Three-Dimensional Optical Trapping with a Low-NA Objective using a Flat-top Beam 

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We achieved this by shaping asymmetric counter-propagating (ACP) beams comprised of a flat-top beam on one side and a multifocal spot on the other. Here, we study this trapping system both experimentally and theoretically and demonstrate stable trapping. Unlike most previous techniques, here we use low numerical aperture (NA) optics resulting in long manipulation distances and a wide field of view for side and front microscopy of the sample chamber. Moreover, the setup is easy-to-align and less sensitive to misalignments compared to most 3D structure forming methods. Our system can find application in the development of novel materials and microscopy studies on trapped particles. Physical sciences/Materials science Physical sciences/Optics and photonics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction An optical tweezer, also known as optical trapping (OT), is a widely spread tool to trap and manipulate microscopic-sized objects. This method has a large range of applications in biology, physics, chemistry, and engineering [ 1 – 8 ]. In this technique, the laser beam is tightly focused to a small volume inducing strong optical forces (gradient and scattering) leading to a 3D trap. The gradient force pulls particles with a higher refractive index than the background towards the point of highest laser beam intensity and the scattering force mainly pushes particles along the laser beam propagation direction. In order to generate a stable optical trap, the gradient force has to balance the scattering force. One of the ways to achieve 3D trapping is to use single-beam optical trapping [ 1 , 9 , 10 ]. In this method, a high-NA microscope objective tightly focuses the laser beam achieving strong axial gradient forces that balance scattering forces. However, a high-NA objective results in a short working distance, a narrow field of view, and could generate undesirable thermal effects due to its tight focus. An alternative method is to use counter-propagating beams [ 1 , 11 – 16 ]. In this approach, two moderately focused counter-propagating beams generate counter scattering forces. At the location where scattering forces cancel out, a 3D trap is achieved. However, due to the strict optical symmetry required for this trapping method and the low gradient forces, a slight misalignment of the system leads to an unstable trap that can ultimately result in the particle escape. In order to overcome the aforementioned limitations Asymmetric Counter Propagating (ACP) beams have been proposed and utilized [ 17 – 19 ]. Here we will study a more extended type of ACP beams which is suitable for volumetric trapping. Multi-particle trapping and the formation of 3D structures To generate 3D particle arrangements, usually a single beam is configured to produce multiple traps. This can be achieved by utilizing beam-sharing techniques that rapidly re-position the laser beam [ 20 – 30 ]. These techniques include the use of acousto-optic scanners (AOS), electro-optic scanners (EOS), scanning mirrors, and Spatial Light Modulators (SLM). When using an SLM in the setup, a single beam can be transformed into an array of beams by loading properly designed holograms on the SLM, which imposes spatially varying modulation of the laser beam [ 31 – 33 ]. This leads to multifocal spots with controllable axial and lateral foci locations. One way to create multiple 3D traps is to use a high-NA microscope objective to overcome the scattering forces [ 34 – 46 ]. However, as discussed before, this leads to limited manipulation volumes, a narrow frontal view, and hotspot thermal damage [ 47 ]. Also, due to short working distances of high-NA objectives, side-view microscopy would be challenging or impossible. An alternative way to generate 3D configurations is to utilize structured counter-propagating beams [ 23 , 27 , 48 – 51 ]. In this approach, two moderately focused counter-propagating beams with multifocal spots are focused by two identical microscope objectives to create 3D structures. The downside of this method is that the system becomes complex and more sensitive to misalignments due to the perfect symmetry requirement, as discussed in a previous study [ 19 ]. In addition, the axial manipulation distance of the traps is limited to about 30 \(\:\mu\:\) m [ 48 – 51 ]. In order to alleviate the aforementioned disadvantages in 3D multi-traps, here we incorporate the ACP beams trapping system to create stable 3D trapping in extended volumes (50µm x 50µm laterally and 100µm axially) with a low-NA lens. In the method presented here, one of the counter-propagating beams has been shaped to demonstrate a uniform flat-top profile. To create multiple 3D traps for the formation of crystal-like structures, the other beam is shaped to have multifocal spots that are focused by a low-NA microscope objective. These counter-propagating beams have been designed such that once they overlap inside the sample chamber, their overall optical forces generate stable 3D traps at a volume of ~ 25×10 4 µm 3 . The Multifocal spots and square flat-top beams are generated by designing holograms of multiple Fresnel lenses and a Gaussian shaping function respectively, which are described in the experimental setup and methods section below. Due to the uniformity of the square flat-top and the flexibility of the multifocal spots, various 3D structures with different sizes and shapes can be created in a large volume. Furthermore, due to the asymmetry of the setup and the use of low-NA optics, the system is simple to align and microscopy with a wide field of view for both front and side views is easily achieved. In the following sections we demonstrate stable trapping of the proposed system both theoretically and experimentally. Experimental setup and methods The setup for the 3D crystal-like structure formation is based on the ACP trapping beams that was previously reported [ 17 – 19 ]. The laser utilized here is MSquare Equinox with a horizontally polarized constant wave (CW) laser beam at 532 nm. As demonstrated in Fig. 1 the combination of a half-wave plate (λ/2) and polarizing beam splitter (PBS) is placed after the laser source to split the beam and control the power ratio of transmitted and reflected beams which we call beam 1 and beam 2, respectively. Beam 1 is expanded to 20 mm in diameter by the beam expander (BE) and reflected off a computer-controlled phase-only spatial light modulator (SLM 1 : Model Pluto from HOLOEYE Photonics). An algorithm combining several Fresnel lenses and blazed grating is used to generate the hologram on SLM 1 creating multifocal spots with controllable position and intensity for optical trapping. The combination of lenses L 1 and L 2 with f 1 = 50 cm and f 2 = 25 cm are added after SLM 1 to reduce beam diameter (to a diameter slightly larger than microscope objective’s (MO 1 : Nikon 40x/0.5) back aperture) and to conjugate SLM 1 plane and the back focal plane of MO 1 . A spatial filter (SF) is placed between L 1 and L 2 to block all diffraction orders except the first order, which is focused inside the sample (S). The sample chamber is a quartz cuvette with an optical path length of 5mm with all walls polished to have front and side views. The polystyrene particles tested for trapping were in the size ranges varying from about 1µm to 6µm and were all purchased from Spherotech. In order to create stable 3D traps, we generated a flat-top counter-propagating beam, by shaping beam 2. The conversion of the Gaussian laser beam into a square shaped beam with a flat-top profile is achieved by creating the appropriate hologram described below on SLM 2 (Model Pluto from HOLOEYE Photonics). Note that before being reflected off SLM 2 , beam 2 is expanded by a BE to 20 mm in diameter. The desired hologram to shape a square flat-top beam is generated by using the following function: $$\:f\left(x,y\right)=A{e}^{\left(-\frac{{x}^{2}+{y}^{2}}{{\sigma\:}^{2}}\right)}\cdot\:rect\left(\frac{x}{w}\right)\cdot\:rect\left(\frac{y}{l}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(1\right)$$ where \(\:A\) is the amplitude of the Gaussian function, \(\:\sigma\:\) is the