Dual-fiber optical tweezers integrating high-sensitivity structured-light displacement measurement system on fiber end-face

Dual-fiber optical tweezers integrating high-sensitivity structured-light displacement measurement system on fiber end-face | 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 Dual-fiber optical tweezers integrating high-sensitivity structured-light displacement measurement system on fiber end-face Guofeng Li, Wei Xiong, Haining Feng, Zijian Feng, Tengfang Kuang, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5758813/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Mar, 2025 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract The dual-fiber optical tweezers have become widespread in trapping, assembling, and sensing due to their simple fabrication process and flexible operation. However, the miniaturization and integration of their displacement measurement optical paths remain challenging. Here, we propose and experimentally demonstrate an integration of structured-light displacement (SLD) measurement method tailored for dual-fiber optical tweezers. A key component split-waveplate is integrated onto the fiber end via coating and etching in the SLD method. The etched fiber and another single mode fiber form an optical tweezers, which enables to trap particle and measure its position simultaneously without additional optics. More importantly, it demonstrates a superior signal-to-noise ratio after filtering out the trapping field by the etched fiber. Our results demonstrate a displacement sensitivity reaching the 0.1 pm/Hz 1/2 level, which surpasses the performance of most results using the quadrant photodiode method. Ultimately, we discussed the possibilities of using two etched fibers to detect displacements in different directions, or integrating this method into a single optical fiber. This method has significant potential applications in precision sensing, contributes to the integration of optical tweezers and fosters the development of lab-on-fiber applications. Physical sciences/Optics and photonics/Optical techniques/Optical manipulation and tweezers Physical sciences/Optics and photonics/Applied optics/Optical sensors Dual-fiber optical tweezers Structured-light displacement method High Sensitivity Miniaturization and integration Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction In 1970, Arthur Ashkin demonstrated the use of optical forces to manipulate the motion of microparticles [1] . This pioneering work evolved into optical tweezers technology, driving significant advancements in biology [2, 3] , precision measurement [4–6] , quantum sensing [7, 8] , and various other fields [9–13] . Although optical tweezers in vacuum offer unmatched precision in object manipulation and ultra-high sensitivity in detection, they present challenges such as complex optical path structures and the large volume of system. In 1993, Constable et al. proposed a promising scheme involving dual-fiber optical tweezers characterized by a compact structure, simple fabrication process and flexible operation [14] . This setup is not only compatible with chip devices [15] , but also exhibits versatile in functions, including optical stretchers [16, 17] , optical rotators [18, 19] , and optical binding [20] . With the advancement of integrated photonics, the innovative concept of lab-on-fiber has emerged, integrating multiple optical paths or devices within a single fiber [21, 22] . As lab-on-fiber technology has advanced, an array of functionalities, including sensing [23, 24] , trapping particles [25, 26] , and manipulating light [27, 28] , have been meticulously incorporated into the fiber platform, demonstrating its versatility and potential. The majority of optical tweezers applications fundamentally rely on displacement measurements of the trapped object. The video-based position detection method offers the advantage of direct observation of the particle and is suitable for measuring low-frequency displacements [29, 30] . High-precision displacement measurements primarily utilize the back focal plane method, which employs scattered light to extract the particle displacement information [7, 31–33] . Among these methods, the quadrant photodiode (QPD) method and differential displacement measurement using D-shaped mirrors are the most commonly employed techniques [34, 35] . Nevertheless, it’s difficult to miniaturizing such measurement methods to match the fiber optical tweezers. The challenge mainly arises from the necessity to preserve the mode shape of the scattered light. Several studies have attempted to integrate displacement measurement into fiber optical tweezers [36–38] . However, no highly sensitive displacement measurement technologies tailored for that. It has constrained their advancement for integrated quantum sensing. In 2021, Lars. S. Madsen et al. presented an ingenious structured-light detection (SLD) method [39] . This method filters the trapping mode by flipping its transmission phase, so that it can directly measure displacement of particle using light intensity. It provides an alternative for the miniaturization of displacement measurement in fiber optical tweezers. In this paper, we simultaneously capture a microsphere and measure its displacement using an integrated structured-light displacement measurement method tailored for the dual-fiber optical tweezers. A critical component, the split-waveplate in the SLD method is integrated into a fiber end-face through coating and etching. The scattered light is collected by the etched fiber (EF) in the fiber optical tweezers, and the trapping field in the scattered light is partially filtered out. Consequently, this setup successfully achieves radial displacement detection with a superior signal-to-noise ratio. This work advances high-precision sensing technology and provides new insights into integrating optical tweezers. It enables the fabrication of MEMS devices capable of on-chip acceleration sensing [40, 41] , non-Newtonian force detection [42] , and viscosity coefficient measurement [43] , thereby promoting the development of lab-on-fiber technology. 2. Pinciple In the field of optical tweezers, most trapping systems use fundamental Gaussian beams (TEM 00 ) as the trapping light, except for specific applications that require special light fields. The trapping light is partially disturbed by the microsphere and converted into the information-containing field (TEM 01 ), while the undisturbed trapping light remains as the fundamental mode TEM 00 . TEM 00 mode is symmetric about the trap center and occupies the majority of the probe beam, serving as background noise in displacement detection. The TEM 01 mode is antisymmetric and contains the particle's displacement information, constituting a small portion of the probe beam [33] . In the SLD method, a π phase difference introduced by the split-waveplate is crucial for filtering the trapping field before coupling the probe beam into the single mode fiber (SMF) [39] . This phase difference reverses the symmetry of two modes in the probe beam, converting the TEM 00 mode into an anti-symmetric flipped TEM 00 mode and the TEM 01 mode into a flipped TEM 01 mode. Due to the symmetry of guided modes in SMF, the antisymmetric flipped TEM 00 mode cannot propagate through the fiber. However, despite the structural differences between the symmetric flipped TEM 01 mode and the LP 01 mode, there exists a limited overlap in amplitude and phase within certain regions, enabling the flipped TEM 01 mode to couple into the SMF [44, 45] . In a word, the split-waveplate combined with single mode fiber (SMF) acts as a spatial filter to diminish the trapping field and enhance the transmission of the information-containing field, thereby enabling high signal-to-noise ratio displacement detection. Figure. 1(a) depicts the schematic of the integration of structured-light displacement measurement method tailored for dual-fiber optical tweezers. The etched fiber and another SMF form a dual-fiber optical tweezer to trap particles. The etched fiber is fabricated in two steps. First, a standard SMF is coated with a Ta 2 O 5 layer (depicted as the pink layer in the figure) [46] . Then, the coating layer is etched to a certain depth using a Focused Ion Beam (FIB). As a result, a phase difference of π is generated between the etched and unetched regions on the end face of the fiber due to the optical path difference. As the trapping light (TEM 00 mode) transmits through the trapped particle, the perturbative caused by the particle transforms a portion of the light into the TEM 01 mode (the blue curve in the orange inset) [39] . When the light passes through the coating layer with an etching structure, the symmetries of the two modes are reversed. The TEM 00 mode is converted to the antisymmetric flipped TEM 00 mode, and the TEM 01 mode is altered to symmetric flipped TEM 01 mode. Consequently, the antisymmetric trapping field cannot propagate in the single-mode fiber portion of the etched fiber. In this configuration, the probe beam received by the etched fiber enters the circulator through port 2. Then, it transmits via port 3 to a photodetector (PD). As a result, the PD predominantly detect the flipped TEM 01 mode, thereby extracting the displacement information of the microsphere. This configuration significantly enhances the signal-to-noise ratio for displacement measurements by utilizing mode transformation to maximize the transmission of the displacement signal. Figure.1(b) is the schematic of the etched fiber end-face with etching structure, where r 1 is the radius of the fiber core and r 2 indicates the radius of the etched area (crimson semi-circle). In the simulation, the monitor is positioned between the coating layer and the optical fiber. As shown in Fig. 1(c), the phase map clearly indicates a π phase difference between the etched and unetched regions. This phase difference is realized by the optical path difference during the transmission of light in the film layer. Figure. 1(d) demonstrates Scanning Electron Microscopy images (SEM) of the end face of the etched fiber. An etching semicircle within the white dotted box has a depth equal to the film thickness. We utilized the finite difference time domain (FDTD) method to build the simulation model. Both simulations and experiments were conducted in a water environment. The fiber (Corning, HI 1060) with a core radius of r 1 2.65 µm and a mode-field diameter of 5.9 ± 0.3 µm @980 nm. To match the two-dimensional profile size of the beam emitted from the SMF to the dimensions of the etched semicircle in the fiber coating layer. It enables to introduce a phase difference of π between the etched and unetched regions. Consequently, the radius r 2 of the etched semicircle is precisely selected to be 6 µm. The transmission phase formula is as follows: is the free space wave vector, n is the refractive index difference of the uniform medium, and d is its thickness. The thickness of the Ta 2 O 5 layer in fiber end face is designed as 600 nm. We deposited Ta 2 O 5 films on the fiber end-face using ion sputtering technology, achieving a thickness of 606.0 nm, as shown in Fig. 2 (a). The ideal refractive index of Ta₂O₅ at a wavelength of 980 nm is 2.157, while the experimentally measured refractive index, determined using an ellipsometer, is slightly lower at n 1 = 2.155. The depth of the etched semi-circle is the same as the thickness of the film, as shown in Fig. 2 (b). The refractive index of water is n 2 = 1.33, thus the phase difference between the etched and non-etched parts is 1.01π. In this way, approximately π phase is achieved. It satisfies the phase requirements of the structured-light displacement measurement method for flipping mode. Figure 2 (c) presents the diameter of the etched semicircle, while Fig. 2 (d) displays the mark on the lateral aspect of the etched fiber. This mark is designed to locate the x direction during the subsequent assembly of dual-fiber optical tweezers. It is worth noting that before carry out the experiment, the gold film sprayed by the FIB processing needs to be removed using aqua regia to avoid affecting the transmission phase. 