Levitation and controlled MHz rotation of a nanofabricated rod by a high-NA metalens

Levitation and controlled MHz rotation of a nanofabricated rod by a high-NA metalens | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Levitation and controlled MHz rotation of a nanofabricated rod by a high-NA metalens Chuang Sun, Hailong Pi, Kian Shen Kiang, Tiberius Georgescu, Jun-Yu Ou, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4313334/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 21 Apr, 2025 Read the published version in Microsystems & Nanoengineering → Version 1 posted 12 You are reading this latest preprint version Abstract An optically levitated nanoparticle in a vacuum provides an ideal platform for ultra-precision measurements and fundamental physics studies because of the exceptionally high-quality factor and rich motional modes, which can be engineered by manipulating the optical field and the geometry of the nanoparticle. Nanofabrication technology with the ability to create arbitrary nanostructure arrays offers a precise way of engineering the optical field and the geometry of the nanoparticle. Here, for the first time, we optically levitate and rotate a nanofabricated nanorod via a nanofabricated a-Si metalens which strongly focuses a 1550nm laser beam with a numerical aperture of 0.91. By manipulating the laser beam’s polarization, the levitated nanorod’s translation frequencies can be tuned, and the spin rotation mode can be switched on and off. Then, we demonstrated that the rotational frequency relies on the laser beam’s intensity and polarization as well as the air pressure. Finally, a MHz spin rotation frequency of the nanorod is achieved in the experiment. This is the first demonstration of controlled optical spin in a metalens-based compact optical levitation system. Our research holds promise for realizing scalable on-chip integrated optical levitation systems. Physical sciences/Optics and photonics/Optical physics/Nanophotonics and plasmonics Physical sciences/Nanoscience and technology/Nanoscale devices/Nanophotonics and plasmonics Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction Optomechanics is related to utilizing light to control mechanical objects. Levitated optomechanics has become an exciting research field with the advantages of low dissipation and minimal thermal contact with the environment 1–3 . In high vacuum conditions, optical levitation systems exhibit extremely low damping loss, enabling a very high-quality factor 4 . Levitated nanoparticles possess multiple motion modes, such as centre-of-mass (COM) motions, libration, rotation, and precession 1–6 . These advantages enable optical levitation systems to be ideal platforms for studying thermal dynamics 7 and sensing forces 8 , acceleration 9 , and torque 10 . Recently, the advances in cooling an optically trapped nanoparticle into its quantum ground state of motion in a vacuum show great potential for studying macroscopic quantum mechanics. 11–13 Arising from the light-matter interaction, the dynamics of an optically levitated nanoparticle is determined by the trapping light field and the nanoparticle’s geometry property. Manipulating the light field and nanoparticle’s geometry would enable the levitated system for various sensing and physics exploration scenarios. In the aspect of manipulating light field, multi-point focusing of light provides a research platform for multi-particle coupling 14 , cooling 15 and on-demand assembly 16 , setting an important stage for achieving macroscopic many-body physics. Structured light enables novel control of particle's rotational dynamics through OAM transfer 17 and facilitates stable trapping using a doughnut-shaped beam 18 . In the aspect of engineering nanoparticle’s geometry, unique structures such as prisms make it possible to search for high-frequency gravitational waves 19 and polarization-based inverse optical torque 20 . Nanofabrication technologies capable of producing nanostructure arrays offer a precise method for engineering light fields and nanoparticle’s geometry for optical levitation. In terms of manipulating the light field, the nanofabricated metalens would be powerful in controlling the light beam’s phase 21 , amplitude 22 , and polarization 23 . In recent years, optical trapping in liquid based on compact metalens has been reported 24–27 . Optical levitation in a vacuum faces greater challenges than in liquid, requiring a larger numerical aperture (NA) to provide a large trapping potential well. Following a pioneering work of optically levitating one nanoparticle via a metalens with an NA of 0.88 28 , our group reported on-chip optical traps for levitating two nanoparticles via a dual-foci metalens with an NA of 0.9 29 . In terms of engineering nanoparticles, nanofabrication provides a precise way to achieve good uniformity and well-controlled size of particles. The combination of nanofabricated metalens and nanofabricated particles can fully exploit their advantages to achieve highly controllable and scalable on-chip integrated optical levitation systems in a vacuum. While levitation of nanofabricated particles was demonstrated in conventional bulky optical systems, an extra pulsed laser system is required for loading the nanofabricated parrticles into optical trapps in previous studies 30,31 , which significantly increased the complexity of a compact optical levitation system. Here, we demonstrate a fully nanofabricated optical levitation system where the trapping laser beam is highly focused by a nanofabricated metalens with a NA of 0.91 and the trapped nanorod is nanofabricated and loaded via a Nebulizer (Fig. 1 a). The nanofabrication process of the metalens and the silicon nanorods is illustrated at first. Then, a metalens-based optical levitation system is built to study the levitated dynamics of the nanofabricated nanorods. We demonstrate the full manipulation of the nanorod’s translational and rotational modes. The nanoparticle’s rotation is the first reported rotation in a vacuum by a metalens-based optical levitation system. 2. Nanofabricated metalens and nanorods for optical levitation 2.1 Fabrication and characterization of metalens In order to achieve the desired focusing effect, the metalens needs to impart a focusing hyperbolic phase distribution to the wavefront, as described by the following Eq. 3 2 $$\phi \left(r\right)=2\pi /\lambda \left(f-\sqrt{{r}^{2}+{f}^{2}}\right)$$ 1 where λ = 1550 nm is the wavelength, r represents the radial distance from the lens centre, and f = 200 µm is the designed focal length. A dense pattern of square a-Si nanopillars on a glass substrate is adopted to encode the phase profile on the incoming laser beam. Each a-Si nanopillar (Fig. 1 b) acts as a miniature antenna, giving a phase shift to the transmitted light. By varying the side length (W) of the pillars from 110 nm to 440 nm, we can obtain a 2π phase coverage with high, relatively uniform transmittances (Fig. 1 c). The nanopillars maintain a uniform height (H) of 800 nm, with a centre-to-centre distance of 600 nm between neighbouring nanopillars. The designed and fabricated metalens has a diameter of 1.2 mm. The designed metalens is fabricated using a nanofabrication process. Firstly, an 800 nm thick