standard deviation of the Gaussian function, \(\:w\) is the width of the rectangular function and \(\:l\) is the length of the rectangular function. In addition, this function is multiplied by a blazed grating to shift the first diffracted order and maximize its power [ 52 , 53 ]. This product and the resulting phase mask used to create the flat-top beam is shown in Fig. 2 (a). As seen in Fig. 1 , once the flat-top beam is produced it passes lenses L 3 and L 4 with f 3 = 100 cm and f 4 = 2.5 cm, to reduce beam diameter and allow for the surface of SLM 2 and the focal plane of L 4 to become conjugate planes. Another SF is added between L 3 and L 4 to block all diffraction orders except the first order. Two transmitted light microscopy systems for side and front view imaging of the formed 3D structures were designed and implemented. To acquire the front-view image, two dichroic mirrors (DM) are used to guide the illumination light (IL) through the sample chamber to the front-view camera. The trapping objective MO 1 is also utilized to form the front-view image. Lens L 5 with f 5 = 30 cm is placed on a motorized stage (MS) to form the front-view image on the camera. The side-view image is achieved by adding a second IL and a microscope objective (MO 2 : Nikon 20x or 40x) which forms the image on the side-view camera. To block the scattered 532 nm laser beam, two notch filters (NF) are placed in front of each camera. Figure 2 (b) depicts the generated square flat-top beam profile (of beam 2) that was captured with a beam profiling device (LaserCam-HR from Coherent). The laser power used the square flat-top beam was 150 mW. The square flat-top beam sides were measured to have a length of 75 \(\:\:\mu\:\) m as shown in Fig. 2 (b). This is the case for the profile of beam 2, up to 100 \(\:\:\mu\:\) m of its axial propagation before it starts degrading, which will be discussed in more detail in Fig. 6 . It is worth noting that for this setup multiple objectives could be integrated (top, bottom and side of the sample) to either obtain different observation angles or achieve different types of microscopies, simultaneously. Theoretical Analysis In the asymmetric counter-propagating beam arrangement presented here, axial trapping is achieved at the location where the radiation pressure exerted by the focused beam is compensated by the radiation pressure exerted by the flat-top beam. The time-averaged radiation pressure force F rad exerted by two counter-propagating beams on a particle is given by: (2) where C ext is the extinction cross-section of the particle, I FT ( x,y,z ) is the intensity of the flat top beam propagating in the axial direction \(\:\widehat{z}\) , and I TR ( x,y,z ) is the intensity of the trapping beam propagating in the negative \(\:\widehat{z}\) direction. For the beam parameters used in our experiments, to an excellent approximation, I FT ( x,y,z ) ≈ I FT ( z ) within the beam cross-section. We have verified this fact by simulating the propagation of a square flat-top beam of width 75 µm (the same width we generated) through a length of 100 µm , as shown in the Fig. 3 . From the simulation, which is in good agreement with our measurements (Fig. 6 .c), it is evident that diffraction effects are minor in terms of beam-spreading, and that the intensity profile stays constant over most of the beam. As seen in Fig. 3 , after 100 µm of axial propagation, the edge of the flat top beam profile demonstrates a change in intensity which we also observed experimentally shown in Fig. 6 .c. As mentioned before, the trap is formed by the combination of a focused and a flat top beam, counterpropagating. For the focused beam we used the parameters of MO 1 (40X with 0.5 NA ) with an effective focal length of about 4 mm . With these specifications, the angular divergence of the beam around the focus is ∼ 60. With the extinction cross-section C ext = 2.2 µm 2 as calculated and shown in the Supplementary Fig. S1 for a 2 µm polystyrene bead in water, we computed the force from Eq. (2) as presented in Fig. 4 . From the slope of the force profile around the stable trap, we found the axial trap stiffness to be 1.15 pN/µm . For our calculation, the power of the flat top beam (with area 75 µm x 75 µm) is 150mW and the one for the focused beam (to create a single trap) is 10mW. These are the same powers used in our experimental section and when measuring trap stiffness (Fig. 7 ). Experimental Results and Discussion By judiciously shaping the ACP beams as described earlier, we have successfully constructed several 3D crystal-like structures. Examples such as square pyramid-like and cube-like structures are shown in Fig. 5 . Here we used 2 \(\:\:\mu\:\) m polystyrene particles inside a quartz cuvette filled with distilled water. Figure 2 depicts the phase mask used on SLM 2 and the generated square flat-top beam profile (of beam 2) that was captured with a beam profiling device. Figure 5 (a,c) demonstrates examples of phase masks used on SLM 1 (shaping beam 1) to form the desired 3D structures. If SLM 2 was off or beam 2 was blocked, beam 1 by itself could not form any optical traps. Only when both beams were shaped via SLM 1 and SLM 2 with the phase masks described, and counter-propagated inside the sample chamber, 3D structures such as those shown in Fig. 5 (b,d) were stably constructed. The laser power used for the square flat-top beam was measured to be 150 mW and the total power distributed between the multi-traps generated by beam 1 varied between 30 mW to 60 mW, depending on the structure generated. We deliberately avoided forming the 3D structures near the sample chamber walls to avoid surface tension forces. The successful formation and stability of these structures demonstrates the potential of our proposed system to generate other pre-defined crystal-like structures. Since polystyrene particles have a higher refractive index than the background (water) they are attracted to the higher intensity regions of beam 1 multifocal spots, due to the gradient forces. At the same time, the undesired axial scattering forces are cancelled by the counterpropagating flat-top beam. So, by controlling the multifocal spots position and phase on SLM 1 , we can form 3D structures within a very large volume compared to the symmetrical CP beams. The range for both lateral and axial optical trapping of our proposed system is illustrated in Fig. 6 . Even though the side of the square flat top generated is 75 \(\:\mu\:\) m, stable lateral trapping range is limited to 50 \(\:\:\mu\:\) m experimentally, as shown in Fig. 6 (a). Trapping beyond 50 \(\:\:\mu\:\) m is less stable and as we get closer to the edges of the flat-top beam, due to the plateau non-uniformities, particles can no longer be trapped. On the other hand, stable axial 3D trapping was possible experimentally for axial distances up to 100 \(\:\mu\:\) m as seen in Fig. 6 (b). As demonstrated in Fig. 4 column (c) from right to left; the flat-top beam profile becomes slightly less uniform as the beam propagates from axial position 0 \(\:\mu\:\) m to 100 \(\:\mu\:\) m, but that does not affect trapping in the 50x50 lateral range since Fig. 6 (a) was reproducible for all axial positions between 0 \(\:\mu\:\) m and 100 \(\:\mu\:\) m. However, as we see in column (d) from left to right; beyond 100 \(\:\mu\:\) m, the flat-top beam profile intensity distribution becomes more and more nonuniform, making stable trapping quite challenging or impossible. It is worth mentioning that all the positions in Fig. 6 were far from the cuvette’s walls. Using this technique, we were able to optically trap polystyrene particles between 1 \(\:\mu\:\) m to 6 \(\:\mu\:\) m in size. The axial and lateral trapping range achieved here demonstrate that stable 3D trapping and manipulation of single particles or crystal-like structures is possible within 100 \(\:\:\mu\:\) m x 50 \(\:\:\mu\:\) m x 50 \(\:\:\mu\:\) m volume. The ability to form and manipulate 3D structures (with micrometer precision) in such a large volume and without using high-NA objectives is quite unique and can be very practical, which is the result of utilizing a square flat-top counter-propagating beam. Next, utilizing a high-speed CMOS camera (model SC1 from edgertronic) with 2,000 