Polarization-modulation-based orientation metrology of optically levitated rotating birefringent particles

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Polarization-modulation-based orientation metrology of optically levitated rotating birefringent particles

Kai Zeng, Yulie Wu, Xuezhong Wu, and Dingbang Xiao

Phys. Rev. Research 6, 013160 – Published 12 February 2024

Abstract

The ultrafast rotation of optically levitated particles has propelled advancements in sensing and precision measurement, while its orientation remains largely unexplored for the spherical shape. Here, we proposed an orientation measurement method for the birefringent rotating particles, which extracts both the azimuthal and polar angles of the optical axis from the polarization of the transmitted laser. A bulk birefringent crystal with a known orientation is measured by this method to verify its effectiveness, and then the orientation of vaterite particles is extracted from the rotational signal. This method paves the way to investigate the orientational dynamics and gyroscope application.

Received 2 September 2023
Revised 16 November 2023
Accepted 11 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.013160

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Optomechanics

Optical tweezers Particle detectors

Atomic, Molecular & Optical

Authors & Affiliations

Kai Zeng, Yulie Wu^*, Xuezhong Wu, and Dingbang Xiao ^†

College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China

^*ylwu@nudt.edu.cn
^†dingbangxiao@nudt.edu.cn

Article Text

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Issue

Vol. 6, Iss. 1 — February - April 2024

Subject Areas

Optics

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Images

Figure 1
Orientation definition and measurement principle. (a) Scanning electron microscope image of a vaterite particle. (b) Orientation definition of the optical axis. OA: optical axis; BC: birefringent crystal. (c)–(d) Transmitting characteristics of ordinary laser (OL) and extraordinary laser (EL) in BC for (c) $θ = 0$ and (d) $θ \neq 0$ , and the azimuths are both 0. The green circle indicates uniform velocity of OL in all directions, while the pink ellipse illustrates the elliptical distribution of velocity for EL.
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Figure 2
Simulated results and experimental verification. (a) Simulated results of laser intensity versus polar angle $θ$ . The azimuthal angle $α = 45^{\circ}$ , electric field amplitude $E_{0} = 1$ . (b) Simulated intensity when the crystal rotate. The rotating angular frequency is $ω = 5 \times 2 π$ . (c) Experimental setup for a circularly polarized (CP) laser transmitting the birefringent crystal (BC). Labels denote the half wave plate ( $λ$ /2), polarizing beam splitter (PBS), quarter wave plate ( $λ$ /4), lens (L), photodetector (PD). Inset shows the birefringence effect, and the double image of lines can be seen through the birefringent crystal. The signals from two detectors are differentiated to improve the signal-to-noise ratio. (d) The measured voltage signal under different manipulation. I represents the tilt ( $θ$ ) of the crystal, and II represents the rotation ( $α$ ). The same color represents the same manipulation.
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Figure 3
Experimental setup and orientation measurement method of the vaterite particles. (a) Diagram of the experimental setup. The trapping laser ( $1064 nm, 20 mW$ ) is focused from the bottom to the vacuum chamber (VC) using a high numerical aperture (NA $= 1.25$ ) objective. The transverse laser is horizontally oriented, featuring a weaker focus (NA $= 0.25$ ) and low power ( $0.5 mW$ ). Inset shows the focusing and collecting objective of the two lasers. (b) Sketch map of the laser polarization before and after the particles. $P 1$ – $P 4$ represent different planes. Case I: optical axis in $x o y$ plane. (c) Illustration of the polar angle of the optical axis respect to the trapping laser ( $θ$ ) and transverse laser polarization plane ( $γ$ ). (d) The deviation of the optical axis from the trapping laser polarization plane under the centrifugal torque $T_{G}$ . GA and OA represents the geometrical long axis and optical axis respectively. $T_{O}$ represents the optical alignment torque.
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Figure 4
Measured orientation results of optically levitated particles. (a)–(b) Rotational signal from (a) trapping laser and (b) transverse laser under different pressure. The rotational frequencies at 700 Pa and 80 Pa are 791 Hz and 9925 Hz, respectively. PD represents photodetector. (c) Azimuth $α$ of the optical axis. The dashed line indicates the converting from the rotational signal to azimuth. (d) Calculated amplitude of rotational signal versus polar angle $θ$ . The value is calibrated when $θ = 0^{\circ}$ , and the polar angle can be read out from the measured rotational signal. (e) Measured amplitude of rotational signal under different pressure. Error bar comes from the standard deviation. (f) Spin frequency and polar angle of five particles versus pressure. The polar angle is expressed as $90^{\circ} − θ$ for visualization purposes.
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