a-Si layer is deposited on a glass substrate using a plasma-enhanced chemical vapour deposition (PECVD) tool. Then, the metalens is patterned using electron beam (e-beam) lithography, followed by reactive-ion etching (RIE) of 800 nm into the a-Si layer. Figure 1 d presents a top-view scanning electron microscopy (SEM) image of the central region of the fabricated metalens. In order to determine the numerical aperture (NA) of the fabricated metalens, the laser intensity distribution at the focal spot is measured. In the measurement, a 1550 nm laser with a beam waist much larger than the diameter of the metalens is used to ensure a plane wave input with a constant amplitude. The focused laser beam image after it passes through the metalens is captured by using an objective lens and a camera. Figure 1 e shows the measured intensity distribution of the focus in the xy plane, revealing a clear and well-defined focal spot. Figure 1 f presents a cut across the x-axis passing through the focus (dotted line in Fig. 1 e), along with the fitting to the Airy pattern. The Airy radius (r A ), defined as the radius from the central peak of the Airy function to its first minimum, is 1.036 µm. So the corresponding NA is 0.91, calculated based on the relationship r A = 0.61λ/NA. 2.2 Nanofabrication of nanorods In this section, we show the nanofabrication of nanorods used in optical levitation in a vacuum. Here, rectangular nanorods are fabricated based on a silicon-on-insulator (SOI) wafer. The process outlined here can be adapted to fabricate particles with any desired shape. Figure 2 a shows an SEM image of a fabricated rectangular nanorod. The nanorod has a width of 214 nm, a length of 753 nm and a height of 220 nm. Figure 2 b illustrates the fabrication process of the nanorods. The SOI wafer used in this procedure has a 220 nm thick silicon layer and a 2 µm thick buried oxide layer. The nanorod pattern is transferred to a 300 nm thick ZEP520A resist layer using single-step e-beam lithography (Fig. 2 b(ii)). A 40 nm thick Cr layer is deposited by e-beam evaporation, and then the particle patterns are transferred to the Cr surface through a liftoff step (Fig. 2 b(iii)). Using Cr as a hard mask, the patterns are then transferred to the Si layer using reactive-ion etching (RIE) (Fig. 2 b(iv)). The Cr layer is subsequently removed using a Cr etchant and then the buried oxide layer is removed using HF vapour to release the silicon particles (Fig. 2 b(v)). At last, the Si nanorods are transferred from the silicon substrate to deionized (DI) water using an ultrasonic tank (Fig. 2 b(vi)). The nanorods dispersed in DI water are suitable for loading with an ultrasonic nebulizer. The fabrication process shown here can also be used for other particle loading methods, such as laser-induced acoustic desorption 33 . The HF etching time can be controlled, enabling the fabrication of Si nanoparticles with a well-defined breaking point in SiO 2 . 3. Optical levitation experiment 3.1 Translational motions The experimental setup for levitating a nanofabricated nanorod using a metalens is shown in Fig. 3 a. A 1550 nm laser, amplified by an erbium-doped fibre amplifier (EDFA), is collimated to a polarizer for obtaining linearly polarized light. A quarter-wave plate (QWP) is utilized to control the light's polarization state. The scattering light is collected by an objective lens and detected by a photodetector to record the nanorod's motion. A polarizing beam splitter (PBS) is utilized before the photodetector for detecting rotation signals. A focused 532 nm laser is used to illuminate the levitated nanorod for capturing the nanorod’s picture (i.e., the inset picture in Fig. 3 a). A dichroic mirror (DM) is used to split the 532 nm and 1550 nm lasers before the detection. Nanorods are loaded into the optical trap in ambient conditions via an ultrasonic nebulizer. Once a nanorod is trapped, we reduce the vacuum chamber's pressure to 4 mbar. Figure 3 b shows the power spectral density (PSD) signal of the particle's motions when the trapping laser beam is linearly polarized. The PSD is defined as 34 $${S_{qq}}(\omega )=\frac{{{\Gamma _{CM}}{k_B}{T_{CM}}/(\pi M)}}{{{{\left( {{\omega ^2} - \omega _{q}^{2}} \right)}^2}+\Gamma _{{CM}}^{2}{\omega ^2}}}$$ 2 where Γ CM is the damping rate of the COM motion, k B is the Boltzmann constant, T CM is the temperature of the COM, M is the particle's mass, and ω q is the mechanical oscillation frequency of the trapped nanorod. Using Eq. ( 2 ) to fit each peak, we can obtain that the oscillation frequencies in the z, x, and y directions are 43.6 kHz, 78.3 kHz and 122.8 kHz, respectively. The frequency in the z-direction is lower than the other frequencies because the optical field is elongated along the direction of the propagating beam. A second harmonic signal along the z-direction in the PSD (Fig. 3 b) arises from the non-perfectly harmonic trapping potential in the axial direction. As the trapping laser’s focal field depends on the laser beam’s polarization, which can affect the levitated nanorod’s motion. Figure 3 c shows that the COM motions of the levitated nanorod can be manipulated by changing the trapping laser beam’s polarization. The waveplate angle in the figure refers to the angle between the optical axis of the QWP and the polarizing axis of the polarizer. The ellipticity of the polarized light increases with increasing angle. We use the frequency difference (Δf x−y ) between the x and y directions to show the polarization’s dependency of the translational motions in x and y directions. It can be seen that the Δf x−y gradually reduces when adjusting the input beam's polarization from linear to elliptical polarization, indicating the translational motion frequencies in the x and y directions are becoming closer. The mechanical oscillation frequency in the z direction remains constant as the field distribution in the z direction is not affected by the laser beam’s polarization. For an optically levitated nanorod, anisotropic damping rates for COM motions in the air are expected 5 . The ratio of damping rates depends on the aspect ratio of the levitated particle. Thus, we use the ratio of damping rates to identify that the levitated particle is a fabricated nanorod. Figure 3 d shows the PSD signals of the detected particle motion with a QWP angle of 30º and pressure of 4 mbar. The red curves are the Lorentzian fittings based on Eq. ( 2 ). A maximum damping ratio Γ x /Γ z of 1.467 is obtained when the QWP angle is 30º. This ratio closely matches the damping ratio calculated for a chain tetramer 5 , indicating a nanorod is optically levitated. The damping rate in the z direction suggests that the nanorod's long axis is oriented parallel to the optical axis, as shown in the inset of Fig. 3 d. 3.2 MHz spin rotation and manipulation In this section, we demonstrate the control over the rotational dynamics of an optically levitated nanorod by a metalens. The pressure inside the vacuum chamber is reduced to 0.11 mbar in order to mitigate the damping effect caused by gas molecules and to observe a clear rotational signal. Figure 4 a (4b) show the PSD spectra from 0 to 200KHz (200–1500KHz) for circularly polarized (orange curve) and linearly polarized (blue curve) light