fps, we track a trapped particle’s motion in both axial and lateral directions to measure the trap stiffness. The stiffness values are found for a 2 µm polystyrene bead trapped at several different locations on the same flat top plane (the z = 0 plane shown in Fig. 6 .c) along the diagonal line shown in Fig. 7 (a). Starting from the center of the flat-top beam (point 0) we trap the particle every 5 µm along the line, up to r = 40 µm. At each location, both axial (b) and lateral (c) trap stiffness values are measured. To avoid surface effects, the z = 0 plane was at least 50 µm away from any cuvette wall. The results of both axial and lateral stiffness measurements are shown in Fig. 7 (b) and (c) respectively. The maximum trap stiffness happens for a radius (r) up to about r = 15 µm from the center, but the decay is quite slow beyond that. Only after r > 30µm, the axial stiffness values drop more noticeably. That is due to the less uniform power distribution of our generated flat-top beam at its edges. Further work is required to improve the uniformity of the generated flat-top beam. The maximum axial trap stiffness measured is 1 PN/µm which is in good agreement with the theoretical value (1.15 PN/µm) found earlier. Conclusions In summary, we have demonstrated that our previously reported ACP trapping beams [ 17 – 19 ] can be further engineered to generate much larger trapping volumes. This was achieved by shaping the counter-propagating laser beams into a square flat-top from one side and multifocal spots from the other. The multifocal spots were generated by utilizing a hologram with Fresnel lenses and the square flat-top beam was created by using a hologram with the Gaussian beam shaping function. Our theoretical analysis demonstrates that the optical forces from the two asymmetrical CP beams result in a stable trap. We also experimentally measured the axial trapping stiffness for a 2 µm polystyrene bead, which was in good agreement with our theoretical calculation. Future efforts will focus on generating a more uniformly distributed flat-top beam. Since the counter propagating beams are asymmetric and only low-NA lenses have been used for 3D trapping, the setup is quite easy to align and less sensitive to misalignments compared to the single-beam or counter-propagating beams trapping methods used to form 3D crystal-like structures [ 34 – 46 , 48 – 51 ]. Moreover, the use of low-NA optics reduces the cost and undesirable thermal effects that are a result of tight focusing with high-NA objectives. We investigated several of the particles that had been trapped for more than 20 minutes with our setup and did not find any noticeable damage. This can be valuable in the case of biological samples or in tissue engineering applications, where thermal effects should be minimized. Another important advantage of this method is that its axial trapping stiffness value is at least one order of magnitude larger compared to most of the traditional CP traps that have used similar experimental parameters [ 54 – 57 ]. This has to do with the asymmetry of the CP beams used here and the location where the trap is formed with respect to the two beams, compared to when the two CP trapping beams are symmetric. On the other hand, since low-NA objectives have significantly larger working distances, this allows for a larger trapping volume, especially axially, as demonstrated here. Consequently side-view imaging would be possible due to the increase of trapping depths. In this case we can trap particles inside a larger volume such as a cuvette, which has been used here, and the sample chamber will no longer be limited to the use of cover slips and microscope slides which usually do not permit side views. Consequently, this setup allows for the simultaneous integration of different types of microscopies from multiple sides, in addition to the frontal-view microscopy. To trap a micron size particle in our study, the power entering the low-NA objective is comparable to previous reports and only a few milliwatts. However, to create the CP flat-top beam with enough power to form a stable trap, a 400mW laser beam was used before SLM 2, to generate a 150mW flat-top beam at the location of the trap (with an intensity of about 0.027 mW/µm 2 ). This is mainly due to the low efficiency of the SLM. So, in order to generate 3D crystal-like structures using this technique, in addition to two SLMs, about half a watt of power is needed, which are the main disadvantages of this method. Declarations Competing interests The authors declare no competing interests. Additional information Supplementary Information Correspondence and requests for materials should be addressed to S.F. Author Contribution S.F. conceptualized the research, directed and supervised the study. L.L. developed the theoretical framework, designed, built the experimental setup and collected data. All authors participated in the analysis of the collected data and the interpretation of results. All authors contributed on drafting the manuscript and figures. Acknowledgements S.F. acknowledges the support of the National Science Foundation through a grant with Award Number DMR-2414301, and the support from the Office of Naval Research (ONR) National Defense Education Program through the grant HQ0034231007. Data Availability The datasets generated and/or analyzed during the current study are available from the corresponding author upon request. References Ashkin, A. Acceleration and Trapping of Particles by Radiation Pressure. Phys. Rev. Lett. 24 (4), 156–159. https://doi.org/10.1103/physrevlett.24.156 (Jan. 1970). Ashkin, A., Dziedzic, J. M., Bjorkholm, J. E. & Chu, S. 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(2021). https://doi.org/10.1002/adma.202101965 Yang, Y., Ren, Y. X., Chen, M., Arita, Y. & Rosales-Guzmán, C. Optical trapping with structured light: a review. Adv. Photonics . 3, 03 , https://doi.org/10.1117/1.ap.3.3.034001 (May 2021). Čižmár, T., Romero, L. C. D., Dholakia, K. & Andrews, D. L. Multiple optical trapping and binding: new routes to self-assembly. J. Phys. B: At. Mol. Opt. Phys. 43 (10), 102001. https://doi.org/10.1088/0953-4075/43/10/102001 (Apr. 2010). Jordan, P. et al. Permanent 3D microstructures in a polymeric host created using holographic optical tweezers, vol. 51, no. 5, pp. 627–632, Mar. (2004). https://doi.org/10.1080/09500340310001625768 Leach, J. et al. 3D manipulation of particles into crystal structures using holographic optical tweezers. Opt. Express . 12 (1), 220. https://doi.org/10.1364/opex.12.000220 (Jan. 2004). Sun, F. et al. May., Three-dimensional dynamic optical trapping using non-iterative computer-generated holography, 164 , pp. 107500–107500, (2023). https://doi.org/10.1016/j.optlaseng.2023.107500 Kim, K., Yoon, J. & Park, Y. Simultaneous 3D visualization and position tracking of optically trapped particles using optical diffraction tomography, vol. 2, no. 4, pp. 343–343, Mar. (2015). https://doi.org/10.1364/optica.2.000343 Volpe, G. et al. Roadmap for Optical Tweezers., vol. 5, no. 2, pp. 022501–022501, Jan. 2023, (2023). https://doi.org/10.1088/2515-7647/acb57b Rodrigo, P. J. & Daria, V. R. Four-dimensional optical manipulation of colloidal particles. Appl. Phys. Lett. 86 (7), 074103. https://doi.org/10.1063/1.1866646 (2005). Perch-Nielsen, I. R., Rodrigo, P. J. & Glückstad, J. Real-time interactive 3D manipulation of particles viewed in two orthogonal observation planes, Optics Express , vol. 13, no. 8, p. 2852, Apr. (2005). https://doi.org/10.1364/opex.13.002852 Perch-Nielsen, I. R., Rodrigo, P. J., Alonzo, C. & Glückstad, J. Autonomous and 3D real-time multi-beam manipulation in a microfluidic environment, Optics Express , vol. 14, no. 25, pp. 12199–12199, Dec. (2006). https://doi.org/10.1364/oe.14.012199 Rodrigo, P. J., Perch-Nielsen, I. R., Alonzo, C. A. & Glückstad, J. GPC-based optical micromanipulation in 3D real-time using a single spatial light modulator. Opt. Express . 14 , 13107. https://doi.org/10.1364/oe.14.013107 (2006). Zhai, Z. et al. Flattop Beam Shaping Using Hybrid Gratings. IEEE Photonics J. 14 (4), 1–5. https://doi.org/10.1109/jphot.2022.3186902 (Aug. 2022). Nakata, Y., Osawa, K. & Miyanaga, N. Utilization of the high spatial-frequency component in adaptive beam shaping by using a virtual diagonal phase grating, vol. 9, no. 1, Mar. (2019). https://doi.org/10.1038/s41598-019-40829-7 Pitzek, M., Steiger, R., Thalhammer, G., Bernet, S. & Ritsch-Marte, M. Optical mirror trap with a large field of view. Opt. Express . 