Manipulation of particle rotation in optical tweezers has found many applications such as viscosity sensing, fluidic pumping
Opto-Electronic Advances, Volume. 3, Issue 8, 200022-1(2020)
Robust and high‐speed rotation control in optical tweezers by using polarization synthesis based on heterodyne interference
The rotation control of particles in optical tweezers is often subject to the spin or orbit angular momentum induced optical torque, which is susceptible to the mechanical and morphological properties of individual particle. Here we report on a robust and high-speed rotation control in optical tweezers by using a novel linear polarization synthesis based on optical heterodyne interference between two circularly polarized lights with opposite handedness. The synthesized linear polarization can be rotated in a hopping-free scheme at arbitrary speed determined electronically by the heterodyne frequency between two laser fields. The experimental demonstration of a trapped vaterite particle in water shows that the precisely controlled rotation frequency of 300 Hz can be achieved. The proposed method will find promising applications in optically driven micro-gears, fluidic pumps and rotational micro-rheology.
Introduction
Manipulation of particle rotation in optical tweezers has found many applications such as viscosity sensing, fluidic pumping
In contrast to the use of circularly polarized or vortex beam, the torque induced by the misalignment between the linearly polarized laser field and optical axis of the trapped particle is insusceptible to ambient viscosity and therefore can generate synchronized particle rotation with the rotating linear polarization
By using a novel linear polarization synthesis based on optical heterodyne interference between two circularly polarized lights with opposite handedness, we report on a robust and high-speed linear polarization rotation control method. The synthesized linear polarization can be rotated unidirectionally at arbitrary speed determined electronically by the heterodyne frequency between two laser fields. High-speed rotation manipulation of single birefringent particle in optical trapping systems using the synthesized linearly polarized light was also experimentally demonstrated. The particle rotation speed was demonstrated to be synchronized to the laser heterodyne frequency and only limited by the optical torque induced by the maximum laser power.
Theory and experiments
A linearly polarized light can be expressed as the superposition of a right-handed circularly polarized light and a left-handed circularly polarized light as shown in below:
where the basis vector of left-handed circularly polarized light and right-handed circularly polarized light can be expressed by $\hat L = {1 / {\sqrt 2 }}(\mathit{\boldsymbol{\hat x}} + {\rm{i}}\mathit{\boldsymbol{\hat y}})$ and $\hat R = {1 / {\sqrt 2 }}(\mathit{\boldsymbol{\hat x}} - {\rm{i}}\mathit{\boldsymbol{\hat y}})$ respectively, the$\mathit{\boldsymbol{\hat x}}$, $\mathit{\boldsymbol{\hat y}}$ are the basis vectors in Cartesian coordinate. θ is the polarization angle with respect to the x axis given that the phase difference between the two orthogonal circularly polarized beams is 2θ as shown in
Figure 1.Design principle of generating a linearly polarized beams with a rotating polarization angle based on optical heterodyne interference.(
where ${f_1}$ and ${f_2}$ are the frequencies of two beams respectively; ${\varphi _1}$ and ${\varphi _2}$ are the initial phase of two beams. As shown in equation (2), the phase difference between the two beams at time t can be expressed as $2{\rm{ \mathsf{ π} }}({f_2} - {f_1})t + {\varphi _2} - {\varphi _1}$, where ${\varphi _2} - {\varphi _1}$ is constant and determined by the initial phase of the two beams. The item ${{\rm{e}}^{{\rm{ - i}}2{\rm{ \mathsf{ π} }}{f_1}t + {\varphi _1}}}$ represents the carrier phase and has no effect on the modulation of the polarization plane. Comparing equation (2) to equation (1), the time dependent linear polarization angle can be expressed as:
If $\left| {{f_1} - {f_2}} \right| < < {f_1}$, noting that the modulated linear polarization rotation is periodical at the angle of ${\rm{ \mathsf{ π} }}$, the continuous rotation of the polarization over time then is at the frequency of ${f_2} - {f_1}$. Furthermore, the accumulated phase is monotonously increasing and therefore leads to a hopping-free polarization modulation.
The schematic diagram of the experiment is shown in
Figure 2.Schematic diagram of the experiment.The trapping beam is produced by a 532 nm laser and a Mach-Zehnder interferometer based on heterodyne interference. Devices in the green dashed box: a polarization detector made of a liquid crystal vortex half wave-plate and a polarizer which determines the polarization angle of the output trapping field. WP: wave plate; DM: 561 nm long pass dichroic mirror mounted on a flippable frame; PD: photodiode; PBS 1-4: polarized beam splitter; LC-VP: Liquid crystal based vortex half-wave plate; Obj 1: 10x objective; Obj 2: 100x objective with NA of 1.4; Filter 1-2: 635 nm long-pass filter.