3. Result and analysis 3.1 Optical trap We calculate the axial forces on the microspheres at different distances (from 120 μm to 40 μm) between two optical fibers. Results indicate that at an output power of 100 mW for each fiber, a point where the axial force is 0 pN with a negative slope appears when the distance is reduced to approximately 40 μm. It means that the microsphere is subjected to equal from the dual beams and in a stable trapped state. In linear optics, all forces scale linearly with the light intensity. If a larger fiber spacing is chosen, it is evident that the output optical power of the etched fiber needs to be increased. However, there is a concern that under high-power output in a liquid environment, the liquid could be heated and may cause bubble formation. Consequently, we chose a fiber spacing of 40 μm between the two fibers to set up the dual-fiber optical tweezers. Figure 3(a) shows a schematic diagram of the optical fiber output mode field testing system, and the cuvette in the illustration features two coaxial holes. The etched fiber extends through the hole into the water-filled cuvette during testing. When the focus of the objective lens coincides with the end face of etched fiber, the measured beam mode field diameter is minimized, marked as z = 0 μm. By moving translation stage 1 along z axis, the beam intensity distribution at different transmission distances can be measured. Figure 3(b) presents the simulated intensity distribution of the beam emitted from the etched fiber, and its exhibit a bimodal distribution with two distinct peaks of similar intensity. In the FDTD simulations, the amplitude of the light source was set to 1, and the polarization was aligned along the x-axis. The electric field strength distribution was normalized. Consequently, the intensity plots of simulation are on the same scale. In the actual process of etched fiber, it is difficult to ensure that the etching demarcation line is entirely centered on the fiber core. Consequently, we have introduced a 300 nm offset of the diameter of the semicircle from the central position of the fiber core in the simulations. In the experiments, we coupled white light into the other end of the etched fiber. Under a microscope, we excluded samples with excessive offsets of the etched boundary from the fiber core center. Using the testing setup in Fig. 3(a), the intensity distribution of the beam emitted from the etched fiber at different transmission distances was measured, as shown in Fig. 3(c). A dark fringe appears at the center of the beam intensity distribution, as indicated by the direction of the red arrow, which is due to destructive interference caused by the π phase difference between the etched and unetched regions. These results closely align with the simulation intensity distribution, demonstrating a consistent trend. It is expected that the microsphere near the optical axis will interact less strongly with the light emitted by the etched fiber, given the split nature of its spot. To effectively trap a particle near the central position between the two fibers, it is necessary to increase the output power of the etched fiber. Figure 4 shows the dual-fiber optical tweezers system with the integrated structured-light displacement method and the QPD method. A LED light and a CCD camera form an illumination imaging optical path for observing trapped particle. In order to easily adjust the input power P 2 of the etched fiber, the etched fiber and the SMF use different lasers for input. The light (orange) input by laser 1 enters the SMF through the circulator 1, passes through the particle and couples into the etched fiber, and is finally received by the PD. In order to facilitate light path adjustment, the laser wavelength used in the QPD method is 532 nm (green). The detection beam of the QPD method is collected by objective 2 and finally enters the QPD. The PD and QPD are connected to the DAQ card to store data on a computer. The sampling frequencies of the SLD method and QPD method are 1000 k/s and 200 k/s, respectively. Based on the calculations from the previous section, we set the power output for the SMF ( P 1 ) to 100 mW and for the etched fiber ( P 2 ) to 200 mW. The simulation results for the radial force on a silica microsphere with a diameter of 5 μm is presented in Fig. 5(a), two points with zero net force and negative slope (blue arrow) indicates the existence of two stable trapping points in the radial direction. The two equilibrium points are similarly distant from the central axis with similar slopes, suggesting that the axial optical force and displacement response of the particle are essentially the same. The corresponding radial force curve is depicted in Fig. 5(b). An axial equilibrium point (red arrow) is observed near the central region between two fibers. These simulation results confirm that our dual-fiber tweezers can stably capture particles. We performed experiments to successfully trap a silica microsphere with diameter of 5 μm, and its screenshot is provided in Fig. 5(c). In liquid environments, measuring the optical power output from fibers poses significant challenges. However, due to the inherently low loss of single-mode fibers, the discrepancy between input and output power is minimal. Consequently, using the input power for experiments can ensure both accuracy and repeatability. Figure 5(d) illustrates the relationship between the input power of the etched fiber and the equilibrium position of the microsphere. It is observed that as P 2 increases, the microsphere gradually moves from a position which close to the etched fiber towards the center. The experimental data align with the simulated trends, thereby validating the accuracy of the simulation. 3.2 Displacement measurement In this study, we simulated the coupling efficiency of the dual-fiber optical tweezer with a microsphere inside. Light from a SMF passes through the microsphere and couples into the other fiber. The coupling efficiency spectra of the SMF-SMF and SMF-EF configuration are depicted in Fig. 6(a) and (b), respectively. In Fig. 6(a), the coupling efficiency follows a symmetrical parabolic distribution with the displacement of the trapped microsphere. The largest coupling efficiency is approximately 24% when the microsphere locates on the optical axis ( x =0). In comparison, the coupling efficiency of the SMF-EF configuration is reduced to about 12% when x =0, representing a half decrease [see Fig. 6(b)]. More importantly, the coupling efficiency is proportional to the displacement of the microsphere near x =0, due to an offset of the etched semicircle. This provides a linear response region for displacement measurement and orientation determination of moving microspheres. For the construction of dual-fiber optical tweezers, precise alignment of the two fibers was achieved by engraving V-grooves on an acrylic plate [47] . Initially, we constructed an optical tweezers system with a separation of 40 μm using two single-mode fibers [inset of Fig. 6(c)]. To mitigate thermal effects and ensure the stability of the trapped microsphere, the input power of the etched fiber was reduced. This adjustment also enabled long-term experimentation. Consequently, the input powers P 1 and P 2 of the two fibers were set to 100 mW and 200 mW, respectively. Subsequently, a silica microsphere with a diameter of 5 μm was successfully trapped. The data were collected by a data-acquisition card controlled by a LabVIEW program. The corresponding voltage signal is presented in Fig. 6(c), showing an average signal amplitude of 5.25 V. Under identical experimental conditions, we established an optical tweezers using a SMF and an etched fiber (inset of Fig. 6d). The input power from the SMF P 1 and from the etched fiber P 2 were maintained at 100 mW and 200 mW respectively. The photodetector (PD) connected to the etched fiber recorded an average voltage of 2.87 V. Compared to the SMF-SMF optical tweezers, the coupling power is reduced by 45.33% with the same trapped optical power. The experimental results correspond well with the simulation results. These results suggest that the trapping field was significantly filtered, which is conducive to the extraction of the information-containing field. Figure 7(a) presents the power spectrum density of experimentally recorded displacement of the trapped particle (the pink dots). The fitting curve (black solid line) was derived using the Lorentz fitting method [48] . The corner frequency of the displacement spectrum is f c 1 = 3.21 Hz, and the trapping stiffness k x 1 in the x direction was calculated to be 1.05 pN/μm. For comparison, another displacement measurement optical path was established using the QPD method. The displacement spectrum corresponding to the x direction signal measured by the QPD method is shown in Fig. 7(a) and (b). The blue solid line in Fig7. (b) is its Lorentz fitting curve, which has a corner frequency f c 2 = 3.34 Hz, indicating a trapping stiffness k x 2 of 1.09 pN/um. The spectra of the QPD and SLD methods overlap almost entirely in the low-frequency range up to 10 4 Hz. The displacement spectrum of the y direction signal measured by the QPD method (in orange) is plotted in Fig 7. (b). It can be observed that there is a significant difference compared to the displacement spectrum of the x direction in the low-frequency region. These results indicate that the SLD method can accurately measure the x direction displacement of microsphere. Moreover, the gray curve in Fig. 7(a) represents the signal PSD at the same optical power without the microsphere. This PSD indicates that the displacement detection sensitivity of the SLD method reaches 0.13 pm/Hz 1/2 , with a frequency range of 1–500 kHz. It is approximately half an order of magnitude higher than the QPD method in this experiment. Although using a higher sampling rate in the QPD method might offer comparable detection sensitivity, the advantage of the SLD method is that it can filter out the trapping field without the attenuating information-containing field. Compared with other displacement measurement methods [49, 50] , our approach achieves comparable sensitivity while also realizing significant miniaturization. The aforementioned advantages enable this method to provide a higher signal-to-noise ratio and can be used in conjunction with commonly available commercial detectors in any strong optical trap. 4. Summary and outlook We have demonstrated the integration of a structured-light displacement measurement method for dual-fiber optical tweezers. The method enables to simultaneously trap a particle and measure its displacement without additional optics. A split-waveplate was integrated into the end-face of fiber through coating and etching. Unlike standard SMF, simulation and experiment reveal that the beam profile of the etched fiber divided into two parts. Based on optical force calculations, we selected a 40 µm fibers spacing to construct a dual-fiber optical tweezer, and successfully trapped a microsphere in experiments. In addition, we confirmed the effectiveness of the proposed method in the enhancing information-containing field. This method achieves a displacement measurement sensitivity of 0.1 pm/Hz 1/2 level, surpassing the QPD method under comparable experimental conditions. With this research integrating structured light displacement detection into the fiber end face, some limitations still remain, such as the lack