17 (22), 19414–19423. https://doi.org/10.1364/OE.17.019414 (2009). Bowman, R. et al. Position clamping in a holographic counterpropagating optical trap. Opt. Express . 19 (10), 9908–9914. https://doi.org/10.1364/OE.19.009908 (2011). Yang, Z., Piksarv, P., Ferrier, D., Gunn-Moore, F. & Dholakia, K. Macro-optical trapping for sample confinement in light sheet microscopy. Biomed. Opt. Express . 6 (8), 2778–2785. https://doi.org/10.1364/BOE.6.002778 (2015). Lindballe, M. et al. Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps. J. Eur. Opt. Soc. 6 , 11057. https://doi.org/10.2971/jeos.2011.11057 (2011). Additional Declarations No competing interests reported. Supplementary Files SupplementaryMaterialFardad.docx Cite Share Download PDF Status: Published Journal Publication published 16 May, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Accepted 09 May, 2025 Reviews received at journal 09 May, 2025 Reviews received at journal 07 May, 2025 Reviewers agreed at journal 29 Apr, 2025 Reviewers agreed at journal 25 Apr, 2025 Reviewers invited by journal 25 Apr, 2025 Submission checks completed at journal 20 Apr, 2025 First submitted to journal 07 Apr, 2025 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-5039529","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":448223282,"identity":"4dbfbc25-4c95-4870-aa07-2bd9e26be708","order_by":0,"name":"Laurynas Lialys","email":"","orcid":"","institution":"University of Kansas","correspondingAuthor":false,"prefix":"","firstName":"Laurynas","middleName":"","lastName":"Lialys","suffix":""},{"id":448223283,"identity":"209bcc84-57bd-4808-90e4-35e28169ce7d","order_by":1,"name":"Shima Fardad","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtElEQVRIiWNgGAWjYDAC5gMMDDwMzHISIA4PUVrYEsBajEnXkjiDaC3ybczPPrypsU6fOSOB8cHbNiK0GBxjM54551h67myJBGbDuURpkW8wZuZhO5w7TyKBTZqXGC3ybeyfmXn+HU6Xk0hg/02UFoZjPMbMvG2HE6SBtjATpcXgGE8x49y+dMOZPQ+bJeecI85hmxnefLOWlziefPDDmzJiHIYAjA2kqR8Fo2AUjIJRgBsAANwNL+UA2H0XAAAAAElFTkSuQmCC","orcid":"","institution":"University of Kansas","correspondingAuthor":true,"prefix":"","firstName":"Shima","middleName":"","lastName":"Fardad","suffix":""}],"badges":[],"createdAt":"2024-09-05 16:09:04","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5039529/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5039529/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-01974-4","type":"published","date":"2025-05-16T15:57:07+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":81542194,"identity":"7c3a315b-b644-425e-8d6c-7c4428fcc95e","added_by":"auto","created_at":"2025-04-28 11:17:44","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":264391,"visible":true,"origin":"","legend":"\u003cp\u003eThe setup to generate structured ACP beams to manipulate and trap 3D configurations. PBS: polarized beam splitter, half-wave (λ/2) plate, BE: 4x beam expander is used to expand a laser beam to fill the spatial light modulator screen (SLM). Two spatial light modulators are exploited to shape the laser beam into multifocal spots (SLM\u003csub\u003e1\u003c/sub\u003e) and the square flat-top (SLM\u003csub\u003e2\u003c/sub\u003e), M: silver mirror, L\u003csub\u003e1\u003c/sub\u003e and L\u003csub\u003e2\u003c/sub\u003e; lenses with f\u003csub\u003e1\u003c/sub\u003e=50 cm and f\u003csub\u003e2\u003c/sub\u003e=25 cm. S: sample chamber, SF: spatial filter, DM: dichroic mirror, L\u003csub\u003e3\u003c/sub\u003e and L\u003csub\u003e4\u003c/sub\u003e; lenses with f\u003csub\u003e3\u003c/sub\u003e=100 cm and f\u003csub\u003e4\u003c/sub\u003e=2.5 cm. IL: illumination light, MS: motorized stage, and NF: notch filter. L\u003csub\u003e5\u003c/sub\u003e: lens with f\u003csub\u003e5\u003c/sub\u003e=30 cm used to form the front-view image. MO\u003csub\u003e1\u003c/sub\u003e: trapping and front-view imaging microscope objective (Nikon 40x/0.5) and MO\u003csub\u003e2\u003c/sub\u003e: side-view imaging microscope objective (Nikon 20x or 40x). Both side-view and front-view cameras are CMOS cameras.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-5039529/v1/6eb31dcc4eadb7f07a16cb1b.jpeg"},{"id":81543777,"identity":"7d26f632-c025-4d99-9d2a-3e501309e0e5","added_by":"auto","created_at":"2025-04-28 11:25:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":56181,"visible":true,"origin":"","legend":"\u003cp\u003eDeveloped phase mask to shape a square flat-top beam and the experimental result. (a) The sequence of phase masks, (b) An image of the square flat-top beam profile generated.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5039529/v1/d4a0edf3bd6adb53908e130b.png"},{"id":81542193,"identity":"ec546c16-7330-4ab9-a0e0-1364eabc8121","added_by":"auto","created_at":"2025-04-28 11:17:44","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":133626,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the intensity profiles of a square flat-top beam of width 75\u003cem\u003eµm \u003c/em\u003eand \u003cem\u003eλ \u003c/em\u003e= 532\u003cem\u003enm \u003c/em\u003eover two planes separated by an axial propagation distance of 100\u003cem\u003eµm\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5039529/v1/29ea6a37c49b6e8aa6a8e623.png"},{"id":81542205,"identity":"eaf4415b-3755-4d8b-9f57-c1e700fe7309","added_by":"auto","created_at":"2025-04-28 11:17:44","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":156976,"visible":true,"origin":"","legend":"\u003cp\u003e(left) Radiation pressure force calculation around the trap formed by the combination of beams 1 and 2. The solid blue line indicates a stable trapping site, and the dashed blue line indicates the unstable trapping site. (right) Detail of radiation pressure force profile around the stable trap. From the slope of the force profile we can extract a trap stiffness of 1\u003cem\u003e.\u003c/em\u003e15 \u003cem\u003epN/µm\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5039529/v1/a6ed181244c6e665b5084595.png"},{"id":81542202,"identity":"fa088d93-f80d-421c-969d-25d36c00e238","added_by":"auto","created_at":"2025-04-28 11:17:44","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":270705,"visible":true,"origin":"","legend":"\u003cp\u003eExamples of 3D crystal-like structures formed inside the colloidal suspension using our proposed method. (a) square pyramid-like hologram (c) cube-like hologram used to generate the corresponding structures formed by trapping 2μm polystyrene particles. (b) and (d) are the created 3D structures using (a) and (c) holograms respectively.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-5039529/v1/72e3af359451b991bc772ecc.jpeg"},{"id":81543783,"identity":"75dcd3be-9b99-4288-9786-dbe7fec05b7a","added_by":"auto","created_at":"2025-04-28 11:25:45","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":560362,"visible":true,"origin":"","legend":"\u003cp\u003eDemonstrating the extent of optical trapping using structured ACP beams. (a) front-view and (b) side-view images of 2 μm polystyrene trapped particles (using the setup shown in Fig.1) illustrating the (a) lateral and (b) axial trapping range of our proposed setup which are 50 μm and 100 μm respectively. Scale bars shown on the right corner of (a) and (b) represent 10µm. (c) Shows the evolution of the flat-top beam profile as it propagates from right to left. The flat-top beam profiles are taken every 50 μm starting from the first trapped particle at location 0 μm. Panel (d) shows the flat-top beam profile as it continues to propagate up to location 500 μm and has been presented from left to right. All positions were far from the cuvette’s walls.\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-5039529/v1/f580f49957e0572693b65773.jpeg"},{"id":81542211,"identity":"f640e79b-2c21-45d3-aac9-ba5caf25563c","added_by":"auto","created_at":"2025-04-28 11:17:45","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":205757,"visible":true,"origin":"","legend":"\u003cp\u003eTrap stiffness measurements. The stiffness values are found for a 2 µm polystyrene bead trapped at several locations, 5 µm apart, on the diagonal line shown in (a). Position 0 is at the center of the flat-top beam. At each location, both axial (b) and lateral (c) trap stiffness values are measured. The laser power used to generate the optical trap at each location is 10 mW from the objective side and 150mW from the flat beam side. The total area of the flat top beam is 75 μm x 75 μm.