The beam waist of the output linearly polarized beam was expanded to 6 mm by a beam expander made of an objective and a plano-convex lens. The beam was then reflected by a 561 nm long-pass dichroic mirror (DM) to the back focal plane of the objective lens and formed optical trapping after being focused by the objective with numerical aperture (NA) of 1.4. The DM was customized in its coating for minimizing the depolarization effect in reflection. The trapped particles were illuminated with Kohler illumination and imaged with an infinity calibrated imaging system. The rotational dynamics of the particles can be directly characterized by the camera in the case of slow rotation. A horizontally polarized probe laser of 671 nm wavelength was used to detect the rotation frequency by logging the scattering fluctuation of rotating particle with a photodetector (PD) at the vertical polarization direction. The time-lapsed scattering signal can be used to determine the particle rotation speed.
Results and discussion
To visualize the rotation of the linear polarization synthesized, a passive liquid crystal vortex half-wave plate (LC-VP) combined with a polarizer was used to detect the polarization direction of linearly polarized beam
where φ is the azimuth angle around the axis of the beam;
Figure 3.Verifying the polarization orientation distribution after passing through a LC-VP device.(
The modulated linear polarization then was used to achieve particle rotation in optical tweezers. Vaterite particles with 1 μm diameter suspending in distilled water were used in the optical trapping experiment. Vaterite is a poly-crystalline structure of calcium carbonate consisting of 20-30 nm nanocrystals
where S is the particle cross-section area, ε is the permittivity, and f0 is the frequency of input light field. In the first sinusoidal term in equation (7), no and ne are optical indices along the ordinary axis and extraordinary axis, respectively, d is the thickness of the particle, and k0 is the wave number of the laser beam in vacuum. θ is the offset angle between the linear polarization direction of the beam and the optic axis of particle in the second sine term.
The synthesis of vaterite particles was based on the modification of a previously published protocol
Figure 4.Video snapshots of disc-shaped vaterite particles recorded by optical tweezer apparatus.(
In order to systematically study the applicability and control accuracy of the proposed method for high-speed rotation operation, the heterodyne frequency was adjusted from 100 Hz to 600 Hz at intervals of 100 Hz for a smaller vaterite particle with a diameter of 1 μm and a thickness of 0.7 μm.
Figure 5.The scattered li ght signals o f one trapped vaterite particle.(
Conclusions
In summary, we propose a novel method for hopping-free rotation of linear polarization by electronically tuning the laser heterodyne interference, showing its promising applications in robust and high-speed particle rotation manipulation in optical tweezers. The modulation speed and stability of generated rotating linear polarization is only limited by the AOM detuning frequency range and the resolution of the driving RF source. Therefore, it can potentially reach MHz scale with sub-Hz accuracy. High speed rotation of vaterite particles synchronized to polarization modulation is demonstrated in optical tweezers. The reported rotation control in optical trapping will find important applications in on chip micro-pumping, viscosity sensing, rotational manipulation in biophysical studies, and measurements of torque
Acknowledgements
The work was supported by grants from the National Natural Science Foundation of China (91750203 and 91850111), State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences and the High-performance Computing Platform of Peking University.
Competing interests
The authors declare no competing financial interests.
Supplementary information
[3] [3] Ahn J, Xu Z J, Bang J, Ju P, Gao X Y et al. Ultrasensitive torque detection with an optically levitated nanorotor. Nat Nanotechnol15, 89-93 (2020).
[4] J M Zhu, X Q Zhu, Y F Zuo, X J Hu, Y Shi et al. Optofluidics: the interaction between light and flowing liquids in integrated devices. Opto-Electron Adv, 2, 190007(2019).
[39] P Fei, J Nie, J Lee, Y C Ding, S R Li et al. Subvoxel light-sheet microscopy for high-resolution high-throughput volumetric imaging of large biomedical specimens. Adv Photon, 1, 016002(2019).
[40] J J Li, A C Matlock, Y Z Li, Q Chen, C Zuo et al. High-speed
[41] S J Feng, Q Chen, G H Gu, T Y Tao, L Zhang et al. Fringe pattern analysis using deep learning. Adv Photon, 1, 025001(2019).
[43] [43] Rocco D, Gili V F, Ghirardini L, Carletti L, Favero I et al. Tuning the second-harmonic generation in AlGaAs nanodimers via non-radiative state optimization[Invited]. Photon Res6, B6-B12 (2018).
Get Citation
Copy Citation Text
Wei Liu, Dashan Dong, Hong Yang, Qihuang Gong, Kebin Shi. Robust and high‐speed rotation control in optical tweezers by using polarization synthesis based on heterodyne interference[J]. Opto-Electronic Advances, 2020, 3(8): 200022-1
Received: Jul. 11, 2020
Accepted: Jul. 15, 2020
Published Online: Jan. 7, 2021
The Author Email: Shi Kebin (kebinshi@pku.edu.cn)