beams, respectively. While the central frequencies of COM motions in Fig. 4 a are similar to that (Fig. 3 b) at 4 mbar pressure, the linewidth of the peaks in Fig. 4 a is much narrower than that in Fig. 3 b. It means that the air pressure only acts as a damping factor which goes down with lowing the air pressure. Figure 4 (b) clearly shows that two new trapping frequencies (f rot and 2f rot ) appear on the PSD curve for the circularly polarized laser beam, in comparison to the linearly polarized light. As the pressure is reduced further, the frequencies f rot and 2f rot increase as shown in Fig. 4 c. This is a typical feature of the spin rotation of a levitated nanorod. In the PSD spectrum, the amplitude of 2f rot is much larger than that of f rot , due to the geometrical symmetry of the nanofabricated nanorod. The rotation of the levitated nanorod can be attributed to the torque exerted by the circularly polarized light. The strength of this optical torque depends on the laser power and the particle’s polarizability, and can be expressed as 35 $${\tau _z}=\frac{1}{2}E_{0}^{2}\frac{{{k^3}}}{{6\pi {\varepsilon _0}}}{\left( {\Delta {\alpha _0}} \right)^2}$$ 3 where E 0 is the amplitude of the optical input field, k is the wavenumber, ε 0 is the dielectric constant in vacuum, and Δα 0 is given by $$\Delta {\alpha _0}=\frac{{{\alpha _x}}}{{1+i{k^3}{\alpha _x}/(6\pi {\varepsilon _0})}} - \frac{{{\alpha _y}}}{{1+i{k^3}{\alpha _y}/(6\pi {\varepsilon _0})}}$$ 4 with α x and α y being the nanorod’s polarization along the x and y axis, respectively. The maximum steady-state rotation frequency of the particle can be represented as $${f_{rot}}=\frac{{{\tau _z}}}{{2\pi I\Gamma }}$$ 5 where I is the rectangular nanorod’s momentum of inertia, and Γ is the rotational damping rate for diffuse reflection of gas molecules. Figure 4 c shows the calculated rotation frequency (blue curve) of the nanorod at different pressures using Eqs. ( 2 – 4 ). The detailed calculation is shown in the supplementary materials. For complex-shaped nanoparticles, their optical torque can be calculated by combining the finite difference in the time-domain method with the discrete dipole approximation method 36 . The calculated rotation frequency closely matches the experimentally measured frequency. The difference between measured and calculated frequencies originates from the deviations between the measured and actual sizes of the nanorod. The dependency of the nanorod’s rotation frequency on the laser beam’s power and polarization is experimentally explored as shown in Figs. 4 d and 4 e. Figure 4 d shows that the measured rotational frequency is proportional to the laser power, which is consistent with Eq. ( 3 ). The polarization is tuned by rotating the QWP. As shown in Fig. 4 e, when the angle is within the range from 0 to 30º, there is no rotational signal in the PSD spectrum, indicating that the optical torque applied to the nanorod is smaller than the air drag. When the QWP angle is larger than 30º, the nanorod starts to rotate and the rotational PSD signal appears. With furtherly increasing the QWP angle, more spin angular momentum can be transferred to the nanorod, thereby a higher rotation frequency can be obtained. The blue curves in Figs. 4 d and 4 e show the calculated results, which agree well with the experimental measurements (orange curves). 4. Discussion Here, we demonstrated the optical levitation of a nanofabricated nanorod in a vacuum environment using nanofabricated metalens. Controllable COM motions and rotation of the levitated nanorod have also been demonstrated. In our experiment, a metalens is utilized to achieve a single-point focus of the light beam. In future studies, the metalens can combine single-point focusing with an adjustable focus 37 to explore short-range forces or with vortex light fields to stable trap large-sized particles for enhancing force detection sensitivity. In addition, single focal points can be extended to multi-focal points 29 for research into macroscopic many-body quantum mechanics. In our experiment, a nanofabricated silicon rectangular nanorod was used for levitation in a vacuum. The nanofabrication techniques are not limited to the fabrication of the nanorods. They can be utilized to fabricate nanoparticles of any shape and size, enabling the highlight of specific motions of a levitated particle and the exploration of novel particle manipulation techniques. In this proof-of-concept experiment, we employed e-beam lithography to define the size and shape of nanorods. For high-throughput and low-cost fabrication of particles, conventional photolithography can be used 38 . The demonstrated translation and rotation of nanofabricated particles in a vacuum based on metalens can combine the powerful light field control capability of the metalens with the customization advantage of nanoparticles. This can provide an ideal platform for further expanding the applications of optical levitation. Meanwhile, this system using nanofabricated ultrathin metalens can provide a compact solution for integrated on-chip sensing applications, such as acceleration (translation) and torque (rotation). In the future, this can be combined with chip-based light source 39 and vacuum packaging technology 40 to realize a miniaturized, robust, and scalable on-chip integrated optical levitation system. This approach holds the potential to significantly transit vacuum optical levitation systems from the laboratory into practical applications. 5. Conclusion We have demonstrated an optical levitation system in a vacuum by combining a nanofabricated metalens and a nanofabricated Si nanorod. The COM motions and rotation of the levitated nanorod can be controlled. The system can combine the advantages of light manipulation from metalens and the customizability of a nanoparticle. The combined advantages would enable the generation of specific light fields and particle motions, for various sensing applications, investigating macroscopic many-body physics and quantum sensing. In addition, this system using compact metalens holds great potential for achieving miniaturized, robust and scalable on-chip integrated optical levitation systems. This integration solution can pave the way to significantly expedite the transition of optical levitation systems in the vacuum from laboratory to practical applications. Declarations Conflict of Interest The authors have no conflicts to disclose. 