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-5039529/v1/c53d336bb44749dd945bd839.png"},{"id":83067704,"identity":"7a38646c-dfce-453b-bf87-6b014dda0eb5","added_by":"auto","created_at":"2025-05-19 16:04:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2257283,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5039529/v1/c73c975f-dbf6-4d2c-917f-3cb6cd732172.pdf"},{"id":81543780,"identity":"3709fae6-a7a5-4763-8374-63e94900106c","added_by":"auto","created_at":"2025-04-28 11:25:44","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1112187,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterialFardad.docx","url":"https://assets-eu.researchsquare.com/files/rs-5039529/v1/883b3ebc3e55917f7507cd87.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Three-Dimensional Optical Trapping with a Low-NA Objective using a Flat-top Beam ","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAn optical tweezer, also known as optical trapping (OT), is a widely spread tool to trap and manipulate microscopic-sized objects. This method has a large range of applications in biology, physics, chemistry, and engineering [\u003cspan additionalcitationids=\"CR2 CR3 CR4 CR5 CR6 CR7\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In this technique, the laser beam is tightly focused to a small volume inducing strong optical forces (gradient and scattering) leading to a 3D trap. The gradient force pulls particles with a higher refractive index than the background towards the point of highest laser beam intensity and the scattering force mainly pushes particles along the laser beam propagation direction. In order to generate a stable optical trap, the gradient force has to balance the scattering force. One of the ways to achieve 3D trapping is to use single-beam optical trapping [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. In this method, a high-NA microscope objective tightly focuses the laser beam achieving strong axial gradient forces that balance scattering forces. However, a high-NA objective results in a short working distance, a narrow field of view, and could generate undesirable thermal effects due to its tight focus. An alternative method is to use counter-propagating beams [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan additionalcitationids=\"CR12 CR13 CR14 CR15\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. In this approach, two moderately focused counter-propagating beams generate counter scattering forces. At the location where scattering forces cancel out, a 3D trap is achieved. However, due to the strict optical symmetry required for this trapping method and the low gradient forces, a slight misalignment of the system leads to an unstable trap that can ultimately result in the particle escape. In order to overcome the aforementioned limitations Asymmetric Counter Propagating (ACP) beams have been proposed and utilized [\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Here we will study a more extended type of ACP beams which is suitable for volumetric trapping.\u003c/p\u003e\n\u003ch3\u003eMulti-particle trapping and the formation of 3D structures\u003c/h3\u003e\n\u003cp\u003eTo generate 3D particle arrangements, usually a single beam is configured to produce multiple traps. This can be achieved by utilizing beam-sharing techniques that rapidly re-position the laser beam [\u003cspan additionalcitationids=\"CR21 CR22 CR23 CR24 CR25 CR26 CR27 CR28 CR29\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. These techniques include the use of acousto-optic scanners (AOS), electro-optic scanners (EOS), scanning mirrors, and Spatial Light Modulators (SLM). When using an SLM in the setup, a single beam can be transformed into an array of beams by loading properly designed holograms on the SLM, which imposes spatially varying modulation of the laser beam [\u003cspan additionalcitationids=\"CR32\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. This leads to multifocal spots with controllable axial and lateral foci locations. One way to create multiple 3D traps is to use a high-NA microscope objective to overcome the scattering forces [\u003cspan additionalcitationids=\"CR35 CR36 CR37 CR38 CR39 CR40 CR41 CR42 CR43 CR44 CR45\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. However, as discussed before, this leads to limited manipulation volumes, a narrow frontal view, and hotspot thermal damage [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. Also, due to short working distances of high-NA objectives, side-view microscopy would be challenging or impossible. An alternative way to generate 3D configurations is to utilize structured counter-propagating beams [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan additionalcitationids=\"CR49 CR50\" citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e]. In this approach, two moderately focused counter-propagating beams with multifocal spots are focused by two identical microscope objectives to create 3D structures. The downside of this method is that the system becomes complex and more sensitive to misalignments due to the perfect symmetry requirement, as discussed in a previous study [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. In addition, the axial manipulation distance of the traps is limited to about 30 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em [\u003cspan additionalcitationids=\"CR49 CR50\" citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e]. In order to alleviate the aforementioned disadvantages in 3D multi-traps, here we incorporate the ACP beams trapping system to create stable 3D trapping in extended volumes (50\u0026micro;m x 50\u0026micro;m laterally and 100\u0026micro;m axially) with a low-NA lens. In the method presented here, one of the counter-propagating beams has been shaped to demonstrate a uniform flat-top profile. To create multiple 3D traps for the formation of crystal-like structures, the other beam is shaped to have multifocal spots that are focused by a low-NA microscope objective. These counter-propagating beams have been designed such that once they overlap inside the sample chamber, their overall optical forces generate stable 3D traps at a volume of ~\u0026thinsp;25\u0026times;10\u003csup\u003e4\u003c/sup\u003e \u0026micro;m\u003csup\u003e3\u003c/sup\u003e. The Multifocal spots and square flat-top beams are generated by designing holograms of multiple Fresnel lenses and a Gaussian shaping function respectively, which are described in the experimental setup and methods section below.\u003c/p\u003e \u003cp\u003eDue to the uniformity of the square flat-top and the flexibility of the multifocal spots, various 3D structures with different sizes and shapes can be created in a large volume. Furthermore, due to the asymmetry of the setup and the use of low-NA optics, the system is simple to align and microscopy with a wide field of view for both front and side views is easily achieved. In the following sections we demonstrate stable trapping of the proposed system both theoretically and experimentally.