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Abstract
We propose and demonstrate a novel approach to transport a strongly absorbing particle in an X-typed trajectory reciprocally in pure liquid glycerol based on a dual-beam optical fiber trap. We perform the X-typed light field by integrating a glass microsphere on the tip of a two-core fiber. The motion of the absorbing particle in pure liquid glycerol is dominated by the Δα-type photophoretic forces (FΔα). The incident laser power determines the direction of FΔα. Therefore, we may perform the reciprocating transport of the absorbing particle by changing and controlling the laser power. It is simple to manufacture the fiber probe and convenient to operate the transport of the microparticle. Our research expands the applications of absorbing particles in targeted drug delivery, biological sampling, and optically mediated particle clearing.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical manipulation, such as optical cooling [1–7], trapping [8,9], stretching [10,11], rotating [12,13] and transporting [14,15], has experienced intensive development in the past 50 years. Particle transport, as an important branch of the optical manipulation, has numerous applications, including optical pushing and pulling absorbing irregularly shaped carbon nanotubes [16]; trapping and transporting absorbing silicon particles [17] and optical transporting and pinpointing positioning of objects over a meter-scale distance [18]. For transparent particles, there are various configurations and methods for trapping and transporting them in air or liquid. For example, Ashkin [19] firstly demonstrated that a weakly focused laser could move particles in liquid via the dominant axial scattering force. However, the laser only pushes the particles along the optical axis, and the divergence of the Gaussian beams limits the transport distance to the Rayleigh length. Bessel [20–22] and Airy beams [23,24] exhibit greater depth of fields than Gaussian beams and allow long-distance linear or curved transporting. Unfortunately, the optical energy distributes among the rings, which causes the waste of laser power [20–24]. In addition, most experimental setups need bulk optical elements [20,23,24] or extremely precise alignment of fibers [21] or complicated fiber grinding process [22]. Optical vortex beam with orbital angular momentum is successfully used for guiding atom [25] and particles in moving along a linear or a curved direction [26,27]. However, vortex beams are normally together with complex optical systems. Optothermal waveguides [28] could also manipulate and transport transparent particles. However, the particle trajectory and motion are affected by the temperature gradient, and the number of transporting particles is uncontrollable. Recently, people find that tractor beams can pull the particles toward the source of light. In order to perform the traction function, people have to construct the light field to be specific distribution [29–31] or have to modify the target particles to be specific materials or structure [32]. However, neither complicated light field distributions nor special particle structures are conducive to practical applications. In addition, the evanescent fields from optical waveguides can also confine and transport transparent particles over long-distance [33]. However, particle trajectory and movement distance are strictly limited by the scattering and absorption losses in the system. Hollow-core photonic crystal fibers (HC-PCF) can guide light without leakage using a photonic bandgap, which can be used for optical transportation [34–36]. However, the HC-PCF has to confine the particles inside the hollow channels. It is difficult to observe the transport process and to perform a remote and noncontact particle transport.
Although there are a large number of methods to achieve the transport manipulation of transparent particles, unfortunately, it is challenging to perform the transport manipulation of the absorbing particles. For absorbing particles suspended in liquid, there are more absorptions on the illuminated side and the positive photophoretic forces will always push the particles to move away from the light source. Therefore, it is difficult to optical trap and transport absorbing particles in the liquid. Considering optical manipulating absorbing particles can be applied in biology, colloidal science and medicine fields [16–18], it is interesting and meaningful to study the absorbing particles. Therefore, optical manipulation of the absorbing particles needs to be solved. Although there are many ways to achieve the trapping and transporting transparent particles in liquid or air, there are few reports about trapping [37–39] or transporting strongly absorbing particles in a liquid. In this paper, on the base of our previous work [40,41], we propose and demonstrate an X-typed curvilinear transport of strongly absorbing particle in pure liquid glycerol by using strong Δα-type photophoretic force. It is worthy to say, compared with the previous transport manipulations, which are unidirectional, the proposed X-typed curvilinear transport may perform the bidirectional, reciprocating motion of the trapped microparticle. In addition, the manufacture of the fiber probe is simple, and the operation is convenient. Our research can be applied in targeted drug delivery [42], biological sampling [43] and optically mediated particle clearing [44].