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Additional Declarations (Not answered) Supplementary Files Supplementary.docx Supporting material for 'Levitation and controlled MHz rotation of a nanofabricated rod by a high-NA metalens' Cite Share Download PDF Status: Published Journal Publication published 21 Apr, 2025 Read the published version in Microsystems & Nanoengineering → Version 1 posted Editorial decision: revise 25 Aug, 2024 Review # 2 received at journal 18 Aug, 2024 Review # 3 received at journal 30 Jul, 2024 Reviewer # 3 agreed at journal 25 Jul, 2024 Reviewer # 2 agreed at journal 22 Jul, 2024 Review # 1 received at journal 15 Jul, 2024 Reviewer # 1 agreed at journal 04 Jul, 2024 Reviewers invited by journal 31 May, 2024 Submission checks completed at journal 28 Apr, 2024 First submitted to journal 27 Apr, 2024 Unknown event 25 Apr, 2024 Editor assigned by journal 23 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4313334","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":308945787,"identity":"8a8f02bd-6a8b-48ca-8cdf-a852588d3e82","order_by":0,"name":"Chuang Sun","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuUlEQVRIiWNgGAWjYNCCCiS2BHFazjAw8JCmhbGNFC38DezPpAvn1cnZs/ceYPhRw5A4s4GAFokDPGbSM7cdNubhOZfA2HOMIXE2IVsMGHjYpHm3HUjskcgxYOBtYEicR1gL0GG8c+rAWhj/EqeFwUyat4EZrIUZZAtBh0kc5jG25jkG9MuZMwaHZY5JGBP0Pn97+8PbPDV1cuztPYYP39TYyM44QMgaZiT2AaLjfhSMglEwCkYBfgAALOsy3W0vceMAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-7024-1916","institution":"University of Southampton","correspondingAuthor":true,"prefix":"","firstName":"Chuang","middleName":"","lastName":"Sun","suffix":""},{"id":308945788,"identity":"a6b733b0-89ee-43ab-93d3-0314919366b6","order_by":1,"name":"Hailong Pi","email":"","orcid":"","institution":"University of Southampton","correspondingAuthor":false,"prefix":"","firstName":"Hailong","middleName":"","lastName":"Pi","suffix":""},{"id":308945789,"identity":"8d56946a-1213-4890-8b33-030aec14eaa5","order_by":2,"name":"Kian Shen Kiang","email":"","orcid":"","institution":"University of Southampton","correspondingAuthor":false,"prefix":"","firstName":"Kian","middleName":"Shen","lastName":"Kiang","suffix":""},{"id":308945790,"identity":"892ea8c6-659c-4feb-b5b9-16e5d98bc0d5","order_by":3,"name":"Tiberius Georgescu","email":"","orcid":"","institution":"University of Southampton","correspondingAuthor":false,"prefix":"","firstName":"Tiberius","middleName":"","lastName":"Georgescu","suffix":""},{"id":308945791,"identity":"d0db2e6d-7a13-4f0d-8ae5-3504fbf10a9c","order_by":4,"name":"Jun-Yu Ou","email":"","orcid":"https://orcid.org/0000-0001-8028-6130","institution":"University of Southampton","correspondingAuthor":false,"prefix":"","firstName":"Jun-Yu","middleName":"","lastName":"Ou","suffix":""},{"id":308945792,"identity":"2aa3f6e2-21bd-445a-b738-eae0670e760e","order_by":5,"name":"Hendrik Ulbricht","email":"","orcid":"","institution":"University of Southampton","correspondingAuthor":false,"prefix":"","firstName":"Hendrik","middleName":"","lastName":"Ulbricht","suffix":""},{"id":308945793,"identity":"03a50e3f-6aed-490d-be7f-52948ffb263f","order_by":6,"name":"Jize Yan","email":"","orcid":"","institution":"University of Southampton","correspondingAuthor":false,"prefix":"","firstName":"Jize","middleName":"","lastName":"Yan","suffix":""}],"badges":[],"createdAt":"2024-04-23 16:20:54","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4313334/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4313334/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41378-025-00886-7","type":"published","date":"2025-04-21T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":58309361,"identity":"27001691-6a6b-449b-af8c-b22a573fccd7","added_by":"auto","created_at":"2024-06-13 18:53:49","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":93745,"visible":true,"origin":"","legend":"\u003cp\u003eMetalens-based optical levitation system and the metalens’ performance. (a) Schematic of the optical levitation in vacuum combining the nanofabricated metalens and a nanofabricated nanorod. (b) The periodical element of the metalens: an a-Si nanopillar on a glass substrate. (c) Simulated propagation phase and transmission as a function of the nanopillar's width W (110nm to 440nm). (d) Top-view SEM of the fabricated metalens. (e) Measured intensity distribution in the focal plane. (f) The intensity profile along the x-axis passes through the focus, together with the fitting to the Airy profile.\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4313334/v1/1e825a8b2c19087a3b9ea168.jpg"},{"id":58309360,"identity":"ce35013a-9815-4c32-bd9b-1af7e0d35db0","added_by":"auto","created_at":"2024-06-13 18:53:49","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":46050,"visible":true,"origin":"","legend":"\u003cp\u003e(a) SEM image of a fabricated nanorod. (b) Nanofabrication process for Si nanorods with a designed shape and size.\u003c/p\u003e","description":"","filename":"Picture2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4313334/v1/0fec5c4b2a4f49497baf897b.jpg"},{"id":58309362,"identity":"c321fe7b-0468-4196-bfb7-e59dfcfc3e2e","added_by":"auto","created_at":"2024-06-13 18:53:49","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":180478,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic of the experimental setup for levitating nanofabricated nanorod with metalens. The insert shows the optical image of a levitated nanorod. (b) Power spectral density (PSD) of the motions of levitated nanorod at 4 mbar. (c) The measured mechanical oscillation frequencies as a function of the laser’s polarization. The QWP angle of 0° means the light is linearly polarized. (d) Lorentzian fittings of measured PSDs of the COM motions for obtaining damping rates of the motions, and the inset shows the orientation of the trapped nanorod.\u003c/p\u003e","description":"","filename":"Picture3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4313334/v1/c3a8afc51672684d399e6758.jpg"},{"id":58309359,"identity":"2fa4cb2b-8ad0-4c62-af86-ef9c43c0c8ec","added_by":"auto","created_at":"2024-06-13 18:53:49","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":169946,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Power spectral density (PSD) at 0.11 mbar, with linear (blue line) and circular (orange line) polarization states, respectively. The frequency ranges from (a) 0 to 200 kHz and (b) 200 to 1500 kHz. The rotation frequency’s dependency on air pressure (c), laser power (d), and the polarization (e).\u003c/p\u003e","description":"","filename":"Picture4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4313334/v1/e2f6d4485add9715e9fd74c8.jpg"},{"id":81091373,"identity":"2b0c7215-4665-4b86-9b4b-a4f3348915ae","added_by":"auto","created_at":"2025-04-22 07:10:01","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1023504,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4313334/v1/4004af37-f911-4cb1-86ee-52bc65b5f22f.pdf"},{"id":58309364,"identity":"da9c0a58-65e0-48c2-99db-0707c73303fc","added_by":"auto","created_at":"2024-06-13 18:53:50","extension":"docx","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":36588,"visible":true,"origin":"","legend":"Supporting material for 'Levitation and controlled MHz rotation of a nanofabricated rod by a high-NA metalens'","description":"","filename":"Supplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-4313334/v1/d8da0abb9dc15fe4c489f634.docx"}],"financialInterests":"(Not answered)","formattedTitle":"Levitation and controlled MHz rotation of a nanofabricated rod by a high-NA metalens","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eOptomechanics is related to utilizing light to control mechanical objects. Levitated optomechanics has become an exciting research field with the advantages of low dissipation and minimal thermal contact with the environment\u003csup\u003e1\u0026ndash;3\u003c/sup\u003e. In high vacuum conditions, optical levitation systems exhibit extremely low damping loss, enabling a very high-quality factor\u003csup\u003e4\u003c/sup\u003e. Levitated nanoparticles possess multiple motion modes, such as centre-of-mass (COM) motions, libration, rotation, and precession\u003csup\u003e1\u0026ndash;6\u003c/sup\u003e. These advantages enable optical levitation systems to be ideal platforms for studying thermal dynamics\u003csup\u003e7\u003c/sup\u003e and sensing forces\u003csup\u003e8\u003c/sup\u003e, acceleration\u003csup\u003e9\u003c/sup\u003e, and torque\u003csup\u003e10\u003c/sup\u003e. Recently, the advances in cooling an optically trapped nanoparticle into its quantum ground state of motion in a vacuum show great potential for studying macroscopic quantum mechanics.