\u003c/p\u003e "},{"header":"Experimental setup and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe setup for the 3D crystal-like structure formation is based on the ACP trapping beams that was previously reported [\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The laser utilized here is MSquare Equinox with a horizontally polarized constant wave (CW) laser beam at 532 nm. As demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e the combination of a half-wave plate (λ/2) and polarizing beam splitter (PBS) is placed after the laser source to split the beam and control the power ratio of transmitted and reflected beams which we call beam 1 and beam 2, respectively. Beam 1 is expanded to 20 mm in diameter by the beam expander (BE) and reflected off a computer-controlled phase-only spatial light modulator (SLM\u003csub\u003e1\u003c/sub\u003e : Model Pluto from HOLOEYE Photonics). An algorithm combining several Fresnel lenses and blazed grating is used to generate the hologram on SLM\u003csub\u003e1\u003c/sub\u003e creating multifocal spots with controllable position and intensity for optical trapping. The combination of lenses L\u003csub\u003e1\u003c/sub\u003e and L\u003csub\u003e2\u003c/sub\u003e with f\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;50 cm and f\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;25 cm are added after SLM\u003csub\u003e1\u003c/sub\u003e to reduce beam diameter (to a diameter slightly larger than microscope objective\u0026rsquo;s (MO\u003csub\u003e1\u003c/sub\u003e: Nikon 40x/0.5) back aperture) and to conjugate SLM\u003csub\u003e1\u003c/sub\u003e plane and the back focal plane of MO\u003csub\u003e1\u003c/sub\u003e. A spatial filter (SF) is placed between L\u003csub\u003e1\u003c/sub\u003e and L\u003csub\u003e2\u003c/sub\u003e to block all diffraction orders except the first order, which is focused inside the sample (S). The sample chamber is a quartz cuvette with an optical path length of 5mm with all walls polished to have front and side views. The polystyrene particles tested for trapping were in the size ranges varying from about 1\u0026micro;m to 6\u0026micro;m and were all purchased from Spherotech.\u003c/p\u003e \u003cp\u003eIn order to create stable 3D traps, we generated a flat-top counter-propagating beam, by shaping beam 2. The conversion of the Gaussian laser beam into a square shaped beam with a flat-top profile is achieved\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eby creating the appropriate hologram described below on SLM\u003csub\u003e2\u003c/sub\u003e (Model Pluto from HOLOEYE Photonics). Note that before being reflected off SLM\u003csub\u003e2\u003c/sub\u003e, beam 2 is expanded by a BE to 20 mm in diameter. The desired hologram to shape a square flat-top beam is generated by using the following function:\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Equa\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:f\\left(x,y\\right)=A{e}^{\\left(-\\frac{{x}^{2}+{y}^{2}}{{\\sigma\\:}^{2}}\\right)}\\cdot\\:rect\\left(\\frac{x}{w}\\right)\\cdot\\:rect\\left(\\frac{y}{l}\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(1\\right)$$\u003c/div\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e\u003c/span\u003e is the amplitude of the Gaussian function, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:\\)\u003c/span\u003e\u003c/span\u003e is the standard deviation of the Gaussian function, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:w\\)\u003c/span\u003e\u003c/span\u003e is the width of the rectangular function and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:l\\)\u003c/span\u003e\u003c/span\u003e is the length of the rectangular function. In addition, this function is multiplied by a blazed grating to shift the first diffracted order and maximize its power [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]. This product and the resulting phase mask used to create the flat-top beam is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a).\u003c/p\u003e \u003cp\u003eAs seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, once the flat-top beam is produced it passes lenses L\u003csub\u003e3\u003c/sub\u003e and L\u003csub\u003e4\u003c/sub\u003e with f\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;100 cm and f\u003csub\u003e4\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.5 cm, to reduce beam diameter and allow for the surface of SLM\u003csub\u003e2\u003c/sub\u003e and the focal plane of L\u003csub\u003e4\u003c/sub\u003e to become conjugate planes. Another SF is added between L\u003csub\u003e3\u003c/sub\u003e and L\u003csub\u003e4\u003c/sub\u003e to block all diffraction orders except the first order. Two transmitted light microscopy systems for side and front view imaging of the formed 3D structures were designed and implemented. To acquire the front-view image, two dichroic mirrors (DM) are used to guide the illumination light (IL) through the sample chamber to the front-view camera. The trapping objective MO\u003csub\u003e1\u003c/sub\u003e is also utilized to form the front-view image. Lens L\u003csub\u003e5\u003c/sub\u003e with f\u003csub\u003e5\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;30 cm is placed on a motorized stage (MS) to form the front-view image on the camera. The side-view image is achieved by adding a second IL and a microscope objective (MO\u003csub\u003e2\u003c/sub\u003e : Nikon 20x or 40x) which forms the image on the\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eside-view camera. To block the scattered 532 nm laser beam, two notch filters (NF) are placed in front of each camera. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (b) depicts the generated square flat-top beam profile (of beam 2) that was captured with a beam profiling device (LaserCam-HR from Coherent). The laser power used the square flat-top beam was 150 mW. The square flat-top beam sides were measured to have a length of 75\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (b). This is the case for the profile of beam 2, up to 100\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em of its axial propagation before it starts degrading, which will be discussed in more detail in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eIt is worth noting that for this setup multiple objectives could be integrated (top, bottom and side of the sample) to either obtain different observation angles or achieve different types of microscopies, simultaneously.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eTheoretical Analysis\u003c/h3\u003e\n\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIn the asymmetric counter-propagating beam arrangement presented here, axial trapping is achieved at the location where the radiation pressure exerted by the focused beam is compensated by the radiation pressure exerted by the flat-top beam. The time-averaged radiation pressure force \u003cb\u003eF\u003c/b\u003e\u003csub\u003erad\u003c/sub\u003e exerted by two counter-propagating beams on a particle is given by:\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/69519_bce2c0439cd956a6/69519_custom_files/img1745838603.png\"\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp;(2)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003ewhere \u003cem\u003eC\u003c/em\u003e\u003csub\u003eext\u003c/sub\u003e is the extinction cross-section of the particle, \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eFT\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex,y,z\u003c/em\u003e) is the intensity of the flat top beam propagating in the axial direction \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{z}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eTR\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex,y,z\u003c/em\u003e) is the intensity of the trapping beam propagating in the negative \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{z}\\)\u003c/span\u003e\u003c/span\u003e direction. For the beam parameters used in our experiments, to an excellent approximation, \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eFT\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex,y,z\u003c/em\u003e)\u0026thinsp;\u0026asymp;\u0026thinsp;\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eFT\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ez\u003c/em\u003e) within the beam cross-section. We have verified this fact by simulating the propagation of a square flat-top beam of width 75\u003cem\u003e\u0026micro;m\u003c/em\u003e (the same width we generated) through a length of 100\u003cem\u003e\u0026micro;m\u003c/em\u003e, as shown in the Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. From the simulation, which is in good agreement with our measurements (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.c), it is evident that diffraction effects are minor in terms of beam-spreading, and that the intensity profile stays constant over most of the beam. As seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, after 100 \u003cem\u003e\u0026micro;m\u003c/em\u003e of axial propagation, the edge of the flat top beam profile demonstrates a change in intensity which we also observed experimentally shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.c.