Absorbing particle 3D trap based on annular core fiber tweezers

Optics Communications 437 (2019) 399–402

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Absorbing particle 3D trap based on annular core fiber tweezers Zhihai Liu a,b , Zhenyu Zhang a , Yu Zhang a ,∗, Yaxun Zhang a,c , Xiaoyun Tang a , Keqiang Liu d , Xinghua Yang a , Jianzhong Zhang a , Jun Yang a , Libo Yuan a,e a

Key Lab of In-fiber Integrated Optics, Ministry Education of China, Harbin Engineering University, Harbin 150001, China National Demonstration Center for Experimental Physics Education, Harbin Engineering University, Harbin 150001, China c Centre for Micro-Photonics Swinburne University of Technology, P.O. Box 218 Hawthorn, VIC 3122, Australia d Shanghai Radio Equipment Research Institute, Shanghai, 200090, China e Photonics Research Center, Guilin University of Electronics Technology, Guilin 541004, China b

ARTICLE

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Keywords: Optical tweezers 𝛥𝛼-type photophoretic forces Absorbing particles Annular core fiber Non-contact trapping

ABSTRACT We proposed and demonstrated a new method to trap and manipulate a strongly absorbing particle by harnessing strong 𝛥𝛼-type photophoretic forces in pure liquid glycerol with a focused annular beam, which was introduced by an annular core fiber optical tweezers. We performed the focused annular light field by integrating a high refractive index silica microsphere on the annular core fiber end facet. The silica microsphere, which acted as a lens, focused laser beam for trapping. We tested and calculated 𝛥𝛼-type photophoretic forces tendency by using the fluorescence dye method, and the simulated results were in agreement with the experimental results. The proposed optical fiber tweezers were small in size, large in capture range, simple to manipulate, and inexpensive in cost. It provided a new approach for absorbing particles trapping. Tailoring the trapping and manipulation of absorbing particles in liquid environments will open avenues for studying the special, yetunexplored characteristics of absorbing particles.

1. Introduction Optical tweezers have been widely used to trap and manipulate particles in physics [1,2], colloidal science [3,4] and biology [5,6] since the pioneering work of Ashkin et al. Generally, optical trapping employs the radiation pressure and gradient force to trap particles, which are transparent and immersed in liquid environment [7,8]. But for the opaque particles (light absorbing particles), they always suffered from strong scattering force and break the stable trapping. In recent years, researchers have begun to use photophoretic force to trap absorbing particles in the gas media, including reshaping of the optical vortex beams [9–11], utilizing the Moiré techniques with a spatial light modulator [12], building bottle beams with two coaxial conical beams [13]. But there have been few reports to study the trapping of absorbing particles in the liquid environment. The major problem was that the illuminated side of the particle will have more absorption and produce 𝛥T-type photophoretic force 𝐅ΔT , which always point to the direction from the hot side to cold side and push the absorbing particles away from the laser source, hindering optical trapping [14,15]. Different from 𝐅ΔT , the second type of photophoretic forces, 𝛥𝛼type photophoretic force 𝐅Δ𝛼 , could be negative, which could be used for optical pulling and trapping. 𝐅Δ𝛼 was induced by the difference in thermal accommodation coefficient 𝛼, which defined as the ability

of the particle surface to transfer heat to the surrounding liquid [16– 19]. The force pointed from the side of a higher to the side of a lower accommodation coefficient which varied over the particles surface. In this paper, on the basis of the thermodynamic properties of pure liquid glycerol, we employed 𝛥𝛼-type photophoretic force to demonstrate that the optical trapping of absorbing particles in pure liquid glycerol could be established with a focused annular beam without the need of special beam engineering or gravity-assisted balance [20– 22]. We presented and demonstrated a new idea for trapping absorbing particles in the liquid environment and ensured the trapping process easily. The annular core fiber optical tweezers provided an approach to study various light-absorbing particles, and other novel light-absorbing materials. Tailoring the trapping and manipulation of absorbing particles in liquid environments will open avenues for studying special, yetunexplored characteristics. 2. Experimental result Our experiments were carried out with a focused annular beam from an annular core fiber (ACF, made in our laboratory) at 980 nm (see Fig. 1(a)). Our motivation was to trap absorbing particle by focused annular beam designed with the ACF gluing a silica microsphere at the end facet, and 3-dimensional manipulate it in pure liquid glycerol.