2. Fiber probe fabrication
We employ a two-core fiber (TCF, made in our laboratory) and a silica microsphere to design and fabricate the fiber probe. The core diameter of TCF is 7 µm and the cladding diameter of TCF is 125 µm. The distance between the two cores is 80 µm (see Fig. 1a). The core refractive index of TCF is 1.4681 and the cladding refractive index is 1.4632. We stick a glass microsphere (GS) on the tip of TCF with an ultraviolet curing adhesive (UVA, Apollo UV, JiGATM) to configure the X-typed output light field (see Fig. 1b). The glass microsphere (GS) is made of silica. The diameter of the GS (M-300, Quanzhou Yemingliang Retroreflective Materials Co., Ltd.) is 115 µm, and the refractive index is 2.2. The refractive index of the UVA is 1.5. We align the center of the GS and TCF precisely with two three-dimensional micromanipulators (MP-225, Sutter Instrument). We dip the cleaved end face of the TCF in the bath of UVA to form a symmetric hemispherical shaped liquid droplet. Utilizing the surface tension of the liquid glue, the GS is lifted-up to make a point-contact with the fiber. Under the influence of gravity, the center of the GS will align with the main axis of the fiber. Then we illuminate the microsphere-tip fiber probe with the ultraviolet light for at least 5 minutes to form a stable and integrated microsphere-tip fiber probe [45]. We employ pure liquid glycerol as the solution to perform X-typed transport. The basic parameters of liquid glycerol: the refractive index (ng) is 1.473, the density (ρg) is 1.26×103 kg/m3, the thermal conductivity (kg) is 0.286 W/(m·K), the dynamic viscosity coefficient (ηg) is 1.5 Pa·s at T = 300 K.
Fig. 1. (a) Profile image of the TCF; (b) image of fiber probe. Here UVA means ultraviolet curing adhesive, GS means glass microsphere, XLF means X-typed light field.
3. Trap principle
When an absorbing particle (AP) is in the liquid glycerol, the Δα type photophoretic force (FΔα), which describe the momentum transfer between the AP and the liquid glycerol, dominates the trap and axial shift manipulation and exposes the mechanism. According to the theoretical and experimental results in our previous reports [40,41], in pure liquid glycerol, FΔα dominates the motion of the AP. A glass microsphere with a diameter of 115 µm is attached on the tip of the TCF. When we launch the laser power P1 into core1 and laser power P2 into core2, two output beams from the silica microsphere will focus and configure an X-typed output light field (zp see Fig. 2a). We employ a commercial software (Comsol Multiphysics) to simulate and calculate the photophoretic forces exerting on the AP. The simulated parameters contain: the wavelength of the laser is 980 nm and the incident power of P1 and P2 is 3.5 mW. The real part of the AP refractive index is 1.908, and the imaginary part is 0.519. The thermal conductivity of the AP is ks=3.758 W/(m·K). The diameter of the AP is 6 µm. According to the simulated results (see Fig. 2a), the output light field performs an X-typed distribution, and the distance between zp and the probe tip is 23.7 µm, which means zp=23.7 µm. Due to the weak absorption of the liquid glycerol from the laser energy, the temperature near the probe tip is ∼298 K (25℃), which is near to the room temperature (see Fig. 2b). When the X-typed light field traps an AP on zp, the AP absorbs lots of light field energy, and it blocks the transmission of the propagating beam (see Fig. 2c). Due to the strong absorption of the AP, the temperature of the AP and the temperature of the glycerol near the AP increase by ∼20 K (see Fig. 2d). On the base of the temperature field distribution results, we may calculate the photophoretic force (FΔα) exerting on the AP. According to the calculation method in [40], FΔα can be described as
Fig. 2. (a) Simulated result of the output light field introduced by P1 and P2 without the AP; (b) simulated result of the temperature field distribution introduced by P1 and P2 without the AP; (c) simulated result of the output light field introduced by P1 and P2 with the AP; (d) simulated result of the temperature field distribution introduced by P1 and P2 with the AP; (e) calculated result of the axial photophoretic force FΔα exerting on the AP introduced by P1 and P2; (f) calculated result of the transverse photophoretic force FΔα exerting on the AP when z = 23.7 µm. (g) calculated result of the axial photophoretic force FΔα exerting on the AP when the powers of P1 and P2 change. (h) calculated result of the transverse photophoretic force FΔα exerting on the AP when the powers of P1 and P2 change.