of multi-directional displacement detection capabilities. We propose a conceptual design for multi-directional displacement detection using a dual-fiber optical tweezer, aiming to overcome the limitations of single-direction detection in conventional systems. This design utilizes two etched optical fibers with their etching boundaries oriented orthogonally to each other—one aligned perpendicular to the x-direction and the other perpendicular to the y-direction. By separately detecting the scattered light signals through these two etched fibers, displacement measurements along the x and y directions can be independently achieved. This concept establishes a framework for multi-directional displacement detection within dual-fiber optical tweezers, offering potential applications in microfluidics and precision optical sensing. However, practical implementation requires not only introducing an appropriate phase difference at the fiber end face but also optimizing the design structure to enhance the quality of the outgoing beam. Inspired by the polishing processes of the side of a single-mode fiber [51–53] , it also integrates this detection scheme into a single fiber. The fiber can be etched beyond the core region, and the cross-section at one end can be modified to introduce a phase difference of π. This approach enables simultaneous particle trapping and displacement measurement, significantly reducing system volume while improving integration and functionality. Finally, we propose the potential for achieving multi-directional displacement measurements through the use of two etched optical fibers, or by integrating structured-light displacement detection within a single fiber, highlighting the feasibility of these approaches for advancing lab-on-fiber systems. Although there are still limitations regarding system volume and the implementation of multi-directional displacement detection, this study provides new perspectives for the development of lab-on-fiber technology and lays the foundation for future research in optical tweezers technology. Declarations Funding This work is supported by Science Fund for Distinguished Young Scholars of Hunan Province (2024JJ2055), and the Key Science and Technology Breakthrough Program of Hunan Province (2023ZJ1010). Author Contribution G.L. was involved in the research design, data collection, experimental work, theoretical analysis, software and computational modeling, and visualization. W.X contributed to the research design, data analysis, theoretical analysis, review and editing, interpretation of results, and validation of results. H.F was responsible for software and computational modeling. Z.F contributed to the writing of the manuscript. T.F was involved in review and editing, interpretation of results, and validation of results. Z.L also contributed to software and computational modeling. Xiang.Han provided supervision and resources for the project. Xin.He was involved in experimental work and validation of results. X.C provided supervision and resources. J.Y contributed to funding acquisition, supervision, theoretical analysis, and project guidance. G.X was responsible for funding acquisition, supervision, theoretical analysis, and review and editing. Acknowledgement The authors would like to acknowledge Yinan Li and Li Sun at Kaiple Company for SEM performance. Data Availability The data used and analyzed during the current study are available from the corresponding author on reasonable request. References A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Physical review letters, 1970, 24(4):156–159. A. Ashkin, K. Schütze, and J. M. Dziedzic, and U. Euteneur, “Force generation of organelle transport measured in vivo by an infrared laser trap,” Nature , 1990, 348(6299): 346–348. S. M. Block, L. S. B. Goldstein, and B. J. Schnapp, “Bead Movement by Single Kinesin Molecules Studied with Optical Tweezers”, Nature ,1990, 348(6299): 348–352. S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science , 2014, 343(6178):1493-1496. Y. Zheng, L. Zhou, and Y. Dong, C. Qiu, X. Chen, G. Guo, and F. Sun, “Robust optical-levitation-based metrology of nanoparticle’s position and mass,” Physical review letters , 2020, 124(22): 223603. S. Zhu, Z. Fu, and X. Gao, C. Li, Z. Chen, Y. Wang and H. Hu, “Nanoscale electric field sensing using a levitated nano-resonator with net charge,” Photonics Research, 2023, 11(2): 279-289. T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nature Physics , 2011, 7(7). T. Kuang, R. Huang, and W. Xiong, Y. Zuo, X. Han, F. Nori, C. Qiu, H. Luo, H. Jing and G. Xiao, “Nonlinear multi-frequency phonon lasers with active levitated optomechanics,” Nature Physics , 2023, 19(3): 414–419. M. Peng, G. Xiao, X. Chen, T. Du, T. Kuang, X. Han, W. Xiong, G. Zhu, J. Yang, Z. Tan, K. Yang, and H. Luo, “Optical trapping-enhanced probes designed by a deep learning approach,” Photonics Research , 2024, 12(5): 959-968. G. Xiao, T. Kuang, Y. He, X. Chen, W. Xiong, X. Han, Z. Tan, H. Luo, and H. Jing, “Giant enhancement of higher-order harmonics of an optical-tweezer phonon laser,” eLight , 2024,4(17). Y. Liang, S. Yan, Z. Wang, B. Yao, and M. Lei, “Off-axis optical levitation and transverse spinning of metallic microparticles,” Photonics Research , 2021, 9(11): 2144-2151. P. H. Jones, O. M. Maragò, and G. Volpe, Optical Tweezers: Principles and Applications (Cambridge University, 2015). X. Han, X. Chen, W. Xiong, T. Kuang, Z. Chen, M. Peng, G. Xiao, K. Yang, and H. Luo, “Vacuum optical tweezers system and its research progress in precision measurement,” Chinese Journal of Lasers , 2021, 48(4): 0401011. A. Constable, J. Kim, J. Mervis, F. Zarinetchi, and M.Prentiss, “Demonstration of a fiber-optical light-force trap,” Optics Letters , 1993, 18:1867–1869. C. Jensen-McMullin, H. P. Lee, and E. P. Lyons, “Demonstration of trapping, motion control, sensing and fluorescence detection of polystyrene beads in a multi-fiber optical trap,” Optics Express , 2005,13(7): 2634–2642. J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Käs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophysical journal , 2001, 81: 767–784. N. Bellini, F. Bragheri, and I. Cristiani, J. Guck, R. Osellame, G. Whyte, “Validation and perspectives of a femtosecond laser fabricated monolithic optical stretcher,” Biomedical Optics Express , 2012, 3(10): 2658–2668. X. Chen, G. Xiao, and K. Yang, W. Xiong, H. Luo, “Characteristics of the orbital rotation in dual-beam fiberoptic trap with transverse offset,” Optics Express , 2016, 24(15):16952–16960. G. Xiao, K. Yang, and H. Luo, X. Chen, and W. Xiong, “Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,” IEEE Photonics Journal , 2016, 8(1): 1–8. N. K. Metzger, E. M. Wright and W. Sibbett, and K. Dholakia, “Visualization of optical binding of microparticles using a femtosecond fiber optical trap,” Optics Express , 2006, 14(8): 3677–3687. A. Cusano, M. Consales, and A. Crescitelli, eds. “Lab-on-fiber technology,” Switzerland: Springer International Publishing (2015). Y. Meng, Y. Chen, L. Lu, Y. Ding, A. Cusano, J. A. Fan, Q. Hu, K. Wang, Z. Xie, Z. Liu, Y. Yang, Q. Liu, M. Gong, Q. Xiao, S. Sun, M. Zhang, X. Yuan, X. Ni. “Optical meta-waveguides for integrated photonics and beyond,” Light: Science & Applications , 2021, 10(1): 1-44. A. Ricciardi, A. Crescitelli, P. Vaiano, G Quero, M. Consales, M. Pisco, E. Esposito, and A. Cusano, “Lab-on-fiber technology: a new vision for chemical and biological sensing,”, Analyst , 2015, 140(24): 8068-8079. M. Pisco, F. A. Bruno, D. Galluzzo, L. Nardone, G. Gruca, N. Rijinveld, F. Bianco, A. Cutolo, and A. Cusano, “Opto-mechanical lab-on-fibre seismic sensors detected the Norcia earthquake,” Scientific Reports , 2018, 8(1) (2018) 6680. J. M. Ehtaiba, and R. Gordon, “Template-stripped nanoaperture tweezer integrated with optical fiber,” Optics Express , 2018, 26(8): 9607-9613. Y. Li, H. Xin, and Y. Zhang, “Optical Fiber Technologies for Nanomanipulation and Biodetection: A Review,” Journal of Lightwave Technology , 2020, 39(1): 251-262. N. Bozinovic, Y. Yue and Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science , 2013, 340(6140): 1545-1548. J. Du, S. Chen, and S. Li, L. Zhu, Y. Zhao, and J. Wang, “Design and fabrication of metasurface on conventional optical fiber facet for linearly polarized mode (LP11) generation at visible light wavelength,” CLEO: Science and Innovations, Optica Publishing Group (2016). J. C. Crocker, and D. G. Grier, “Methods of digital video microscopy for colloidal studies,” Journal of Colloid and Interface Science, 1996, 179(1): 298–310. G. M. Gibson, J. Leach, and S. Keen, A. J. Wright, M. J. Padgett, “Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,” Optics Express , 1996, 16(19): 14561–14570. F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Optics Letters , 1998, 23(1): 7–9. W. Xiong, G. Xiao, X. Han, J. Zhou, X. Chen, and H. Luo, “Back-focal-plane displacement detection using side-scattered light in dual-beam fiber-optic traps,” Optics Express , 2017, 25(8): 9449–9457. M. A. Taylor, J. Knittel, and M. T. L. Hsu, W. P. Bowen, “Sagnac interferometer-enhanced particle tracking in optical tweezers,” Journal of Optics , 2011, 13(4): 044014. Z. Chen, T. Kuang, X. Han, G. Li, W. Xiong, G. Xiao, H. Luo, “Differential displacement measurement of the levitated particle using D-shaped mirrors in the optical tweezers,” Optics Express , 2022, 30(17): 30791–30798. W. Li, H. Zhang, M. Hu, Q. Zhu, H. Su, N. Li, & H. Hu, “3D calibration of microsphere position in optical tweezers using the back-focal-plane interferometry method,” Optics Express , 2021, 29(20): 32271–32284. W. Xiong, G. Xiao, X. Han, X. Chen, K. Yang, and H. Luo, “All-fiber interferometer for displacement and velocity measurement of a levitated particle in fiber-optic traps,” Applied Optics , 2019, 58(8): 2081–2084. A. Chen, H. Luo, Z. Chen, H. Feng, T. Kuang, H. An, X. Han, W. Xiong and G. Xiao, “Displacement detection based on four-fiber bundle in dual-beam fiber-optic traps, Ninth Symposium on Novel Photoelectronic Detection Technology and Applications,” SPIE, 2023, Vol. 12617. Q. Xiang, N, Li, X, Chen, L, Liu and H, Hu, “Miniaturized Dual-Beam Optical Trap Based on Fiber Pigtailed Focuser,” Photonics , 2023, 10(9): 1007. L. S. Madsen, M. Waleed, C. A. Casacio, A. Terrasson, A. B. Stilgoe, M. A. Taylor, and W. P. Bowen, “Ultrafast viscosity measurement with ballistic optical tweezers,” Nature Photonics , 2021, 15(5): 386-392. D. L. Butts, Development of a light force accelerometer. Diss. Massachusetts Institute of Technology, (2008). K, Krish. “Toward a demonstration of a light force accelerometer. Diss. Massachusetts Institute of Technology, (2010). G. Ranjit, M. Cunningham, and K. Casey, A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Physical Review A , 2016, 93(5): 053801. A. K. Korzeniewska, and S. Drobczyński. “Local measurement of liquid viscosity in optical tweezers,” Optics and Lasers in Engineering , 2023, 164: 107516. G. Li, T. Kuang, W. Xiong, X. Han, G. Xiao, Z. Tan, and H. Luo, “Structured-light displacement detection method using split-waveplate for dual-beam optical tweezers,” Optics Express , 2023, 31(21): 34459-34469. Gloge, D. “Weakly guiding fibers,” Applied Optics , 1971, 10(10): 2252-2258. Bright, T. J., Watjen, J. I., Zhang, Z. M., Muratore, C., Voevodin, A. A., Koukis, D. I., ... & Arenas, D. J. (2013). “Infrared optical properties of amorphous and nanocrystalline Ta 2 O 5 thin films,” Journal of Applied Physics , 2013, 114(8). D. Collins, R. J. Baskin, and D. G. Howitt, “Micro instrument gradient-force optical trap,” Applied Optics , 1999, 38: 6068–6074. Y. Li and K. Yao, Techniques of Optical Tweezers, Science Press, (2015). A. D. Rider, C. P. Blakemore, and G. Gratta, “Single-beam dielectric-microsphere trapping with optical heterodyne detection,” Physical Review A , 2018, 97: 013842. Y. Jin, X. Yu, and J. Zhang, “Optically levitated nanosphere with high trapping frequency,” Science China ( Physics,Mechanics & Astronomy ),2018, 61: 114221. Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, Y. T. Ding and K. P. Loh, “Broadband graphene polarizer,” Nature Photonics , 2011, 5(7): 411-415. Z. P. Jiang, J. L. Dong, S. Q. Hu. Y. X. Zhang, Y. F. Chen, Y. H. Luo, W. G. Zhu, W. T. Qiu, H. H. Lu, H. Y. Guan, Y. C. Zhong, J. H Yu, J. Zhang, and Z. Chen, “High-sensitivity vector magnetic field sensor based on side-polished fiber plasmon and ferrofluid,” Optics Letters , 2018, 43(19): 4743-4746. Z. D. ZHU, L. Liu, Z. H. Liu, Y. Zhang, and Y. X. Zhang. “Surface-plasmon-resonance-based optical-fiber temperature sensor with high sensitivity and high figure of merit,” Optics Letters , 2017, 42(15): 2948-2951. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Mar, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 28 Jan, 2025 Reviews received at journal 27 Jan, 2025 Reviews received at journal 17 Jan, 2025 Reviewers agreed at journal 09 Jan, 2025 Reviewers agreed at journal 09 Jan, 2025 Reviewers invited by journal 09 Jan, 2025 Editor assigned by journal 09 Jan, 2025 Editor invited by journal 09 Jan, 2025 Submission checks completed at journal 09 Jan, 2025 First submitted to journal 03 Jan, 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. 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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-5758813","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":400288803,"identity":"aed6bf08-bbf3-44bb-8781-a97fef44c345","order_by":0,"name":"Guofeng Li","email":"","orcid":"","institution":"College of Advanced Interdisciplinary Studies, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Guofeng","middleName":"","lastName":"Li","suffix":""},{"id":400288804,"identity":"533993c2-dbce-4492-8030-03e01ee5af5d","order_by":1,"name":"Wei Xiong","email":"","orcid":"","institution":"College of Advanced Interdisciplinary Studies, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Xiong","suffix":""},{"id":400288805,"identity":"11434b72-15c5-4a9c-825f-8d8a0dc28033","order_by":2,"name":"Haining Feng","email":"","orcid":"","institution":"College of Advanced Interdisciplinary Studies, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Haining","middleName":"","lastName":"Feng","suffix":""},{"id":400288806,"identity":"b785bd7f-6390-424e-8b04-148f4d649ca6","order_by":3,"name":"Zijian Feng","email":"","orcid":"","institution":"College of Advanced Interdisciplinary Studies, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Zijian","middleName":"","lastName":"Feng","suffix":""},{"id":400288807,"identity":"48cc5a76-f4ee-46cc-8ada-78428abd3945","order_by":4,"name":"Tengfang Kuang","email":"","orcid":"","institution":"College of Advanced Interdisciplinary Studies, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Tengfang","middleName":"","lastName":"Kuang","suffix":""},{"id":400288808,"identity":"fefa0864-221e-49ba-ba22-ce067b9bfa99","order_by":5,"name":"Zhechun Lu","email":"","orcid":"","institution":"Center of Material Science, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Zhechun","middleName":"","lastName":"Lu","suffix":""},{"id":400288809,"identity":"24c11cd2-30ce-4ec7-b342-924f9ed10d21","order_by":6,"name":"Xiang Han","email":"","orcid":"","institution":"College of Advanced Interdisciplinary Studies, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Xiang","middleName":"","lastName":"Han","suffix":""},{"id":400288810,"identity":"41260924-04d4-4d02-bd1a-f967e44b9b57","order_by":7,"name":"Xin He","email":"","orcid":"","institution":"Center of Material Science, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Xin","middleName":"","lastName":"He","suffix":""},{"id":400288811,"identity":"e17891aa-3a11-4165-9122-e98f6df33e69","order_by":8,"name":"Xinlin Chen","email":"","orcid":"","institution":"College of Advanced Interdisciplinary Studies, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Xinlin","middleName":"","lastName":"Chen","suffix":""},{"id":400288812,"identity":"cf306b4b-1d20-4aea-b349-3f0e13c4f9d9","order_by":9,"name":"Junbo Yang","email":"","orcid":"","institution":"Center of Material Science, National University of Defense Technology","correspondingAuthor":false,"prefix":"","firstName":"Junbo","middleName":"","lastName":"Yang","suffix":""},{"id":400288813,"identity":"b1176d45-eb62-433f-882d-98d93f4cc6fe","order_by":10,"name":"Guangzong Xiao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEElEQVRIiWNgGAWjYDACZhReBRAfAGIe4rWcAeJjhLSgAMY2IrQYHGd++PBrm12evP/hYw+/zruT2He/gfHB2zYGeXMcWiSb2YyNZduSiw0PHEs3lt32LHHmMQZmw7ltDIY7G7Br4WdmMJOWbGNO3NjYA2RsO5y44RgDmzRvG0OCwQHsWtiY2b8BtdQnbmzmAWqZA9bC/hufFn5mHjPJj22HE+ezgRgNEFuY8WmRbOYpNmY4dzxxAw9bmjTDscPGM48lNkvOOSdhuAGHFoPzxzc+/FFWnTi///AxyR81h2X7Dh8++OFNmY08LltAgBkUCyAFzJDoYGwAEhK41YOU/AAS8g1QxigYBaNgFIwCdAAAkj9c6AYrdWEAAAAASUVORK5CYII=","orcid":"","institution":"College of Advanced Interdisciplinary Studies, National University of Defense Technology","correspondingAuthor":true,"prefix":"","firstName":"Guangzong","middleName":"","lastName":"Xiao","suffix":""}],"badges":[],"createdAt":"2025-01-03 14:08:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5758813/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5758813/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-93523-2","type":"published","date":"2025-03-17T15:58:15+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":73618679,"identity":"4b9a7ba9-7eea-4148-a638-d9a0a5369f4f","added_by":"auto","created_at":"2025-01-13 03:41:27","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2599905,"visible":true,"origin":"","legend":"\u003cp\u003ePrinciple of the integrated structured-light displacement measurement method tailored for dual-fiber optical tweezers. (a) Schematic representation of dual-fiber optical tweezers composed of SMF and etched fiber. The end face of the etched fiber is coated with a Ta\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e film (pink layer). PD indicates that the photodetector is used to convert optical signals into electrical signals. Power spectral density (PSD) is obtained by Fourier transform. Orange inset: the TEM\u003csub\u003e00\u003c/sub\u003e mode is the trapping field, and the TEM\u003csub\u003e01\u003c/sub\u003e mode indicates the information-containing field. (b) Schematic of the etched fiber end face with etching structure (crimson), \u003cem\u003er\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e is the radius of the fiber core, and \u003cem\u003er\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003e \u003c/em\u003eis the radius of the etched semicircle. (c) Simulated phase map of etched fiber, showing a phase difference π between the etched and the unetched region. (d) SEM image of the fiber with an etched semicircular structure in a white dotted box.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5758813/v1/5ab89d060951b11794d0d2a8.png"},{"id":73618784,"identity":"afdd462b-947c-40e6-930d-40be4dd1a4b6","added_by":"auto","created_at":"2025-01-13 03:49:27","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":997369,"visible":true,"origin":"","legend":"\u003cp\u003eEtched fiber processing details. (a) Thickness of Ta\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e layer. (b) Etched the depth of the semicircle. (c) Etched the diameter of the semicircle. (d) Marking of the semicircle dividing line on the lateral aspect.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5758813/v1/f0c49440618697ffa071350d.png"},{"id":73618680,"identity":"da6aea49-2388-458d-93ad-6baa18c7d931","added_by":"auto","created_at":"2025-01-13 03:41:27","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":338123,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic diagram of the optical fiber output mode field testing system, and the cuvette in the illustration features two coaxial micropores; (b) The intensity distribution of the etched fiber beam at different transmission distances is obtained by simulation (c) The intensity distribution of the etched fiber beam at different transmission distances is obtained by experiment.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5758813/v1/e92078c629df29b52201aaf9.png"},{"id":73618684,"identity":"daf318a0-e053-4a81-a58c-8da319cea976","added_by":"auto","created_at":"2025-01-13 03:41:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1379508,"visible":true,"origin":"","legend":"\u003cp\u003eThe dual-fiber optical tweezers system with the SLD method and the QPD method. PD stands for Photodetector. QPD, the quadrant photodiode. LED, light emitting diode. CCD, Charge coupled Device. OJ1 \u0026amp; OJ2, objective. BS1 \u0026amp; BS2, beam splitter. DAQ, data-acquisition card. PC, computer. Trash, optical trash can.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5758813/v1/4ed2ada533a65c6c87e1bbf3.png"},{"id":73618693,"identity":"420cb457-3ec6-411e-b914-3a4157a8735c","added_by":"auto","created_at":"2025-01-13 03:41:28","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":716831,"visible":true,"origin":"","legend":"\u003cp\u003eCalculation of optical forces and capture of microsphere with a diameter of 5 μm. (a) The radial force on microsphere. (b) The axial force on microsphere. (c) Screenshot of a silica microsphere (red dotted circle) trapped by the dual-fiber optical tweezer, with the inset displaying the SEM image of the etched fiber's end face. (d) Relationship between the equilibrium position of the microsphere and the input power of the etched fiber (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e).\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5758813/v1/f5abd0f0af1afdfd957926ec.png"},{"id":73618790,"identity":"8a67dcc9-2c6a-4410-83e0-d6f287985e52","added_by":"auto","created_at":"2025-01-13 03:49:28","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1101877,"visible":true,"origin":"","legend":"\u003cp\u003eThe filtering effect of the etched fiber on the trapping field. (a), (b) Coupling efficiency of the SMF-Etched fiber (EF) and the SMF-SMF optical tweezers. (c), (d) The voltage amplitudes of the signal received by the PD in the SMF-SMF and the SMF- EF optical tweezers.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-5758813/v1/2dfd676a3096c3089d4a7e29.png"},{"id":73618695,"identity":"5f43c8fb-6392-4aff-a3f3-9d1d783e997e","added_by":"auto","created_at":"2025-01-13 03:41:28","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1186896,"visible":true,"origin":"","legend":"\u003cp\u003ePower spectral densities a of 5 μm silica microsphere and noise. (a) The pink spectrum represents the power spectral density measured by the SLD method, and the solid black line is its Lorentz fitting curve. The gray spectrum represents the measurement noise of this method. The blue spectrum represents the power spectral density measured by the QPD method (x direction signal). (b) The blue spectrum represents the displacement spectrum in the x-direction measured by the QPD method, which is the same as the spectrum line in (a). The solid blue line is its Lorentz fitting curve. The orange spectrum represents the displacement spectrum in the x-direction measured by the QPD method.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-5758813/v1/fe2cf9a4c191c39b238ffd9f.png"},{"id":79120683,"identity":"05e3c5fd-f445-44a5-94bc-05276b68fd52","added_by":"auto","created_at":"2025-03-24 16:10:59","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8842731,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5758813/v1/3bceb94c-0717-4754-a2ec-6ff1a424dd33.