∗ Corresponding author. E-mail address: [email protected] (Y. Zhang).

https://doi.org/10.1016/j.optcom.2018.12.063 Received 1 November 2018; Received in revised form 12 December 2018; Accepted 16 December 2018 Available online 21 December 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.

Z. Liu, Z. Zhang, Y. Zhang et al.

Optics Communications 437 (2019) 399–402 Table 1 Basic parameters of liquid glycerol [23]. Name

Symbol

Value

Density Thermal conductivity Dynamic viscosity coefficient Kinetic viscosity coefficient Knudsen Number Péclet number Reynolds number Prandtl number

𝜌 𝑘g 𝜂dyn 𝜂kin Kn Pe = 𝜌cp ul/k Re = 𝜌ul/𝜂 Pr = cp 𝜂/k

1.261 × 103 [kg/m3 ] 0.286 [W/(m K)] 1.5 [Pa s] 1.189 × 10−3 [m2 /s] 1.183 × 10−5 <<1 7.388 × 10−10 5.969 × 10−14 1.238 × 104

on the particle was small and reached 0, result in the weakness of 𝐅ΔT . According to Table 1, the Péclet number Pe and the Reynolds number Re are much smaller than the Prandtl number Pr. Therefore, pure glycerol had almost no convection or Laminar flow in the vicinity of the heated absorbing particle. For the heat transfer, the momentum diffusivity between the absorbing particle and the glycerol molecules played the most important role in the temperature changes, which was compared with the thermal diffusivity. Hence, compared with 𝐅g , 𝐅b , 𝐅𝜂 , 𝐅rp and 𝐅ΔT , 𝐅Δ𝛼 which was based on the momentum accommodation dominated the motion of the absorbing particle in pure liquid glycerol. According to the definition of thermal accommodation coefficient [23],

Fig. 1. (a) Schematic diagram of the 3D traps using annular core fiber tweezer; (b) Diagrammatic sketch of the forces exerting on the absorbing particle; (c) Simulated results of the fiber probe with the silica microsphere. (d) Image of the output light field distribution introduced by the fiber probe with the silica microsphere (e) Image of the absorbing particle trapped by the fiber probe with the silica microsphere.

When the absorbing particle was close to the effective area of the fiber probe, it would move towards the output beam focus and then be trapped stably by the annular core fiber optical tweezer (see Video 1). Typical experimental results were shown in Fig. 1(e). For this experiment, an absorbing particle of 6 μm size was used. The laser output power was about 5 mW, and the focal point of the beam was about 𝑧f = 9 μm. Being different from the normal trapping of the transparent particles, the experiments showed that the opaque particle was trapped after the focused point (see Figs. 1(c) and 1(e)), where the temperature distribution of the liquid glycerol satisfied the equilibrium condition of the axial and transverse 𝐅Δ𝛼 . The center of the trapped particle was 𝑧p = 11 μm away from the silica microsphere. Background liquid was crucial during the trapping and we used the pure liquid glycerol because of its thermodynamic properties in the experiment. We failed to trap absorbing particles in aqueous solution instead of the pure liquid glycerol.

𝛼=

𝑇𝑟 − 𝑇𝑖 𝑇𝑠 − 𝑇𝑖

(1)

where 𝑇𝑖 was the incident temperature of the fluid molecules on the surface of the particle, 𝑇𝑟 was the temperature of the fluid molecules leave the surface of the particle, 𝑇𝑠 was the temperature of the particle surface, 𝛼 denoted the thermal accommodation coefficient which was defined as the ability of the material to transfer heat to the surrounding liquid and it was an important indicator of evaluation 𝐅Δ𝛼 . According to the [23], 𝐅Δ𝛼 can be described as 𝐅𝛥𝛼 =