\u003csup\u003e11\u0026ndash;13\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eArising from the light-matter interaction, the dynamics of an optically levitated nanoparticle is determined by the trapping light field and the nanoparticle\u0026rsquo;s geometry property. Manipulating the light field and nanoparticle\u0026rsquo;s geometry would enable the levitated system for various sensing and physics exploration scenarios. In the aspect of manipulating light field, multi-point focusing of light provides a research platform for multi-particle coupling\u003csup\u003e14\u003c/sup\u003e, cooling\u003csup\u003e15\u003c/sup\u003e and on-demand assembly\u003csup\u003e16\u003c/sup\u003e, setting an important stage for achieving macroscopic many-body physics. Structured light enables novel control of particle's rotational dynamics through OAM transfer\u003csup\u003e17\u003c/sup\u003e and facilitates stable trapping using a doughnut-shaped beam\u003csup\u003e18\u003c/sup\u003e. In the aspect of engineering nanoparticle\u0026rsquo;s geometry, unique structures such as prisms make it possible to search for high-frequency gravitational waves\u003csup\u003e19\u003c/sup\u003e and polarization-based inverse optical torque\u003csup\u003e20\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eNanofabrication technologies capable of producing nanostructure arrays offer a precise method for engineering light fields and nanoparticle\u0026rsquo;s geometry for optical levitation. In terms of manipulating the light field, the nanofabricated metalens would be powerful in controlling the light beam\u0026rsquo;s phase\u003csup\u003e21\u003c/sup\u003e, amplitude\u003csup\u003e22\u003c/sup\u003e, and polarization\u003csup\u003e23\u003c/sup\u003e. In recent years, optical trapping in liquid based on compact metalens has been reported\u003csup\u003e24\u0026ndash;27\u003c/sup\u003e. Optical levitation in a vacuum faces greater challenges than in liquid, requiring a larger numerical aperture (NA) to provide a large trapping potential well. Following a pioneering work of optically levitating one nanoparticle via a metalens with an NA of 0.88\u003csup\u003e28\u003c/sup\u003e, our group reported on-chip optical traps for levitating two nanoparticles via a dual-foci metalens with an NA of 0.9\u003csup\u003e29\u003c/sup\u003e. In terms of engineering nanoparticles, nanofabrication provides a precise way to achieve good uniformity and well-controlled size of particles. The combination of nanofabricated metalens and nanofabricated particles can fully exploit their advantages to achieve highly controllable and scalable on-chip integrated optical levitation systems in a vacuum. While levitation of nanofabricated particles was demonstrated in conventional bulky optical systems, an extra pulsed laser system is required for loading the nanofabricated parrticles into optical trapps in previous studies\u003csup\u003e30,31\u003c/sup\u003e, which significantly increased the complexity of a compact optical levitation system.\u003c/p\u003e \u003cp\u003eHere, we demonstrate a fully nanofabricated optical levitation system where the trapping laser beam is highly focused by a nanofabricated metalens with a NA of 0.91 and the trapped nanorod is nanofabricated and loaded via a Nebulizer (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). The nanofabrication process of the metalens and the silicon nanorods is illustrated at first. Then, a metalens-based optical levitation system is built to study the levitated dynamics of the nanofabricated nanorods. We demonstrate the full manipulation of the nanorod\u0026rsquo;s translational and rotational modes. The nanoparticle\u0026rsquo;s rotation is the first reported rotation in a vacuum by a metalens-based optical levitation system.\u003c/p\u003e"},{"header":"2. Nanofabricated metalens and nanorods for optical levitation","content":"\u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Fabrication and characterization of metalens\u003c/h2\u003e \u003cp\u003eIn order to achieve the desired focusing effect, the metalens needs to impart a focusing hyperbolic phase distribution to the wavefront, as described by the following Eq.\u0026nbsp;3\u003csup\u003e2\u003c/sup\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\phi \\left(r\\right)=2\\pi /\\lambda \\left(f-\\sqrt{{r}^{2}+{f}^{2}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere λ\u0026thinsp;=\u0026thinsp;1550 nm is the wavelength, r represents the radial distance from the lens centre, and \u003cem\u003ef\u003c/em\u003e\u0026thinsp;=\u0026thinsp;200 \u0026micro;m is the designed focal length. A dense pattern of square a-Si nanopillars on a glass substrate is adopted to encode the phase profile on the incoming laser beam. Each a-Si nanopillar (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb) acts as a miniature antenna, giving a phase shift to the transmitted light. By varying the side length (W) of the pillars from 110 nm to 440 nm, we can obtain a 2π phase coverage with high, relatively uniform transmittances (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). The nanopillars maintain a uniform height (H) of 800 nm, with a centre-to-centre distance of 600 nm between neighbouring nanopillars. The designed and fabricated metalens has a diameter of 1.2 mm.\u003c/p\u003e \u003cp\u003eThe designed metalens is fabricated using a nanofabrication process. Firstly, an 800 nm thick a-Si layer is deposited on a glass substrate using a plasma-enhanced chemical vapour deposition (PECVD) tool. Then, the metalens is patterned using electron beam (e-beam) lithography, followed by reactive-ion etching (RIE) of 800 nm into the a-Si layer. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed presents a top-view scanning electron microscopy (SEM) image of the central region of the fabricated metalens.\u003c/p\u003e \u003cp\u003eIn order to determine the numerical aperture (NA) of the fabricated metalens, the laser intensity distribution at the focal spot is measured. In the measurement, a 1550 nm laser with a beam waist much larger than the diameter of the metalens is used to ensure a plane wave input with a constant amplitude. The focused laser beam image after it passes through the metalens is captured by using an objective lens and a camera. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee shows the measured intensity distribution of the focus in the xy plane, revealing a clear and well-defined focal spot. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef presents a cut across the x-axis passing through the focus (dotted line in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee), along with the fitting to the Airy pattern. The Airy radius (r\u003csub\u003eA\u003c/sub\u003e), defined as the radius from the central peak of the Airy function to its first minimum, is 1.036 \u0026micro;m. So the corresponding NA is 0.91, calculated based on the relationship r\u003csub\u003eA\u003c/sub\u003e = 0.61λ/NA.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Nanofabrication of nanorods\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this section, we show the nanofabrication of nanorods used in optical levitation in a vacuum. Here, rectangular nanorods are fabricated based on a silicon-on-insulator (SOI) wafer. The process outlined here can be adapted to fabricate particles with any desired shape. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea shows an SEM image of a fabricated rectangular nanorod. The nanorod has a width of 214 nm, a length of 753 nm and a height of 220 nm.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb illustrates the fabrication process of the nanorods. The SOI wafer used in this procedure has a 220 nm thick silicon layer and a 2 \u0026micro;m thick buried oxide layer. The nanorod pattern is transferred to a 300 nm thick ZEP520A resist layer using single-step e-beam lithography (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb(ii)). A 40 nm thick Cr layer is deposited by e-beam evaporation, and then the particle patterns are transferred to the Cr surface through a liftoff step (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb(iii)). Using Cr as a hard mask, the patterns are then transferred to the Si layer using reactive-ion etching (RIE) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb(iv)). The Cr layer is subsequently removed using a Cr etchant and then the buried oxide layer is removed using HF vapour to release the silicon particles (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb(v)). At last, the Si nanorods are transferred from the silicon substrate to deionized (DI) water using an ultrasonic tank (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb(vi)). The nanorods dispersed in DI water are suitable for loading with an ultrasonic nebulizer. The fabrication process shown here can also be used for other particle loading methods, such as laser-induced acoustic desorption\u003csup\u003e33\u003c/sup\u003e. The HF etching time can be controlled, enabling the fabrication of Si nanoparticles with a well-defined breaking point in SiO\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Optical levitation experiment","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Translational motions\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe experimental setup for levitating a nanofabricated nanorod using a metalens is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea. A 1550 nm laser, amplified by an erbium-doped fibre amplifier (EDFA), is collimated to a polarizer for obtaining linearly polarized light. A quarter-wave plate (QWP) is utilized to control the light's polarization state. The scattering light is collected by an objective lens and detected by a photodetector to record the nanorod's motion. A polarizing beam splitter (PBS) is utilized before the photodetector for detecting rotation signals. A focused 532 nm laser is used to illuminate the levitated nanorod for capturing the nanorod\u0026rsquo;s picture (i.e., the inset picture in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). A dichroic mirror (DM) is used to split the 532 nm and 1550 nm lasers before the detection. Nanorods are loaded into the optical trap in ambient conditions via an ultrasonic nebulizer.\u003c/p\u003e \u003cp\u003eOnce a nanorod is trapped, we reduce the vacuum chamber's pressure to 4 mbar. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb shows the power spectral density (PSD) signal of the particle's motions when the trapping laser beam is linearly polarized. The PSD is defined as\u003csup\u003e34\u003c/sup\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${S_{qq}}(\\omega )=\\frac{{{\\Gamma _{CM}}{k_B}{T_{CM}}/(\\pi M)}}{{{{\\left( {{\\omega ^2} - \\omega _{q}^{2}} \\right)}^2}+\\Gamma _{{CM}}^{2}{\\omega ^2}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003eCM\u003c/em\u003e\u003c/sub\u003e is the damping rate of the COM motion, \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e is the Boltzmann constant, \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eCM\u003c/em\u003e\u003c/sub\u003e is the temperature of the COM, \u003cem\u003eM\u003c/em\u003e is the particle's mass, and \u003cem\u003eω\u003c/em\u003e\u003csub\u003e\u003cem\u003eq\u003c/em\u003e\u003c/sub\u003e is the mechanical oscillation frequency of the trapped nanorod. Using Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) to fit each peak, we can obtain that the oscillation frequencies in the z, x, and y directions are 43.6 kHz, 78.3 kHz and 122.8 kHz, respectively. The frequency in the z-direction is lower than the other frequencies because the optical field is elongated along the direction of the propagating beam. A second harmonic signal along the z-direction in the PSD (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb) arises from the non-perfectly harmonic trapping potential in the axial direction.\u003c/p\u003e \u003cp\u003eAs the trapping laser\u0026rsquo;s focal field depends on the laser beam\u0026rsquo;s polarization, which can affect the levitated nanorod\u0026rsquo;s motion. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec shows that the COM motions of the levitated nanorod can be manipulated by changing the trapping laser beam\u0026rsquo;s polarization. The waveplate angle in the figure refers to the angle between the optical axis of the QWP and the polarizing axis of the polarizer. The ellipticity of the polarized light increases with increasing angle. We use the frequency difference (Δf\u003csub\u003ex\u0026minus;y\u003c/sub\u003e) between the x and y directions to show the polarization\u0026rsquo;s dependency of the translational motions in x and y directions. It can be seen that the Δf\u003csub\u003ex\u0026minus;y\u003c/sub\u003e gradually reduces when adjusting the input beam's polarization from linear to elliptical polarization, indicating the translational motion frequencies in the x and y directions are becoming closer. The mechanical oscillation frequency in the z direction remains constant as the field distribution in the z direction is not affected by the laser beam\u0026rsquo;s polarization.\u003c/p\u003e \u003cp\u003eFor an optically levitated nanorod, anisotropic damping rates for COM motions in the air are expected\u003csup\u003e5\u003c/sup\u003e. The ratio of damping rates depends on the aspect ratio of the levitated particle. Thus, we use the ratio of damping rates to identify that the levitated particle is a fabricated nanorod. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed shows the PSD signals of the detected particle motion with a QWP angle of 30\u0026ordm; and pressure of 4 mbar. The red curves are the Lorentzian fittings based on Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). A maximum damping ratio Γ\u003csub\u003ex\u003c/sub\u003e/Γ\u003csub\u003ez\u003c/sub\u003e of 1.467 is obtained when the QWP angle is 30\u0026ordm;. This ratio closely matches the damping ratio calculated for a chain tetramer\u003csup\u003e5\u003c/sup\u003e, indicating a nanorod is optically levitated. The damping rate in the z direction suggests that the nanorod's long axis is oriented parallel to the optical axis, as shown in the inset of Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2 MHz spin rotation and manipulation\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this section, we demonstrate the control over the rotational dynamics of an optically levitated nanorod by a metalens. The pressure inside the vacuum chamber is reduced to 0.11 mbar in order to mitigate the damping effect caused by gas molecules and to observe a clear rotational signal. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea (4b) show the PSD spectra from 0 to 200KHz (200\u0026ndash;1500KHz) for circularly polarized (orange curve) and linearly polarized (blue curve) light beams, respectively. While the central frequencies of COM motions in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea are similar to that (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb) at 4 mbar pressure, the linewidth of the peaks in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea is much narrower than that in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb. It means that the air pressure only acts as a damping factor which goes down with lowing the air pressure.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b) clearly shows that two new trapping frequencies (f\u003csub\u003erot\u003c/sub\u003e and 2f\u003csub\u003erot\u003c/sub\u003e) appear on the PSD curve for the circularly polarized laser beam, in comparison to the linearly polarized light. As the pressure is reduced further, the frequencies f\u003csub\u003erot\u003c/sub\u003e and 2f\u003csub\u003erot\u003c/sub\u003e increase as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec. This is a typical feature of the spin rotation of a levitated nanorod. In the PSD spectrum, the amplitude of 2f\u003csub\u003erot\u003c/sub\u003e is much larger than that of f\u003csub\u003erot\u003c/sub\u003e, due to the geometrical symmetry of the nanofabricated nanorod.\u003c/p\u003e \u003cp\u003eThe rotation of the levitated nanorod can be attributed to the torque exerted by the circularly polarized light. The strength of this optical torque depends on the laser power and the particle\u0026rsquo;s polarizability, and can be expressed as\u003csup\u003e35\u003c/sup\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$${\\tau _z}=\\frac{1}{2}E_{0}^{2}\\frac{{{k^3}}}{{6\\pi {\\varepsilon _0}}}{\\left( {\\Delta {\\alpha _0}} \\right)^2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere E\u003csub\u003e0\u003c/sub\u003e is the amplitude of the optical input field, k is the wavenumber, ε\u003csub\u003e0\u003c/sub\u003e is the dielectric constant in vacuum, and Δα\u003csub\u003e0\u003c/sub\u003e is given by\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\Delta {\\alpha _0}=\\frac{{{\\alpha _x}}}{{1+i{k^3}{\\alpha _x}/(6\\pi {\\varepsilon _0})}} - \\frac{{{\\alpha _y}}}{{1+i{k^3}{\\alpha _y}/(6\\pi {\\varepsilon _0})}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewith α\u003csub\u003ex\u003c/sub\u003e and α\u003csub\u003ey\u003c/sub\u003e being the nanorod\u0026rsquo;s polarization along the x and y axis, respectively. The maximum steady-state rotation frequency of the particle can be represented as\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${f_{rot}}=\\frac{{{\\tau _z}}}{{2\\pi I\\Gamma }}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere I is the rectangular nanorod\u0026rsquo;s momentum of inertia, and Γ is the rotational damping rate for diffuse reflection of gas molecules.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec shows the calculated rotation frequency (blue curve) of the nanorod at different pressures using Eqs.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The detailed calculation is shown in the supplementary materials. For complex-shaped nanoparticles, their optical torque can be calculated by combining the finite difference in the time-domain method with the discrete dipole approximation method\u003csup\u003e36\u003c/sup\u003e. The calculated rotation frequency closely matches the experimentally measured frequency. The difference between measured and calculated frequencies originates from the deviations between the measured and actual sizes of the nanorod.\u003c/p\u003e \u003cp\u003eThe dependency of the nanorod\u0026rsquo;s rotation frequency on the laser beam\u0026rsquo;s power and polarization is experimentally explored as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed shows that the measured rotational frequency is proportional to the laser power, which is consistent with Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The polarization is tuned by rotating the QWP. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee, when the angle is within the range from 0 to 30\u0026ordm;, there is no rotational signal in the PSD spectrum, indicating that the optical torque applied to the nanorod is smaller than the air drag. When the QWP angle is larger than 30\u0026ordm;, the nanorod starts to rotate and the rotational PSD signal appears. With furtherly increasing the QWP angle, more spin angular momentum can be transferred to the nanorod, thereby a higher rotation frequency can be obtained. The blue curves in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee show the calculated results, which agree well with the experimental measurements (orange curves).\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eHere, we demonstrated the optical levitation of a nanofabricated nanorod in a vacuum environment using nanofabricated metalens. Controllable COM motions and rotation of the levitated nanorod have also been demonstrated. In our experiment, a metalens is utilized to achieve a single-point focus of the light beam. In future studies, the metalens can combine single-point focusing with an adjustable focus\u003csup\u003e37\u003c/sup\u003e to explore short-range forces or with vortex light fields to stable trap large-sized particles for enhancing force detection sensitivity. In addition, single focal points can be extended to multi-focal points\u003csup\u003e29\u003c/sup\u003e for research into macroscopic many-body quantum mechanics.\u003c/p\u003e \u003cp\u003eIn our experiment, a nanofabricated silicon rectangular nanorod was used for levitation in a vacuum. The nanofabrication techniques are not limited to the fabrication of the nanorods. They can be utilized to fabricate nanoparticles of any shape and size, enabling the highlight of specific motions of a levitated particle and the exploration of novel particle manipulation techniques. In this proof-of-concept experiment, we employed e-beam lithography to define the size and shape of nanorods. For high-throughput and low-cost fabrication of particles, conventional photolithography can be used\u003csup\u003e38\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe demonstrated translation and rotation of nanofabricated particles in a vacuum based on metalens can combine the powerful light field control capability of the metalens with the customization advantage of nanoparticles. This can provide an ideal platform for further expanding the applications of optical levitation. Meanwhile, this system using nanofabricated ultrathin metalens can provide a compact solution for integrated on-chip sensing applications, such as acceleration (translation) and torque (rotation). In the future, this can be combined with chip-based light source\u003csup\u003e39\u003c/sup\u003e and vacuum packaging technology\u003csup\u003e40\u003c/sup\u003e to realize a miniaturized, robust, and scalable on-chip integrated optical levitation system. This approach holds the potential to significantly transit vacuum optical levitation systems from the laboratory into practical applications.