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Dual-fiber optical tweezers integrating high-sensitivity structured-light displacement measurement system on fiber end-face","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn 1970, Arthur Ashkin demonstrated the use of optical forces to manipulate the motion of microparticles \u003csup\u003e[1]\u003c/sup\u003e. This pioneering work evolved into optical tweezers technology, driving significant advancements in biology \u003csup\u003e[2, 3]\u003c/sup\u003e, precision measurement \u003csup\u003e[4\u0026ndash;6]\u003c/sup\u003e, quantum sensing \u003csup\u003e[7, 8]\u003c/sup\u003e, and various other fields \u003csup\u003e[9\u0026ndash;13]\u003c/sup\u003e. Although optical tweezers in vacuum offer unmatched precision in object manipulation and ultra-high sensitivity in detection, they present challenges such as complex optical path structures and the large volume of system. In 1993, Constable et al. proposed a promising scheme involving dual-fiber optical tweezers characterized by a compact structure, simple fabrication process and flexible operation \u003csup\u003e[14]\u003c/sup\u003e. This setup is not only compatible with chip devices \u003csup\u003e[15]\u003c/sup\u003e, but also exhibits versatile in functions, including optical stretchers \u003csup\u003e[16, 17]\u003c/sup\u003e, optical rotators \u003csup\u003e[18, 19]\u003c/sup\u003e, and optical binding \u003csup\u003e[20]\u003c/sup\u003e. With the advancement of integrated photonics, the innovative concept of lab-on-fiber has emerged, integrating multiple optical paths or devices within a single fiber \u003csup\u003e[21, 22]\u003c/sup\u003e. As lab-on-fiber technology has advanced, an array of functionalities, including sensing \u003csup\u003e[23, 24]\u003c/sup\u003e, trapping particles \u003csup\u003e[25, 26]\u003c/sup\u003e, and manipulating light \u003csup\u003e[27, 28]\u003c/sup\u003e, have been meticulously incorporated into the fiber platform, demonstrating its versatility and potential.\u003c/p\u003e \u003cp\u003eThe majority of optical tweezers applications fundamentally rely on displacement measurements of the trapped object. The video-based position detection method offers the advantage of direct observation of the particle and is suitable for measuring low-frequency displacements \u003csup\u003e[29, 30]\u003c/sup\u003e. High-precision displacement measurements primarily utilize the back focal plane method, which employs scattered light to extract the particle displacement information \u003csup\u003e[7, 31\u0026ndash;33]\u003c/sup\u003e. Among these methods, the quadrant photodiode (QPD) method and differential displacement measurement using D-shaped mirrors are the most commonly employed techniques \u003csup\u003e[34, 35]\u003c/sup\u003e. Nevertheless, it\u0026rsquo;s difficult to miniaturizing such measurement methods to match the fiber optical tweezers. The challenge mainly arises from the necessity to preserve the mode shape of the scattered light. Several studies have attempted to integrate displacement measurement into fiber optical tweezers \u003csup\u003e[36\u0026ndash;38]\u003c/sup\u003e. However, no highly sensitive displacement measurement technologies tailored for that. It has constrained their advancement for integrated quantum sensing. In 2021, Lars. S. Madsen et al. presented an ingenious structured-light detection (SLD) method \u003csup\u003e[39]\u003c/sup\u003e. This method filters the trapping mode by flipping its transmission phase, so that it can directly measure displacement of particle using light intensity. It provides an alternative for the miniaturization of displacement measurement in fiber optical tweezers.\u003c/p\u003e \u003cp\u003eIn this paper, we simultaneously capture a microsphere and measure its displacement using an integrated structured-light displacement measurement method tailored for the dual-fiber optical tweezers. A critical component, the split-waveplate in the SLD method is integrated into a fiber end-face through coating and etching. The scattered light is collected by the etched fiber (EF) in the fiber optical tweezers, and the trapping field in the scattered light is partially filtered out. Consequently, this setup successfully achieves radial displacement detection with a superior signal-to-noise ratio. This work advances high-precision sensing technology and provides new insights into integrating optical tweezers. It enables the fabrication of MEMS devices capable of on-chip acceleration sensing \u003csup\u003e[40, 41]\u003c/sup\u003e, non-Newtonian force detection \u003csup\u003e[42]\u003c/sup\u003e, and viscosity coefficient measurement \u003csup\u003e[43]\u003c/sup\u003e, thereby promoting the development of lab-on-fiber technology.\u003c/p\u003e"},{"header":"2. Pinciple","content":"\u003cp\u003eIn the field of optical tweezers, most trapping systems use fundamental Gaussian beams (TEM\u003csub\u003e00\u003c/sub\u003e) as the trapping light, except for specific applications that require special light fields. The trapping light is partially disturbed by the microsphere and converted into the information-containing field (TEM\u003csub\u003e01\u003c/sub\u003e), while the undisturbed trapping light remains as the fundamental mode TEM\u003csub\u003e00\u003c/sub\u003e. TEM\u003csub\u003e00\u003c/sub\u003e mode is symmetric about the trap center and occupies the majority of the probe beam, serving as background noise in displacement detection. The TEM\u003csub\u003e01\u003c/sub\u003e mode is antisymmetric and contains the particle\u0026apos;s displacement information, constituting a small portion of the probe beam\u003csup\u003e[33]\u003c/sup\u003e. In the SLD method, a \u0026pi; phase difference introduced by the split-waveplate is crucial for filtering the trapping field before coupling the probe beam into the single mode fiber (SMF) \u003csup\u003e[39]\u003c/sup\u003e. This phase difference reverses the symmetry of two modes in the probe beam, converting the TEM\u003csub\u003e00\u003c/sub\u003e mode into an anti-symmetric flipped TEM\u003csub\u003e00\u003c/sub\u003e mode and the TEM\u003csub\u003e01\u003c/sub\u003e mode into a flipped TEM\u003csub\u003e01\u003c/sub\u003e mode. Due to the symmetry of guided modes in SMF, the antisymmetric flipped TEM\u003csub\u003e00\u003c/sub\u003e mode cannot propagate through the fiber. However, despite the structural differences between the symmetric flipped TEM\u003csub\u003e01\u003c/sub\u003e mode and the LP\u003csub\u003e01\u003c/sub\u003e mode, there exists a limited overlap in amplitude and phase within certain regions, enabling the flipped TEM\u003csub\u003e01\u003c/sub\u003e mode to couple into the SMF \u003csup\u003e[44, 45]\u003c/sup\u003e. In a word, the split-waveplate combined with single mode fiber (SMF) acts as a spatial filter to diminish the trapping field and enhance the transmission of the information-containing field, thereby enabling high signal-to-noise ratio displacement detection.\u003c/p\u003e\n\u003cp\u003eFigure. 1(a) depicts the schematic of the integration of structured-light displacement measurement method tailored for dual-fiber optical tweezers. The etched fiber and another SMF form a dual-fiber optical tweezer to trap particles. The etched fiber is fabricated in two steps. First, a standard SMF is coated with a Ta\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e layer (depicted as the pink layer in the figure) \u003csup\u003e[46]\u003c/sup\u003e. Then, the coating layer is etched to a certain depth using a Focused Ion Beam (FIB). As a result, a phase difference of \u0026pi; is generated between the etched and unetched regions on the end face of the fiber due to the optical path difference. As the trapping light (TEM\u003csub\u003e00\u003c/sub\u003e mode) transmits through the trapped particle, the perturbative caused by the particle transforms a portion of the light into the TEM\u003csub\u003e01\u003c/sub\u003e mode (the blue curve in the orange inset) \u003csup\u003e[39]\u003c/sup\u003e. When the light passes through the coating layer with an etching structure, the symmetries of the two modes are reversed. The TEM\u003csub\u003e00\u003c/sub\u003e mode is converted to the antisymmetric flipped TEM\u003csub\u003e00\u003c/sub\u003e mode, and the TEM\u003csub\u003e01\u003c/sub\u003e mode is altered to symmetric flipped TEM\u003csub\u003e01\u003c/sub\u003e mode. Consequently, the antisymmetric trapping field cannot propagate in the single-mode fiber portion of the etched fiber. In this configuration, the probe beam received by the etched fiber enters the circulator through port 2. Then, it transmits via port 3 to a photodetector (PD). As a result, the PD predominantly detect the flipped TEM\u003csub\u003e01\u003c/sub\u003e mode, thereby extracting the displacement information of the microsphere. This configuration significantly enhances the signal-to-noise ratio for displacement measurements by utilizing mode transformation to maximize the transmission of the displacement signal.\u003c/p\u003e\n\u003cp\u003eFigure.1(b) is the schematic of the etched fiber end-face with etching structure, where \u003cem\u003er\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e is the radius of the fiber core and \u003cem\u003er\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e indicates the radius of the etched area (crimson semi-circle). In the simulation, the monitor is positioned between the coating layer and the optical fiber. As shown in Fig. 1(c), the phase map clearly indicates a \u0026pi; phase difference between the etched and unetched regions. This phase difference is realized by the optical path difference during the transmission of light in the film layer. Figure. 1(d) demonstrates Scanning Electron Microscopy images (SEM) of the end face of the etched fiber. An etching semicircle within the white dotted box has a depth equal to the film thickness.\u003c/p\u003e\n\u003cp\u003eWe utilized the finite difference time domain (FDTD) method to build the simulation model. Both simulations and experiments were conducted in a water environment. The fiber (Corning, HI 1060) with a core radius of \u003cem\u003er\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e 2.65 \u0026micro;m and a mode-field diameter of 5.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3 \u0026micro;m @980 nm. To match the two-dimensional profile size of the beam emitted from the SMF to the dimensions of the etched semicircle in the fiber coating layer. It enables to introduce a phase difference of \u0026pi; between the etched and unetched regions. Consequently, the radius \u003cem\u003er\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e of the etched semicircle is precisely selected to be 6 \u0026micro;m.\u003c/p\u003e\n\u003cp\u003eThe transmission phase formula is as follows:\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cimg src=\"data:image/png;base64,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\" width=\"417\" height=\"48\"\u003e\u003c/p\u003e\n\u003cp\u003eis the free space wave vector, \u003cem\u003en\u003c/em\u003e is the refractive index difference of the uniform medium, and \u003cem\u003ed\u003c/em\u003e is its thickness. The thickness of the Ta\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e layer in fiber end face is designed as 600 nm. We deposited Ta\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e films on the fiber end-face using ion sputtering technology, achieving a thickness of 606.0 nm, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(a). The ideal refractive index of Ta₂O₅ at a wavelength of 980 nm is 2.157, while the experimentally measured refractive index, determined using an ellipsometer, is slightly lower at \u003cem\u003en\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.155. The depth of the etched semi-circle is the same as the thickness of the film, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(b). The refractive index of water is \u003cem\u003en\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.33, thus the phase difference between the etched and non-etched parts is 1.01\u0026pi;. In this way, approximately \u0026pi; phase is achieved. It satisfies the phase requirements of the structured-light displacement measurement method for flipping mode. Figure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(c) presents the diameter of the etched semicircle, while Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e(d) displays the mark on the lateral aspect of the etched fiber. This mark is designed to locate the x direction during the subsequent assembly of dual-fiber optical tweezers. It is worth noting that before carry out the experiment, the gold film sprayed by the FIB processing needs to be removed using aqua regia to avoid affecting the transmission phase.