The direction of FΔα is determined by Δα/ᾱ. We divide the surface of the AP in two hemispheres possessing the accommodation coefficient of α1 and α2 (see the insert in Fig. 2e). Therefore, Δα=α1-α2 and ᾱ=(α1+α2)/2.
α is the accommodation coefficient, and it is defined as [40],
where Ti is the incident temperature of the fluid molecules on the surface of the particle, Tr is the temperature of the liquid molecules leaves the surface of the particle, Ts is the temperature of the particle surface.We may simulate and calculate the temperature field distribution of the AP and liquid glycerol, and then we may obtain the FΔα. When the temperature field distribution meet the condition of $\Delta \alpha /\bar{\alpha } > 0$, the FΔα will push the AP moving away from the laser source; when the temperature field distribution meet the condition of $\Delta \alpha /\bar{\alpha } < 0$, the FΔα will pull the AP moving towards the laser source; when the temperature field distribution meet the condition of $\Delta \alpha /\bar{\alpha } = 0$, the FΔα exerting on the AP will be zero, performing the optical trap of the AP.
On the base of the simulated results in Fig. 2d, we may obtain the α1 and α2 of AP, and then we may obtain the photophoretic force exerting on the AP. We calculate the axial force (see Fig. 2e) and transverse force (see Fig. 2f) exerting on the AP. The results indicate that, when we launch the laser power P1 into core1 and laser power P2 into core2, we may trap an AP on the zp. When the AP is far away from the probe tip (z > zp), the axial FΔα is negative, which means the photophoretic force will pull the AP towards the probe tip. When the AP is near the probe tip (z < zp), the axial FΔα is positive, which means the photophoretic force will push the AP moving away from the probe tip. The transverse forces ensure the AP to be trapped on the main axis (x = 0) of the fiber probe.
We added a paragraph and two figures (Fig. 2g and 2h) in the revised manuscript: When we launch the laser power P1 into core1 and laser power P2 into core2, each power ranges from 0.5 to 6.5 mW, keeping P1=P2, we simulate the axial FΔα and transverse FΔα exerting on the AP (see Fig. 2g and Fig. 2h). When the laser power increases, both the axial FΔα and transverse FΔα increase. The balance points along the z-axis and x-axis are unchanged (z = zp, x = 0). The AP is trapped in the position of zp when the powers range from 0.5 to 6.5 mW. In the experiment, when the power is larger than 6.8 mW, the AP will be bounced away from zp; When the light power is smaller than 0.3 mW, we will lose the trap. Therefore, we simulate the power range of 0.5 to 6.5 mW. The experimental results indicate that when the incident laser power in a suitable range, the optical fiber probe will perform the optical trap of the AP.
4. Transport principle
When we only launch one laser into the TCF, such as we launch the laser power P1 into core1, the incident power of P1 is 3.5 mW, the output light field performs the half X-typed distribution (see Fig. 3a). The temperature field distribution is determined by the output light field. Due to the weak absorption of the liquid glycerol, the temperature near the probe tip is still ∼298 K (see Fig. 3b).
Fig. 3. (a) The Simulated result of the output light field introduced by P1 without the AP; (b) simulated result of the temperature field distribution introduced by P1 without the AP; (c) simulated result of the output light field introduced by P1 with the AP; (d) simulated result of the temperature field distribution introduced by P1 with the AP; (e) calculated result of the axial photophoretic force FΔα exerting on the AP along the z1-axis with different incident power. (f) calculated result of the transverse photophoretic force FΔα exerting on the AP when z = 23.7 µm.