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eAs mentioned before, the trap is formed by the combination of a focused and a flat top beam, counterpropagating. For the focused beam we used the parameters of MO\u003csub\u003e1\u003c/sub\u003e (40X with 0.5\u003cem\u003eNA\u003c/em\u003e) with an effective focal length of about 4\u003cem\u003emm\u003c/em\u003e. With these specifications, the angular divergence of the beam around the focus is \u0026sim; 60. With the extinction cross-section \u003cem\u003eC\u003c/em\u003e\u003csub\u003eext\u003c/sub\u003e = 2.2\u003cem\u003e\u0026micro;m\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e as calculated and shown in the Supplementary Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e for a 2 \u0026micro;m polystyrene bead in water, we computed the force from Eq.\u0026nbsp;(2) as presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. From the slope of the force profile around the stable trap, we found the axial trap stiffness to be 1.15 \u003cem\u003epN/\u0026micro;m\u003c/em\u003e. For our calculation, the power of the flat top beam (with area 75 \u0026micro;m x 75 \u0026micro;m) is 150mW and the one for the focused beam (to create a single trap) is 10mW. These are the same powers used in our experimental section and when measuring trap stiffness (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Experimental Results and Discussion","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eBy judiciously shaping the ACP beams as described earlier, we have successfully constructed several 3D crystal-like structures. Examples such as square pyramid-like and cube-like structures are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Here we used 2\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em polystyrene particles inside a quartz cuvette filled with distilled water. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e depicts the phase mask used on SLM\u003csub\u003e2\u003c/sub\u003e and the generated square flat-top beam profile (of beam 2) that was captured with a beam profiling device. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (a,c) demonstrates examples of phase masks used on SLM\u003csub\u003e1\u003c/sub\u003e (shaping beam 1) to form the desired 3D structures. If SLM 2 was off or beam 2 was blocked, beam 1 by itself could not form any optical traps. Only when both beams were shaped via SLM\u003csub\u003e1\u003c/sub\u003e and SLM\u003csub\u003e2\u003c/sub\u003e with the phase masks described, and counter-propagated inside the sample chamber, 3D structures such as those shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (b,d) were stably constructed. The laser power used for the square flat-top beam was measured to be 150 mW and the total power distributed between the multi-traps generated by beam 1 varied between 30 mW to 60 mW, depending on the structure generated. We deliberately avoided forming the 3D structures near the sample chamber walls to avoid surface tension forces.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe successful formation and stability of these structures demonstrates the potential of our proposed system to generate other pre-defined crystal-like structures. Since polystyrene particles have a higher refractive index than the background (water) they are attracted to the higher intensity regions of beam 1 multifocal spots, due to the gradient forces. At the same time, the undesired axial scattering forces are cancelled by the counterpropagating flat-top beam. So, by controlling the multifocal spots position and phase on SLM\u003csub\u003e1\u003c/sub\u003e, we can form 3D structures within a very large volume compared to the symmetrical CP beams.\u003c/p\u003e \u003cp\u003eThe range for both lateral and axial optical trapping of our proposed system is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Even though the side of the square flat top generated is 75 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em, stable lateral trapping range is limited to 50\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em experimentally, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a). Trapping beyond 50\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em is less stable and as we get closer to the edges of the flat-top beam, due to the plateau non-uniformities, particles can no longer be trapped. On the other hand, stable axial 3D trapping was possible experimentally for axial distances up to 100 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (b). As demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e column (c) from right to left; the flat-top beam profile becomes slightly less uniform as the beam propagates from axial position 0 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em to 100 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em, but that does not affect trapping in the 50x50 lateral range since Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a) was reproducible for all axial positions between 0 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em and 100 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em. However, as we see in column (d) from left to right; beyond 100 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em, the flat-top beam profile intensity distribution becomes more and more nonuniform, making stable trapping quite challenging or impossible. It is worth mentioning that all the positions in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e were far from the cuvette\u0026rsquo;s walls.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eUsing this technique, we were able to optically trap polystyrene particles between 1 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em to 6 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em in size. The axial and lateral trapping range achieved here demonstrate that stable 3D trapping and manipulation of single particles or crystal-like structures is possible within 100\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em x 50\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em x 50\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003em volume. The ability to form and manipulate 3D structures (with micrometer precision) in such a large volume and without using high-NA objectives is quite unique and can be very practical, which is the result of utilizing a square flat-top counter-propagating beam.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eNext, utilizing a high-speed CMOS camera (model SC1 from edgertronic) with 2,000 fps, we track a trapped particle\u0026rsquo;s motion in both axial and lateral directions to measure the trap stiffness. The stiffness values are found for a 2 \u0026micro;m polystyrene bead trapped at several different locations on the same flat top plane (the z\u0026thinsp;=\u0026thinsp;0 plane shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.c) along the diagonal line shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e (a). Starting from the center of the flat-top beam (point 0) we trap the particle every 5 \u0026micro;m along the line, up to r\u0026thinsp;=\u0026thinsp;40 \u0026micro;m. At each location, both axial (b) and lateral (c) trap stiffness values are measured. To avoid surface effects, the z\u0026thinsp;=\u0026thinsp;0 plane was at least 50 \u0026micro;m away from any cuvette wall. The results of both axial and lateral stiffness measurements are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e (b) and (c) respectively.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe maximum trap stiffness happens for a radius (r) up to about r\u0026thinsp;=\u0026thinsp;15 \u0026micro;m from the center, but the decay is quite slow beyond that. Only after r\u0026thinsp;\u0026gt;\u0026thinsp;30\u0026micro;m, the axial stiffness values drop more noticeably. That is due to the less uniform power distribution of our generated flat-top beam at its edges. Further work is required to improve the uniformity of the generated flat-top beam. The maximum axial trap stiffness measured is 1 PN/\u0026micro;m which is in good agreement with the theoretical value (1.15 PN/\u0026micro;m) found earlier.