\u003c/p\u003e"},{"header":"3. Result and analysis","content":"\u003ch2\u003e3.1 Optical trap\u003c/h2\u003e\n\u003cp\u003eWe calculate the axial forces on the microspheres at different distances (from 120 \u0026mu;m to 40 \u0026mu;m) between two optical fibers. Results indicate that at an output power of 100 mW for each fiber, a point where the axial force is 0 pN with a negative slope appears when the distance is reduced to approximately 40 \u0026mu;m. It means that the microsphere is subjected to equal from the dual beams and in a stable trapped state. In linear optics, all forces scale linearly with the light intensity. If a larger fiber spacing is chosen, it is evident that the output optical power of the etched fiber needs to be increased. However, there is a concern that under high-power output in a liquid environment, the liquid could be heated and may cause bubble formation. Consequently, we chose a fiber spacing of 40 \u0026mu;m between the two fibers to set up the dual-fiber optical tweezers.\u003c/p\u003e\n\u003cp\u003eFigure 3(a) shows a schematic diagram of the optical fiber output mode field testing system,\u0026nbsp;and the cuvette in the illustration features two coaxial holes. The etched fiber extends through the hole into the water-filled cuvette during testing. When the focus of the objective lens coincides with the end face of etched fiber, the measured beam mode field diameter is minimized, marked as z = 0 \u0026mu;m. By moving translation stage 1 along z axis, the beam intensity distribution at different transmission distances can be measured.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFigure 3(b) presents the simulated intensity distribution of the beam emitted from the etched fiber, and its exhibit a bimodal distribution with two distinct peaks of similar intensity. In the FDTD simulations, the amplitude of the light source was set to 1, and the polarization was aligned along the x-axis. The electric field strength distribution was normalized. Consequently, the intensity plots of simulation are on the same scale. In the actual process of etched fiber, it is difficult to ensure that the etching demarcation line is entirely centered on the fiber core. Consequently, we have introduced a 300 nm offset of the diameter of the semicircle from the central position of the fiber core in the simulations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn the experiments, we coupled white light into the other end of the etched fiber. Under a microscope, we excluded samples with excessive offsets of the etched boundary from the fiber core center. Using the testing setup in Fig. 3(a), the intensity distribution of the beam emitted from the etched fiber at different transmission distances was measured, as shown in Fig. 3(c). A dark fringe appears at the center of the beam intensity distribution, as indicated by the direction of the red arrow, which is due to destructive interference caused by the \u0026pi; phase difference between the etched and unetched regions. These results closely align with the simulation intensity distribution, demonstrating a consistent trend. It is expected that the microsphere near the optical axis will interact less strongly with the light emitted by the etched fiber, given the split nature of its spot. To effectively trap a particle near the central position between the two fibers, it is necessary to increase the output power of the etched fiber.\u003c/p\u003e\n\u003cp\u003eFigure 4 shows the dual-fiber optical tweezers system with the integrated structured-light displacement method and the QPD method. A LED light and a CCD camera form an illumination imaging optical path for observing trapped particle. In order to easily adjust the input power \u003cem\u003eP\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e of the etched fiber, the etched fiber and the SMF use different lasers for input. The light (orange) input by laser 1 enters the SMF through the circulator 1, passes through the particle and couples into the etched fiber, and is finally received by the PD. In order to facilitate light path adjustment, the laser wavelength used in the QPD method is 532 nm (green). The detection beam of the QPD method is collected by objective 2 and finally enters the QPD. The PD and QPD are connected to the DAQ card to store data on a computer. The sampling frequencies of the SLD method and QPD method are 1000 k/s and 200 k/s, respectively.\u003c/p\u003e\n\u003cp\u003eBased on the calculations from the previous section, we set the power output for the SMF (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e) to 100 mW and for the etched fiber (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e) to 200 mW. The simulation results for the radial force on a silica microsphere with a diameter of 5 \u0026mu;m is presented in Fig. 5(a), two points with zero net force and negative slope (blue arrow) indicates the existence of two stable trapping points in the radial direction. The two equilibrium points are similarly distant from the central axis with similar slopes, suggesting that the axial optical force and displacement response of the particle are essentially the same. The corresponding radial force curve is depicted in Fig. 5(b). An axial equilibrium point (red arrow) is observed near the central region between two fibers. These simulation results confirm that our dual-fiber tweezers can stably capture particles. We performed experiments to successfully trap a silica microsphere with diameter of 5 \u0026mu;m, and its screenshot is provided in Fig. 5(c). In liquid environments, measuring the optical power output from fibers poses significant challenges. However, due to the inherently low loss of single-mode fibers, the discrepancy between input and output power is minimal. Consequently, using the input power for experiments can ensure both accuracy and repeatability. Figure 5(d) illustrates the relationship between the input power of the etched fiber and the equilibrium position of the microsphere. It is observed that as \u003cem\u003eP\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e increases, the microsphere gradually moves from a position which close to the etched fiber towards the center. The experimental data align with the simulated trends, thereby validating the accuracy of the simulation.\u003c/p\u003e\n\u003ch2\u003e3.2 Displacement measurement\u003c/h2\u003e\n\u003cp\u003eIn this study, we simulated the coupling efficiency of the dual-fiber optical tweezer with a microsphere inside. Light from a SMF passes through the microsphere and couples into the other fiber. The coupling efficiency spectra of the SMF-SMF and SMF-EF configuration are depicted in Fig. 6(a) and (b), respectively. In Fig. 6(a), the coupling efficiency follows a symmetrical parabolic distribution with the displacement of the trapped microsphere. The largest coupling efficiency is approximately 24% when the microsphere locates on the optical axis (\u003cem\u003ex\u003c/em\u003e=0). In comparison, the coupling efficiency of the SMF-EF configuration is reduced to about 12% when \u003cem\u003ex\u003c/em\u003e=0, representing a half decrease [see Fig. 6(b)]. More importantly, the coupling efficiency is proportional to the displacement of the microsphere near \u003cem\u003ex\u003c/em\u003e=0, due to an offset of the etched semicircle. This provides a linear response region for displacement measurement and orientation determination of moving microspheres.\u003c/p\u003e\n\u003cp\u003eFor the construction of dual-fiber optical tweezers, precise alignment of the two fibers was achieved by engraving V-grooves on an acrylic plate \u003csup\u003e[47]\u003c/sup\u003e. Initially, we constructed an optical tweezers system with a separation of 40 \u0026mu;m using two single-mode fibers [inset of Fig. 6(c)]. To mitigate thermal effects and ensure the stability of the trapped microsphere, the input power of the etched fiber was reduced. This adjustment also enabled long-term experimentation. Consequently, the input powers \u003cem\u003eP\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e and \u003cem\u003eP\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003eof the two fibers were set to 100 mW and 200 mW, respectively. Subsequently, a silica microsphere with a diameter of 5 \u0026mu;m was successfully trapped. The data were collected by a data-acquisition card controlled by a LabVIEW program. The corresponding voltage signal is presented in Fig. 6(c), showing an average signal amplitude of 5.25 V. Under identical experimental conditions, we established an optical tweezers using a SMF and an etched fiber (inset of Fig. 6d). The input power from the SMF \u003cem\u003eP\u003csub\u003e1\u003c/sub\u003e\u003c/em\u003e and from the etched fiber \u003cem\u003eP\u003csub\u003e2\u003c/sub\u003e\u003c/em\u003e were maintained at 100 mW and 200 mW respectively. The photodetector (PD) connected to the etched fiber recorded an average voltage of 2.87 V. Compared to the SMF-SMF optical tweezers, the coupling power is reduced by 45.33% with the same trapped optical power. The experimental results correspond well with the simulation results. These results suggest that the trapping field was significantly filtered, which is conducive to the extraction of the information-containing field.\u003c/p\u003e\n\u003cp\u003eFigure 7(a) presents the power spectrum density of experimentally recorded displacement of the trapped particle (the pink dots). The fitting curve (black solid line) was derived using the Lorentz fitting method \u003csup\u003e[48]\u003c/sup\u003e. The corner frequency of the displacement spectrum is \u003cem\u003ef\u003csub\u003ec\u003c/sub\u003e\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e = 3.21 Hz, and the trapping stiffness \u003cem\u003ek\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e in the \u003cem\u003ex\u003c/em\u003e direction was calculated to be 1.05 pN/\u0026mu;m. For comparison, another displacement measurement optical path was established using the QPD method. The displacement spectrum corresponding to the x direction signal measured by the QPD method is shown in Fig. 7(a) and (b). The blue solid line in Fig7. (b) is its Lorentz fitting curve, which has a corner frequency \u003cem\u003ef\u003csub\u003ec\u003c/sub\u003e\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e = 3.34 Hz, indicating a trapping stiffness \u003cem\u003ek\u003csub\u003ex\u003c/sub\u003e\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e of 1.09 pN/um. The spectra of the QPD and SLD methods overlap almost entirely in the low-frequency range up to 10\u003csup\u003e4\u003c/sup\u003e Hz. The displacement spectrum of the y direction signal measured by the QPD method (in orange) is plotted in Fig 7. (b). It can be observed that there is a significant difference compared to the displacement spectrum of the x direction in the low-frequency region. These results indicate that the SLD method can accurately measure the \u003cem\u003ex\u003c/em\u003e direction displacement of microsphere. Moreover, the gray curve in Fig. 7(a) represents the signal PSD at the same optical power without the microsphere. This PSD indicates that the displacement detection sensitivity of the SLD method reaches 0.13 pm/Hz\u003csup\u003e1/2\u003c/sup\u003e, with a frequency range of 1\u0026ndash;500 kHz. It is approximately half an order of magnitude higher than the QPD method in this experiment. Although using a higher sampling rate in the QPD method might offer comparable detection sensitivity, the advantage of the SLD method is that it can filter out the trapping field without the attenuating information-containing field. Compared with other displacement measurement methods \u003csup\u003e[49, 50]\u003c/sup\u003e, our approach achieves comparable sensitivity while also realizing significant miniaturization. The aforementioned advantages enable this method to provide a higher signal-to-noise ratio and can be used in conjunction with commonly available commercial detectors in any strong optical trap.