𝐽1 𝐼 𝜋𝜂 2 𝜎𝐼 𝛥𝛼 1 𝜋𝜂 2 𝜎𝐼 𝒆̂ = ( ) 𝒆̂ 𝒛 32𝜌𝑟0 𝑘𝑇∞ 𝛼 𝒛 12 𝜌 𝑘𝑇∞ 𝑘 𝑇 − 𝑇 𝑠 i

(2)

where 𝜂 was the dynamic viscosity of the liquid glycerol, 𝜎 was the scattering cross section of the absorbing particle, 𝐼 was determined by the incident laser irradiation, 𝜌 was the density of the liquid glycerol, 𝑇∞ was the room temperature, 𝑇𝑠 was the average temperature of the particle surface, 𝑟0 was the radius of the particle, 𝑘 was the thermal conductivity of suspended particle in Wm−1 K−1 , 𝐽1 was a weighted integration of the heat source distribution over the particle volume. According ( ) to the Eq. (2), the direction of 𝐅Δ𝛼 was dominated by 𝐽1 ∕ 𝑇𝑠 − 𝑇𝑖 in the glycerol. Whatever 𝐽1 was positive or negative, 𝐅Δ𝛼 will always provide an attractive force by adjusting the positive and negative of 𝑇𝑠 − 𝑇𝑖 . Here, 𝐽1 = −1∕2, 𝐅Δ𝛼 will provide an attractive force if 𝑇𝑠 − 𝑇𝑖 > 0. Thus, the difference between the average temperature of the particle surface 𝑇𝑠 and the initial temperature of the glycerol molecule near the absorbing particle 𝑇𝑖 determined 𝐅Δ𝛼 . Therefore, we can investigate the temperature distribution of the particle to assess the direction of 𝐅Δ𝛼 . In the glycerol, ( )the direction of 𝐅Δ𝛼 was also determined by 𝛥𝛼∕𝛼 (𝛥𝛼∕𝛼∼𝐽1 ∕ 𝑇𝑠 − 𝑇𝑖 ). According to the Eq. (2), 𝐅Δ𝛼 provided an attractive force if 𝛥𝛼∕𝛼 < 0 and provided a repulsive force ( ) if 𝛥𝛼∕𝛼 > 0 (see Fig. 2). Here 𝛥𝛼 = 𝛼1 − 𝛼2 and 𝛼 = 𝛼1 + 𝛼2 ∕2.

3. Force distribution of the particle and 𝜟𝜶-type photophoretic force theory The strongly absorbing particle used in the experiment was made of a mixture of carbon black and silica with a diameter of 6 μm. The density of the black sphere was 𝜌p = 2.27×103 kg/m3 , and the complex refractive index of the black sphere was m = 1.908 +0.519i. The particle was completely opaque for the 980 nm laser used in the experiment. For the absorbing particle in pure liquid glycerol, the force of gravity 𝐅g was 2.52 pN, and the direction was along the — x-axis. The buoyancy 𝐅b was 1.40 pN, and along the 𝑥-axis. Due to the large viscous coefficient (𝜂 = 1.5 Pa s at T = 300 K) of glycerol, the viscous resistance 𝐅𝜂 was big enough to make the absorbing particle in an equilibrium state along the vertical (x-axis) direction, satisfying 𝐅g + 𝐅b + 𝐅𝜂 = 0, which meant that the direction of 𝐅𝜂 was along the 𝑥-axis (see Fig. 1(b)). When the spherical absorbing particle was trapped inside the beam, the radiation pressure and the photophoretic force were directed exactly parallel to the beam axis owing to the perfect axial symmetry. When the incident laser power was 1 mW, the magnitude of the radiation pressure 𝐅rp was on the scale of pN, and the direction was along the 𝑧-axis. The magnitude of the photophoretic force, which was normally 106 times larger than that of 𝐅rp [9], was on the scale of μN, and the direction was along the 𝑧-axis. In our experiment, the thermal conductivity of the absorbing particle was large (k = 3.758 [W/(m K)]), therefore, the temperature gradient

4. Fiber probe design and experimental setup It can be seen the profile of the annular core fiber we used in the experiment from Fig. 3(a). The internal diameter of the annular core was 72 μm, and the external diameter of the annular core was 80 μm. The diameter of the surrounding cladding was 125 μm. The core refractive index was 1.4717, and the cladding refractive index was 1.4632. For a silica microsphere (M-300, Quanzhou Yemingliang retroreflective materials Co.,Ltd) with the refractive index of 2.2, and 400

Z. Liu, Z. Zhang, Y. Zhang et al.

Optics Communications 437 (2019) 399–402

Fig. 4. The schematic diagram of the experimental setup.

