Line cuts along the focus showing normalized power flow. It is obvious that the lower left. (e) Line cuts along the focus showing normalized power flow. It is obvious that with with the increase in N.A., the FWHM size of the focus decreases. the increase in N.A., the FWHM size of the focus decreases.

AppendixAppendix D D PossiblePossible Way Way to to Implement Implement Reflective Reflective Metalens Metalens in in Practical Practical Applications Applications SinceSince the the incident incident light light and and reflected reflected light light is on is the on same the same side of side the of reflective the reflective metalenses,metalenses, special special care care needs needs to be to taken be taken for practicalfor practical applications. applications. One One possible possible way way we we suggestsuggest is is the the off-axis off-axis focusing focusing method, method, i.e., i.e., deflecting deflecting the the beam beam off off from from the the optical optical axis axis whilewhile focusing focusing it. it. This This can can be be accomplished accomplished by by adding adding a a linear linear phase phase gradient gradient to to the the phase phase profileprofile of of the the lens, lens, so so that that the the reflective reflective metalens metalens achieves achieves beam beam deflection deflection and and focusing focusing at theat samethe same time time [48]. [48] To demonstrate. To demonstrate this, wethis, plot we in plot Figure in Figure A4 the A4 reflected the reflected power power flow for flow a metalensfor a metalens designed designed for λ = 441for nmλ = with441 nm a focal with length a focal of length 20 µm, of which 20 μm, deflects which the deflects incident the lightincident to different light to angles different while angles focusing while them. focusing The focal them. length The focal used inlength the simulations used in the is simu- set tolations an affordable is set to value,an affordable which is value, constrained which is by constrained our computation by our resources. computation In principle, resources. theIn focalprinciple, length the can focal be much length larger can sobe thatmuc theh larger deflected so that focus the can deflected be completely focus can separated be com- frompletely the incidentseparated beam, from thus the enabling incident implementation beam, thus enabling of reflective implementation metalens in of practical reflective applications.metalens in practical applications.

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FigureFigure A4. A4.Simulated Simulated reflected reflected power power flow flow for for a metalensa metalens designed designed for forλ = λ 441 = 441 nm nm with with a focal a focal length length of 20 μm and a deflection angle of (a) 0, (b) 5, (c) 10 and (d) 15°. of 20 µm and a deflection angle of (a) 0, (b) 5, (c) 10 and (d) 15◦.

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