\u003c/p\u003e"},{"header":"4. Summary and outlook","content":"\u003cp\u003eWe have demonstrated the integration of a structured-light displacement measurement method for dual-fiber optical tweezers. The method enables to simultaneously trap a particle and measure its displacement without additional optics. A split-waveplate was integrated into the end-face of fiber through coating and etching. Unlike standard SMF, simulation and experiment reveal that the beam profile of the etched fiber divided into two parts. Based on optical force calculations, we selected a 40 \u0026micro;m fibers spacing to construct a dual-fiber optical tweezer, and successfully trapped a microsphere in experiments. In addition, we confirmed the effectiveness of the proposed method in the enhancing information-containing field. This method achieves a displacement measurement sensitivity of 0.1 pm/Hz\u003csup\u003e1/2\u003c/sup\u003e level, surpassing the QPD method under comparable experimental conditions. With this research integrating structured light displacement detection into the fiber end face, some limitations still remain, such as the lack of multi-directional displacement detection capabilities.\u003c/p\u003e \u003cp\u003eWe propose a conceptual design for multi-directional displacement detection using a dual-fiber optical tweezer, aiming to overcome the limitations of single-direction detection in conventional systems. This design utilizes two etched optical fibers with their etching boundaries oriented orthogonally to each other\u0026mdash;one aligned perpendicular to the x-direction and the other perpendicular to the y-direction. By separately detecting the scattered light signals through these two etched fibers, displacement measurements along the x and y directions can be independently achieved. This concept establishes a framework for multi-directional displacement detection within dual-fiber optical tweezers, offering potential applications in microfluidics and precision optical sensing. However, practical implementation requires not only introducing an appropriate phase difference at the fiber end face but also optimizing the design structure to enhance the quality of the outgoing beam.\u003c/p\u003e \u003cp\u003eInspired by the polishing processes of the side of a single-mode fiber \u003csup\u003e[51\u0026ndash;53]\u003c/sup\u003e, it also integrates this detection scheme into a single fiber. The fiber can be etched beyond the core region, and the cross-section at one end can be modified to introduce a phase difference of π. This approach enables simultaneous particle trapping and displacement measurement, significantly reducing system volume while improving integration and functionality.\u003c/p\u003e \u003cp\u003eFinally, we propose the potential for achieving multi-directional displacement measurements through the use of two etched optical fibers, or by integrating structured-light displacement detection within a single fiber, highlighting the feasibility of these approaches for advancing lab-on-fiber systems. Although there are still limitations regarding system volume and the implementation of multi-directional displacement detection, this study provides new perspectives for the development of lab-on-fiber technology and lays the foundation for future research in optical tweezers technology.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis work is supported by Science Fund for Distinguished Young Scholars of Hunan Province (2024JJ2055), and the Key Science and Technology Breakthrough Program of Hunan Province (2023ZJ1010).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eG.L. was involved in the research design, data collection, experimental work, theoretical analysis, software and computational modeling, and visualization. W.X contributed to the research design, data analysis, theoretical analysis, review and editing, interpretation of results, and validation of results. H.F was responsible for software and computational modeling. Z.F contributed to the writing of the manuscript. T.F was involved in review and editing, interpretation of results, and validation of results. Z.L also contributed to software and computational modeling. Xiang.Han provided supervision and resources for the project. Xin.He was involved in experimental work and validation of results. X.C provided supervision and resources. J.Y contributed to funding acquisition, supervision, theoretical analysis, and project guidance. G.X was responsible for funding acquisition, supervision, theoretical analysis, and review and editing.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors would like to acknowledge Yinan Li and Li Sun at Kaiple Company for SEM performance.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data used and analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eA. Ashkin, \u0026ldquo;Acceleration and trapping of particles by radiation pressure,\u0026rdquo; Physical review letters, 1970, 24(4):156\u0026ndash;159.\u003c/li\u003e\n \u003cli\u003eA. Ashkin, K. Sch\u0026uuml;tze, and J. M. Dziedzic, and U. Euteneur, \u0026ldquo;Force generation of organelle transport measured in vivo by an infrared laser trap,\u0026rdquo; \u003cem\u003eNature\u003c/em\u003e, 1990, 348(6299): 346\u0026ndash;348.\u003c/li\u003e\n \u003cli\u003eS. M. Block, L. S. B. Goldstein, and B. J. Schnapp, \u0026ldquo;Bead Movement by Single Kinesin Molecules Studied with Optical Tweezers\u0026rdquo;, \u003cem\u003eNature\u003c/em\u003e,1990, 348(6299): 348\u0026ndash;352.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eS. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, \u0026ldquo;Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,\u0026rdquo; \u003cem\u003eScience\u003c/em\u003e, 2014, 343(6178):1493-1496.\u003c/li\u003e\n \u003cli\u003eY. Zheng, L. Zhou, and Y. Dong, C. Qiu, X. Chen, G. Guo, and F. Sun, \u0026ldquo;Robust optical-levitation-based metrology of nanoparticle\u0026rsquo;s position and mass,\u0026rdquo; \u003cem\u003ePhysical review letters\u003c/em\u003e, 2020, 124(22): 223603.\u003c/li\u003e\n \u003cli\u003eS. Zhu, Z. Fu, and X. Gao, C. Li, Z. Chen, Y. Wang and H. Hu, \u0026ldquo;Nanoscale electric field sensing using a levitated nano-resonator with net charge,\u0026rdquo;\u003cem\u003e\u0026nbsp;Photonics Research,\u0026nbsp;\u003c/em\u003e2023, 11(2): 279-289.\u003c/li\u003e\n \u003cli\u003eT. Li, S. Kheifets, and M. G. Raizen, \u0026ldquo;Millikelvin cooling of an optically trapped microsphere in vacuum,\u0026rdquo; \u003cem\u003eNature\u003c/em\u003e \u003cem\u003ePhysics\u003c/em\u003e, 2011, 7(7).\u003c/li\u003e\n \u003cli\u003eT. Kuang, R. Huang, and W. Xiong, Y. Zuo, X. Han, F. Nori, C. Qiu, H. Luo, H. Jing and G. Xiao, \u0026ldquo;Nonlinear multi-frequency phonon lasers with active levitated optomechanics,\u0026rdquo; \u003cem\u003eNature\u003c/em\u003e \u003cem\u003ePhysics\u003c/em\u003e, 2023, 19(3): 414\u0026ndash;419.\u003c/li\u003e\n \u003cli\u003eM. Peng, G. Xiao, X. Chen, T. Du, T. Kuang, X. Han, W. Xiong, G. Zhu, J. Yang, Z. Tan, K. Yang, and H. Luo, \u0026ldquo;Optical trapping-enhanced probes designed by a deep learning approach,\u0026rdquo; \u003cem\u003ePhotonics Research\u003c/em\u003e, 2024, 12(5): 959-968.\u003c/li\u003e\n \u003cli\u003eG. Xiao, T. Kuang, Y. He, X. Chen, W. Xiong, X. Han, Z. Tan, H. Luo, and H. Jing, \u0026ldquo;Giant enhancement of higher-order harmonics of an optical-tweezer phonon laser,\u0026rdquo; \u003cem\u003eeLight\u003c/em\u003e, 2024,4(17).\u003c/li\u003e\n \u003cli\u003eY. Liang, S. Yan, Z. Wang, B. Yao, and M. Lei, \u0026ldquo;Off-axis optical levitation and transverse spinning of metallic microparticles,\u0026rdquo; \u003cem\u003ePhotonics Research\u003c/em\u003e, 2021, 9(11): 2144-2151.\u003c/li\u003e\n \u003cli\u003eP. H. Jones, O. M. Marag\u0026ograve;, and G. Volpe, Optical Tweezers: Principles and Applications (Cambridge University, 2015).\u003c/li\u003e\n \u003cli\u003eX. Han, X. Chen, W. Xiong, T. Kuang, Z. Chen, M. Peng, G. Xiao, K. Yang, and H. Luo, \u0026ldquo;Vacuum optical tweezers system and its research progress in precision measurement,\u0026rdquo; \u003cem\u003eChinese Journal of Lasers\u003c/em\u003e, 2021, 48(4): 0401011.\u003c/li\u003e\n \u003cli\u003eA. Constable, J. Kim, J. Mervis, F. Zarinetchi, and M.Prentiss, \u0026ldquo;Demonstration of a fiber-optical light-force trap,\u0026rdquo; \u003cem\u003eOptics Letters\u003c/em\u003e, 1993, 18:1867\u0026ndash;1869.\u003c/li\u003e\n \u003cli\u003eC. Jensen-McMullin, H. P. Lee, and E. P. Lyons, \u0026ldquo;Demonstration of trapping, motion control, sensing and fluorescence detection of polystyrene beads in a multi-fiber optical trap,\u0026rdquo; \u003cem\u003eOptics Express\u003c/em\u003e, 2005,13(7): 2634\u0026ndash;2642.\u003c/li\u003e\n \u003cli\u003eJ. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. K\u0026auml;s, \u0026ldquo;The optical stretcher: a novel laser tool to micromanipulate cells,\u0026rdquo; \u003cem\u003eBiophysical journal\u003c/em\u003e, 2001, 81: 767\u0026ndash;784.\u003c/li\u003e\n \u003cli\u003eN. Bellini, F. Bragheri, and I. Cristiani, J. Guck, R. Osellame, G. Whyte, \u0026ldquo;Validation and perspectives of a femtosecond laser fabricated monolithic optical stretcher,\u0026rdquo; \u003cem\u003eBiomedical Optics Express\u003c/em\u003e, 2012, 3(10): 2658\u0026ndash;2668.\u003c/li\u003e\n \u003cli\u003eX. Chen, G. Xiao, and K. Yang, W. Xiong, H. Luo, \u0026ldquo;Characteristics of the orbital rotation in dual-beam fiberoptic trap with transverse offset,\u0026rdquo; \u003cem\u003eOptics Express\u003c/em\u003e, 2016, 24(15):16952\u0026ndash;16960.\u003c/li\u003e\n \u003cli\u003eG. Xiao, K. Yang, and H. Luo, X. Chen, and W. Xiong, \u0026ldquo;Orbital rotation of trapped particle in a transversely misaligned dual-fiber optical trap,\u0026rdquo; \u003cem\u003eIEEE Photonics Journal\u003c/em\u003e, 2016, 8(1): 1\u0026ndash;8.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eN. K. Metzger, E. M. Wright and W. Sibbett, and K. Dholakia, \u0026ldquo;Visualization of optical binding of microparticles using a femtosecond fiber optical trap,\u0026rdquo; \u003cem\u003eOptics Express\u003c/em\u003e, 2006, 14(8): 3677\u0026ndash;3687.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eA. Cusano, M. Consales, and A. Crescitelli, eds. \u0026ldquo;Lab-on-fiber technology,\u0026rdquo; Switzerland: Springer International Publishing (2015).\u003c/li\u003e\n \u003cli\u003eY. Meng, Y. Chen, L. Lu, Y. Ding, A. Cusano, J. A. Fan, Q. Hu, K. Wang, Z. Xie, Z. Liu, Y. Yang, Q. Liu, M. Gong, Q. Xiao, S. Sun, M. Zhang, X. Yuan, X. Ni. \u0026ldquo;Optical meta-waveguides for integrated photonics and beyond,\u0026rdquo; \u003cem\u003eLight: Science \u0026amp; Applications\u003c/em\u003e, 2021, 10(1): 1-44.