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eIn summary, we have demonstrated that our previously reported ACP trapping beams [\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] can be further engineered to generate much larger trapping volumes. This was achieved by shaping the counter-propagating laser beams into a square flat-top from one side and multifocal spots from the other. The multifocal spots were generated by utilizing a hologram with Fresnel lenses and the square flat-top beam was created by using a hologram with the Gaussian beam shaping function. Our theoretical analysis demonstrates that the optical forces from the two asymmetrical CP beams result in a stable trap. We also experimentally measured the axial trapping stiffness for a 2 \u0026micro;m polystyrene bead, which was in good agreement with our theoretical calculation. Future efforts will focus on generating a more uniformly distributed flat-top beam. Since the counter propagating beams are asymmetric and only low-NA lenses have been used for 3D trapping, the setup is quite easy to align and less sensitive to misalignments compared to the single-beam or counter-propagating beams trapping methods used to form 3D crystal-like structures [\u003cspan additionalcitationids=\"CR35 CR36 CR37 CR38 CR39 CR40 CR41 CR42 CR43 CR44 CR45\" citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan additionalcitationids=\"CR49 CR50\" citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e]. Moreover, the use of low-NA optics reduces the cost and undesirable thermal effects that are a result of tight focusing with high-NA objectives. We investigated several of the particles that had been trapped for more than 20 minutes with our setup and did not find any noticeable damage. This can be valuable in the case of biological samples or in tissue engineering applications, where thermal effects should be minimized. Another important advantage of this method is that its axial trapping stiffness value is at least one order of magnitude larger compared to most of the traditional CP traps that have used similar experimental parameters [\u003cspan additionalcitationids=\"CR55 CR56\" citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e]. This has to do with the asymmetry of the CP beams used here and the location where the trap is formed with respect to the two beams, compared to when the two CP trapping beams are symmetric. On the other hand, since low-NA objectives have significantly larger working distances, this allows for a larger trapping volume, especially axially, as demonstrated here. Consequently side-view imaging would be possible due to the increase of trapping depths. In this case we can trap particles inside a larger volume such as a cuvette, which has been used here, and the sample chamber will no longer be limited to the use of cover slips and microscope slides which usually do not permit side views. Consequently, this setup allows for the simultaneous integration of different types of microscopies from multiple sides, in addition to the frontal-view microscopy.\u003c/p\u003e \u003cp\u003eTo trap a micron size particle in our study, the power entering the low-NA objective is comparable to previous reports and only a few milliwatts. However, to create the CP flat-top beam with enough power to form a stable trap, a 400mW laser beam was used before SLM 2, to generate a 150mW flat-top beam at the location of the trap (with an intensity of about 0.027 mW/\u0026micro;m\u003csup\u003e2\u003c/sup\u003e). This is mainly due to the low efficiency of the SLM. So, in order to generate 3D crystal-like structures using this technique, in addition to two SLMs, about half a watt of power is needed, which are the main disadvantages of this method.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eCompeting interests\u003c/h2\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003ch2\u003eAdditional information\u003c/h2\u003e\n\u003cp\u003eSupplementary Information\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence\u003c/strong\u003e and requests for materials should be addressed to S.F.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\n\u003cp\u003eS.F. conceptualized the research, directed and supervised the study. L.L. developed the theoretical framework, designed, built the experimental setup and collected data. All authors participated in the analysis of the collected data and the interpretation of results. All authors contributed on drafting the manuscript and figures.\u003c/p\u003e\n\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eS.F. acknowledges the support of the National Science Foundation through a grant with Award Number DMR-2414301, and the support from the Office of Naval Research (ONR) National Defense Education Program through the grant HQ0034231007.\u003c/p\u003e\n\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eThe datasets generated and/or analyzed during the current study are available from the corresponding author upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAshkin, A. Acceleration and Trapping of Particles by Radiation Pressure. \u003cem\u003ePhys. Rev. 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Soc.\u003c/em\u003e \u003cb\u003e6\u003c/b\u003e, 11057. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2971/jeos.2011.11057\u003c/span\u003e\u003cspan address=\"10.2971/jeos.2011.11057\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2011).\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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5039529/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5039529/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, we demonstrate a novel optical setup that is capable of volumetric 3D trapping and crystal-like structure generation. We achieved this by shaping asymmetric counter-propagating (ACP) beams comprised of a flat-top beam on one side and a multifocal spot on the other. Here, we study this trapping system both experimentally and theoretically and demonstrate stable trapping. Unlike most previous techniques, here we use low numerical aperture (NA) optics resulting in long manipulation distances and a wide field of view for side and front microscopy of the sample chamber. Moreover, the setup is easy-to-align and less sensitive to misalignments compared to most 3D structure forming methods. Our system can find application in the development of novel materials and microscopy studies on trapped particles.\u003c/p\u003e","manuscriptTitle":"Three-Dimensional Optical Trapping with a Low-NA Objective using a Flat-top Beam ","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-28 11:17:39","doi":"10.21203/rs.3.rs-5039529/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Accepted","date":"2025-05-09T09:29:25+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-09T06:19:07+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-08T00:31:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"268475681318620628105357552356893946878","date":"2025-04-30T01:27:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"27724399043524414431793952464083988136","date":"2025-04-26T00:59:08+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-04-25T09:51:19+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-04-20T11:50:09+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-04-08T03:14:05+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"939d047e-7f8b-4523-8564-96f8244ef5c2","owner":[],"postedDate":"April 28th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":47710833,"name":"Physical sciences/Materials science"},{"id":47710834,"name":"Physical sciences/Optics and photonics"}],"tags":[],"updatedAt":"2025-05-19T15:59:12+00:00","versionOfRecord":{"articleIdentity":"rs-5039529","link":"https://doi.org/10.1038/s41598-025-01974-4","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-05-16 15:57:07","publishedOnDateReadable":"May 16th, 2025"},"versionCreatedAt":"2025-04-28 11:17:39","video":"","vorDoi":"10.1038/s41598-025-01974-4","vorDoiUrl":"https://doi.org/10.1038/s41598-025-01974-4","workflowStages":[]},"version":"v1","identity":"rs-5039529","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5039529","identity":"rs-5039529","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}