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eWe have demonstrated an optical levitation system in a vacuum by combining a nanofabricated metalens and a nanofabricated Si nanorod. The COM motions and rotation of the levitated nanorod can be controlled. The system can combine the advantages of light manipulation from metalens and the customizability of a nanoparticle. The combined advantages would enable the generation of specific light fields and particle motions, for various sensing applications, investigating macroscopic many-body physics and quantum sensing. In addition, this system using compact metalens holds great potential for achieving miniaturized, robust and scalable on-chip integrated optical levitation systems. This integration solution can pave the way to significantly expedite the transition of optical levitation systems in the vacuum from laboratory to practical applications.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cstrong\u003eConflict of Interest\u003c/strong\u003e \u003cp\u003eThe authors have no conflicts to disclose.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eACKNOWLEDGMENTS\u003c/h2\u003e \u003cp\u003eThe research has been supported by EPSRC (EP/V000624/1).\u003c/p\u003e\u003ch2\u003eDATA AVAILABILITY\u003c/h2\u003e \u003cp\u003eThe data from this paper can be obtained from the University of Southampton ePrints research repository.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eYin, Z.-Q., Geraci, A. A. \u0026amp; Li, T. Optomechanics of levitated dielectric particles. Int. J. Mod Phys B 27, 1330018, (2013).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMillen, J., Monteiro, T. 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Applied Sciences 10, 8201, (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang, Y. \u003cem\u003eet al.\u003c/em\u003e Integrated metasurfaces for re-envisioning a near-future disruptive optical platform. Light: Sci. Appl. 12, 152, (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQuack, N. \u003cem\u003eet al.\u003c/em\u003e Integrated silicon photonic MEMS. Microsyst. Nanoeng. 9, 27, (2023).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"microsystems-and-nanoengineering","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"micronano","sideBox":"Learn more about [Microsystems \u0026 Nanoengineering](http://www.nature.com/micronano/)","snPcode":"41378","submissionUrl":"https://mts-micronano.nature.com/","title":"Microsystems \u0026 Nanoengineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4313334/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4313334/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAn optically levitated nanoparticle in a vacuum provides an ideal platform for ultra-precision measurements and fundamental physics studies because of the exceptionally high-quality factor and rich motional modes, which can be engineered by manipulating the optical field and the geometry of the nanoparticle. Nanofabrication technology with the ability to create arbitrary nanostructure arrays offers a precise way of engineering the optical field and the geometry of the nanoparticle. Here, for the first time, we optically levitate and rotate a nanofabricated nanorod via a nanofabricated a-Si metalens which strongly focuses a 1550nm laser beam with a numerical aperture of 0.91. By manipulating the laser beam\u0026rsquo;s polarization, the levitated nanorod\u0026rsquo;s translation frequencies can be tuned, and the spin rotation mode can be switched on and off. Then, we demonstrated that the rotational frequency relies on the laser beam\u0026rsquo;s intensity and polarization as well as the air pressure. Finally, a MHz spin rotation frequency of the nanorod is achieved in the experiment. This is the first demonstration of controlled optical spin in a metalens-based compact optical levitation system. Our research holds promise for realizing scalable on-chip integrated optical levitation systems.\u003c/p\u003e","manuscriptTitle":"Levitation and controlled MHz rotation of a nanofabricated rod by a high-NA metalens","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-13 18:53:44","doi":"10.21203/rs.3.rs-4313334/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"revise","date":"2024-08-25T06:01:30+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-08-18T21:51:10+00:00","index":2,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-07-31T01:42:29+00:00","index":3,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-07-25T07:09:41+00:00","index":3,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-07-22T06:56:25+00:00","index":2,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2024-07-15T13:10:16+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2024-07-04T19:36:41+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2024-05-31T06:54:25+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-04-29T03:11:17+00:00","index":"","fulltext":""},{"type":"submitted","content":"Microsystems \u0026 Nanoengineering","date":"2024-04-27T17:29:07+00:00","index":"","fulltext":""},{"type":"checksFailed","content":"","date":"2024-04-26T03:01:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-23T16:16:50+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"microsystems-and-nanoengineering","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"micronano","sideBox":"Learn more about [Microsystems \u0026 Nanoengineering](http://www.nature.com/micronano/)","snPcode":"41378","submissionUrl":"https://mts-micronano.nature.com/","title":"Microsystems \u0026 Nanoengineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e4b82579-a6b5-4181-84b8-069b72be7ebd","owner":[],"postedDate":"June 13th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":32641708,"name":"Physical sciences/Optics and photonics/Optical physics/Nanophotonics and plasmonics"},{"id":32641709,"name":"Physical sciences/Nanoscience and technology/Nanoscale devices/Nanophotonics and plasmonics"}],"tags":[],"updatedAt":"2025-04-22T07:09:56+00:00","versionOfRecord":{"articleIdentity":"rs-4313334","link":"https://doi.org/10.1038/s41378-025-00886-7","journal":{"identity":"microsystems-and-nanoengineering","isVorOnly":false,"title":"Microsystems \u0026 Nanoengineering"},"publishedOn":"2025-04-21 04:00:00","publishedOnDateReadable":"April 21st, 2025"},"versionCreatedAt":"2024-06-13 18:53:44","video":"","vorDoi":"10.1038/s41378-025-00886-7","vorDoiUrl":"https://doi.org/10.1038/s41378-025-00886-7","workflowStages":[]},"version":"v1","identity":"rs-4313334","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4313334","identity":"rs-4313334","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}