\u003c/li\u003e\n \u003cli\u003eA. Ricciardi, A. Crescitelli, P. Vaiano, G Quero, M. Consales, M. Pisco, E. Esposito, and A. Cusano, \u0026ldquo;Lab-on-fiber technology: a new vision for chemical and biological sensing,\u0026rdquo;, \u003cem\u003eAnalyst\u003c/em\u003e, 2015, 140(24): 8068-8079.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eM. Pisco, F. A. Bruno, D. Galluzzo, L. Nardone, G. Gruca, N. Rijinveld, F. Bianco, A. Cutolo, and A. Cusano, \u0026ldquo;Opto-mechanical lab-on-fibre seismic sensors detected the Norcia earthquake,\u0026rdquo; \u003cem\u003eScientific Reports\u003c/em\u003e, 2018, 8(1) (2018) 6680.\u003c/li\u003e\n \u003cli\u003eJ. M. Ehtaiba, and R. Gordon, \u0026ldquo;Template-stripped nanoaperture tweezer integrated with optical fiber,\u0026rdquo; \u003cem\u003eOptics Express\u003c/em\u003e, 2018, 26(8): 9607-9613.\u003c/li\u003e\n \u003cli\u003eY. Li, H. Xin, and Y. Zhang, \u0026ldquo;Optical Fiber Technologies for Nanomanipulation and Biodetection: A Review,\u0026rdquo; \u003cem\u003eJournal of Lightwave Technology\u003c/em\u003e, 2020, 39(1): 251-262.\u003c/li\u003e\n \u003cli\u003eN. Bozinovic, Y. Yue and Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, \u0026ldquo;Terabit-scale orbital angular momentum mode division multiplexing in fibers,\u0026rdquo; \u003cem\u003eScience\u003c/em\u003e, 2013, 340(6140): 1545-1548.\u003c/li\u003e\n \u003cli\u003eJ. Du, S. Chen, and S. Li, L. Zhu, Y. Zhao, and J. Wang, \u0026ldquo;Design and fabrication of metasurface on conventional optical fiber facet for linearly polarized mode (LP11) generation at visible light wavelength,\u0026rdquo; CLEO: Science and Innovations, Optica Publishing Group (2016).\u003c/li\u003e\n \u003cli\u003eJ. C. Crocker, and D. G. Grier, \u0026ldquo;Methods of digital video microscopy for colloidal studies,\u0026rdquo; Journal of Colloid and Interface Science, 1996, 179(1): 298\u0026ndash;310.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eG. M. Gibson, J. Leach, and S. Keen, A. J. Wright, M. J. Padgett, \u0026ldquo;Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy,\u0026rdquo; \u003cem\u003eOptics Express\u003c/em\u003e, 1996, 16(19): 14561\u0026ndash;14570.\u003c/li\u003e\n \u003cli\u003eF. Gittes and C. F. Schmidt, \u0026ldquo;Interference model for back-focal-plane displacement detection in optical tweezers,\u0026rdquo; \u003cem\u003eOptics Letters\u003c/em\u003e, 1998, 23(1): 7\u0026ndash;9.\u003c/li\u003e\n \u003cli\u003eW. Xiong, G. Xiao, X. Han, J. Zhou, X. Chen, and H. Luo, \u0026ldquo;Back-focal-plane displacement detection using side-scattered light in dual-beam fiber-optic traps,\u0026rdquo; \u003cem\u003eOptics Express\u003c/em\u003e, 2017, 25(8): 9449\u0026ndash;9457.\u003c/li\u003e\n \u003cli\u003eM. A. Taylor, J. Knittel, and M. T. L. Hsu, W. P. Bowen, \u0026ldquo;Sagnac interferometer-enhanced particle tracking in optical tweezers,\u0026rdquo; \u003cem\u003eJournal of Optics\u003c/em\u003e, 2011, 13(4): 044014.\u003c/li\u003e\n \u003cli\u003eZ. Chen, T. Kuang, X. Han, G. Li, W. Xiong, G. Xiao, H. Luo, \u0026ldquo;Differential displacement measurement of the levitated particle using D-shaped mirrors in the optical tweezers,\u0026rdquo; \u003cem\u003eOptics Express\u003c/em\u003e, 2022, 30(17): 30791\u0026ndash;30798.\u003c/li\u003e\n \u003cli\u003eW. Li, H. Zhang, M. Hu, Q. Zhu, H. Su, N. Li, \u0026amp; H. Hu, \u0026ldquo;3D calibration of microsphere position in optical tweezers using the back-focal-plane interferometry method,\u0026rdquo; \u003cem\u003eOptics Express\u003c/em\u003e, 2021, 29(20): 32271\u0026ndash;32284.\u003c/li\u003e\n \u003cli\u003eW. Xiong, G. Xiao, X. Han, X. Chen, K. Yang, and H. Luo, \u0026ldquo;All-fiber interferometer for displacement and velocity measurement of a levitated particle in fiber-optic traps,\u0026rdquo; \u003cem\u003eApplied Optics\u003c/em\u003e, 2019, 58(8): 2081\u0026ndash;2084.\u003c/li\u003e\n \u003cli\u003eA. Chen, H. Luo, Z. Chen, H. Feng, T. Kuang, H. An, X. Han, W. Xiong and G. Xiao, \u0026ldquo;Displacement detection based on four-fiber bundle in dual-beam fiber-optic traps, Ninth Symposium on Novel Photoelectronic Detection Technology and Applications,\u0026rdquo; SPIE, 2023, Vol. 12617.\u003c/li\u003e\n \u003cli\u003eQ. Xiang, N, Li, X, Chen, L, Liu and H, Hu, \u0026ldquo;Miniaturized Dual-Beam Optical Trap Based on Fiber Pigtailed Focuser,\u0026rdquo; \u003cem\u003ePhotonics\u003c/em\u003e, 2023, 10(9): 1007.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eL. S. Madsen, M. Waleed, C. A. Casacio, A. Terrasson, A. B. Stilgoe, M. A. Taylor, and W. P. Bowen, \u0026ldquo;Ultrafast viscosity measurement with ballistic optical tweezers,\u0026rdquo; \u003cem\u003eNature Photonics\u003c/em\u003e, 2021, 15(5): 386-392.\u003c/li\u003e\n \u003cli\u003eD. L. Butts, Development of a light force accelerometer. Diss. Massachusetts Institute of Technology, (2008).\u003c/li\u003e\n \u003cli\u003eK, Krish. \u0026ldquo;Toward a demonstration of a light force accelerometer. Diss. Massachusetts Institute of Technology, (2010).\u003c/li\u003e\n \u003cli\u003eG. Ranjit, M. Cunningham, and K. Casey, A. A. Geraci, \u0026ldquo;Zeptonewton force sensing with nanospheres in an optical lattice,\u0026rdquo; \u003cem\u003ePhysical Review A\u003c/em\u003e, 2016, 93(5): 053801.\u003c/li\u003e\n \u003cli\u003eA. K. Korzeniewska, and S. Drobczyński. \u0026ldquo;Local measurement of liquid viscosity in optical tweezers,\u0026rdquo; \u003cem\u003eOptics and Lasers in Engineering\u003c/em\u003e, 2023, 164: 107516.\u003c/li\u003e\n \u003cli\u003eG. Li, T. Kuang, W. Xiong, X. Han, G. Xiao, Z. Tan, and H. Luo, \u0026ldquo;Structured-light displacement detection method using split-waveplate for dual-beam optical tweezers,\u0026rdquo; \u003cem\u003eOptics Express\u003c/em\u003e, 2023, 31(21): 34459-34469.\u003c/li\u003e\n \u003cli\u003eGloge, D. \u0026ldquo;Weakly guiding fibers,\u0026rdquo; \u003cem\u003eApplied Optics\u003c/em\u003e, 1971, 10(10): 2252-2258.\u003c/li\u003e\n \u003cli\u003eBright, T. J., Watjen, J. I., Zhang, Z. M., Muratore, C., Voevodin, A. A., Koukis, D. I., ... \u0026amp; Arenas, D. J. (2013). \u0026ldquo;Infrared optical properties of amorphous and nanocrystalline Ta\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e thin films,\u0026rdquo; \u003cem\u003eJournal of Applied Physics\u003c/em\u003e, 2013, 114(8).\u003c/li\u003e\n \u003cli\u003eD. Collins, R. J. Baskin, and D. G. Howitt, \u0026ldquo;Micro instrument gradient-force optical trap,\u0026rdquo; \u003cem\u003eApplied Optics\u003c/em\u003e, 1999, 38: 6068\u0026ndash;6074.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eY. Li and K. Yao, Techniques of Optical Tweezers, Science Press, (2015).\u003c/li\u003e\n \u003cli\u003eA. D. Rider, C. P. Blakemore, and G. Gratta, \u0026ldquo;Single-beam dielectric-microsphere trapping with optical heterodyne detection,\u0026rdquo; \u003cem\u003ePhysical Review A\u003c/em\u003e, 2018, 97: 013842.\u003c/li\u003e\n \u003cli\u003eY. Jin, X. Yu, and J. Zhang, \u0026ldquo;Optically levitated nanosphere with high trapping frequency,\u0026rdquo; \u003cem\u003eScience China\u0026nbsp;\u003c/em\u003e(\u003cem\u003ePhysics,Mechanics \u0026amp; Astronomy\u003c/em\u003e),2018, 61: 114221.\u003c/li\u003e\n \u003cli\u003eQ. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, Y. T. Ding and K. P. Loh, \u0026ldquo;Broadband graphene polarizer,\u0026rdquo; \u003cem\u003eNature Photonics\u003c/em\u003e, 2011, 5(7): 411-415.\u003c/li\u003e\n \u003cli\u003eZ. P. Jiang, J. L. Dong, S. Q. Hu. Y. X. Zhang, Y. F. Chen, Y. H. Luo, W. G. Zhu, W. T. Qiu, H. H. Lu, H. Y. Guan, Y. C. Zhong, J. H Yu, J. Zhang, and Z. Chen, \u0026ldquo;High-sensitivity vector magnetic field sensor based on side-polished fiber plasmon and ferrofluid,\u0026rdquo; \u003cem\u003eOptics Letters\u003c/em\u003e, 2018, 43(19): 4743-4746.\u003c/li\u003e\n \u003cli\u003eZ. D. ZHU, L. Liu, Z. H. Liu, Y. Zhang, and Y. X. Zhang. \u0026ldquo;Surface-plasmon-resonance-based optical-fiber temperature sensor with high sensitivity and high figure of merit,\u0026rdquo; \u003cem\u003eOptics Letters\u003c/em\u003e, 2017, 42(15): 2948-2951.\u003c/li\u003e\n\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":"Dual-fiber optical tweezers, Structured-light displacement method, High Sensitivity, Miniaturization and integration","lastPublishedDoi":"10.21203/rs.3.rs-5758813/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5758813/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe dual-fiber optical tweezers have become widespread in trapping, assembling, and sensing due to their simple fabrication process and flexible operation. However, the miniaturization and integration of their displacement measurement optical paths remain challenging. Here, we propose and experimentally demonstrate an integration of structured-light displacement (SLD) measurement method tailored for dual-fiber optical tweezers. A key component split-waveplate is integrated onto the fiber end via coating and etching in the SLD method. The etched fiber and another single mode fiber form an optical tweezers, which enables to trap particle and measure its position simultaneously without additional optics. More importantly, it demonstrates a superior signal-to-noise ratio after filtering out the trapping field by the etched fiber. Our results demonstrate a displacement sensitivity reaching the 0.1 pm/Hz\u003csup\u003e1/2\u003c/sup\u003e level, which surpasses the performance of most results using the quadrant photodiode method. Ultimately, we discussed the possibilities of using two etched fibers to detect displacements in different directions, or integrating this method into a single optical fiber. This method has significant potential applications in precision sensing, contributes to the integration of optical tweezers and fosters the development of lab-on-fiber applications.\u003c/p\u003e","manuscriptTitle":"Dual-fiber optical tweezers integrating high-sensitivity structured-light displacement measurement system on fiber end-face","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-13 03:41:23","doi":"10.21203/rs.3.rs-5758813/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-01-28T06:37:01+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-01-27T22:43:14+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-01-17T09:12:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"186299200575862163791409285298017256802","date":"2025-01-09T22:20:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"171487592257143703966255350518902965944","date":"2025-01-09T10:09:49+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-01-09T10:00:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-01-09T09:57:06+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-01-09T09:37:04+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-01-09T09:33:39+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-01-03T14:04:24+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":"a18a9b8b-811d-4e35-9abb-044c7ed33c47","owner":[],"postedDate":"January 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":42662145,"name":"Physical sciences/Optics and photonics/Optical techniques/Optical manipulation and tweezers"},{"id":42662146,"name":"Physical sciences/Optics and photonics/Applied optics/Optical sensors"}],"tags":[],"updatedAt":"2025-03-24T16:07:05+00:00","versionOfRecord":{"articleIdentity":"rs-5758813","link":"https://doi.org/10.1038/s41598-025-93523-2","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-03-17 15:58:15","publishedOnDateReadable":"March 17th, 2025"},"versionCreatedAt":"2025-01-13 03:41:23","video":"","vorDoi":"10.1038/s41598-025-93523-2","vorDoiUrl":"https://doi.org/10.1038/s41598-025-93523-2","workflowStages":[]},"version":"v1","identity":"rs-5758813","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5758813","identity":"rs-5758813","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}