glycerol, temperature of the liquid layer around the particle, and the temperature of the particle surface. Thus, we obtained axial 𝛥𝛼∕𝛼, which represents the axial 𝐅Δ𝛼 exerting on the particle (see Fig. 5(d)). Similarly, we obtained transverse 𝛥𝛼∕𝛼, which represents the transverse 𝐅Δ𝛼 exerting on the particle (see Fig. 5(e)). The simulated results of the axial 𝛥𝛼∕𝛼 indicated that there existed a stable axial trapping position (𝑧0 ) where the axial 𝛥𝛼∕𝛼 = 0. Before the axial trapping position (zz0 ), 𝛥𝛼∕𝛼 was smaller than zero which indicated that the axial 𝐅Δ𝛼 attracted the absorbing particle moving toward the fiber tip. The simulated results of the transverse (x/y-axis direction) 𝛥𝛼∕𝛼 indicated that there existed a stable transverse trapping position (𝑥0 ) where the transverse 𝛥𝛼∕𝛼 = 0. Before the transverse trapping position (xx0 ), the transverse 𝛥𝛼∕𝛼 was smaller than zero which indicated that the transverse 𝐅Δ𝛼 also attracted the absorbing particle moving toward the fiber main axis. Hence, when the absorbing particle was placed on the z axis, the transverse force was zero to make a mechanical equilibrium. And the stable axial trapping position was in agreement with the experimental results.

Fig. 2. Sketch diagram of the direction of 𝐅Δ𝛼 .

Fig. 3. (a) The profile image of the annular core fiber; (b) Image of the annular core fiber tweezers probe with a silica microsphere.

the diameter was 110 μm. The silica microsphere was attached at the end facet of ACF with the ultraviolet curing glue (Apollo UV, JiGA™) whose refractive index was 1.5. To integrate the micro glass sphere to the ACF facet [24], the ACF should be vertically placed and stick the ultraviolet curing glue on the bottom of the fiber. The glue was transferred to the end of ACF to form a liquid droplet. Then made the center of the silica microsphere and the ACF center were carefully aligned with a three-axis high-precision positioner. Lowered the ACF and made a contact with the silica microsphere and the glue. Utilizing the gravity of the silica microsphere and the surface tension of the glue, the silica microsphere was fixed at the facet of ACF, and then irradiated by UV light to form an integrated composite body (see Fig. 3(b)). The experimental setup of the annual core fiber optical tweezers can be seen in Fig. 4. A laser source with the working wavelength of 980 nm was employed to produce trapping power. The range of the laser source power was 0–120 mW. The fiber probe was controlled by a 3D micro-manipulator, whose precise was 62.5 nm. A CCD was equipped to monitor the absorbing particles noncontact trap by the annual core fiber tweezers.

6. Conclusion In summary, we have experimentally demonstrated stable trapping and manipulation of highly absorbing particles by a focused annular beam in the liquid glycerol. Theoretically, we analyzed the 𝛥𝛼-type photophoretic forces exerting on the absorbing particles. The proposed annular core fiber optical tweezer is simple in structure, small in size, and convenient to fabricate. It provided a new feasible method for largescale of light-absorbing materials in trapping and manipulation in the liquid environment. This method can be widely used in studying several light absorbing particles, such as metal particles, graphite pieces, and other novel light-absorbing materials.

5. Numerical calculations

Acknowledgments

By using the fluorescence dye method, we obtained the temperature distribution near the trapped absorbing particle (see Fig. 5(c)). We employed the Rhodamine B (0.1 mM solution) as the fluorescence dye, whose temperature dependence had been well documented [25]. In the measurements, we employed a 532 nm green laser to excite the fluorescence. We employed a CCD to obtain the temperature distribution information (see Figs. 5(a) and 5(b)). The fluorescence dye method provided the difference of the temperatures. On the base of the image processing method, we obtained the initial temperature of the liquid

This work was supported by the National Natural Science Foundation of China (NSFC) (11574061, 61405043, 61675053); 111Project (B13015); Fundamental Research Funds for Harbin Engineering University of China. Appendix A. Supplementary data Supplementary material related to this article can be found online at https://doi.org/10.1016/j.optcom.2018.12.063. 401

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Optics Communications 437 (2019) 399–402

Fig. 5. (a) Images of the trapped absorbing particle in the glycerol solution with the fluorescence dye; (b) Images of the trapped absorbing particle in the glycerol solution when the laser source was suddenly shut off; (c) Calculated results of the temperature field distribution near the absorbing particle in the glycerol solution; (d) Calculated results of the axial 𝛥𝛼/𝛼 exerting on the AP; (e) Calculated results of the transverse 𝛥𝛼/𝛼 exerting on the AP.

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