When an AP falls into the effective zone of the output light field, the AP will be attracted and moved along the direction of the output laser beam (z1-axis). The transverse force (see Fig. 3f) ensures the AP to be moved along the main axis of the output laser beam. We may calculate the photophoretic force exerting on the AP when a single laser beam works based on the simulated results in Figs. 3c and 3d. We set the incident laser power in the range of 1 mW to 11 mW (see Fig. 3e). The calculated results indicate that, for a specific AP, there exists a threshold power (Pth=6.2 mW). When the incident laser power is larger than Pth, the photophoretic force will pull the AP moving towards the probe tip, and when the incident laser power is smaller than or equal to Pth, the photophoretic force will push the AP moving far away from the probe tip. For the axial force introduced by a specific laser power along the z1-axis (see Fig. 3c), the calculated results indicate that the smaller the z1, the larger the value of the axial force FΔα. The results also suggest that the effective range of the photophoretic force is within ∼60 µm (z1<60 µm). Therefore, we may perform the position adjustment of the AP along the output laser beam propagating direction (z1-axis) by changing the incident laser power. In addition, when we launch two lasers into TCF alternately, we may perform the X-typed trajectory transport by changing the power ratio of two laser powers. The direction of the photophoretic force (FΔα) is determined by Δα/ᾱ. FΔα provides an attractive force when Δα/ᾱ<0 and provides a repulsive force when Δα/ᾱ>0. Δα/ᾱ is determined by Ti, Tr, and Ts. These three variables are related to the laser power density exerting on the particle essentially [40,41]. Therefore, the direction of FΔα changes when the power is modified.
5. Experiment and results
5.1 Experimental setup
Figure 4 provides the schematic diagram of the experiment setup. We employ two 980 nm fiber laser sources (0-300 mW) to perform the X-typed light field for AP trap and transport. We employ two 532 nm fiber laser sources (0-1 mW) to display the output light field distribution. We make use of two couplers with the power ratio of 99:1 to perform the complex of 980 nm (99%) laser source and 532 nm laser source (1%). In addition, we employ a fiber power-coupling device (Chiral Photonics, Multicore Fiber Fanout) to perform the simultaneous launching of two laser sources. We mount the TCF probe with the GS on a three-dimensional micromanipulator (MP-225, Sutter Instrument) to control the 3-dimension movement of the AP. We place the APs that disperse in the pure glycerol liquid on the microscope slide. We make use of a 25× objective (NA of 0.40, focal depth of 6.5 mm) and a CCD camera (30 frame/s) to observe and record the motion of the APs. The AP used in the experiment is a silica doped carbon-black microsphere, whose mass ratio is 15%, and the volume ratio is 10%. The diameter of the AP is 6 µm. It is completely opaque for the 980 nm laser. The total coupling efficiency of my setup is about 91%
Fig. 4. The schematic diagram of the experimental setup. Here, TCF means the twin-core fiber, and PC means the personal computer.
5.2 Experimental results 1: “>”-typed transport trajectory
According to the simulated results, when the incident laser power is in the range of 1 mW-6.2 mW, the photophoretic force will push the AP. To ensure the stable transport of the AP, in the experiment, we choose the incident laser power to be 4.8 mW for AP pushing. When the incident laser power is in the range of 6.3 mW-11 mW, the photophoretic force will pull the AP. In the experiment, we choose the incident laser power is 7.6 mW for AP pulling.
We may perform the “>” typed transport trajectory (see Visualization 1 and Fig. 5a) by changing and controlling the powers in two cores (P1 and P2). Firstly, we set the power in core1 p1=3.5 mW and set the power in core2 p2=3.5 mW. Therefore, the fiber probe performs an X-typed output light field, and it will trap an AP in the position of zp (see Fig. 5b). Secondly, we set the p1=7.6 mW, and p2=0 mW. The fiber probe will perform a half X-typed light field and it will pull the trapped AP moving along the upper left of negative z1-axis (see Fig. 5c). When the AP moves and adheres to the probe tip, we set the p1=4.8 mW and keep p2=0 mW. The AP will be pushed to move along the lower right of the positive z1-axis (see Fig. 5d).
Fig. 5. (a) The schematic diagram of the “>” type transport trajectory; (b) the image of the AP trapped by the X-type light field; (c) the AP is pulled by P1=7.6 mW; (d) the AP is pushed by P1=4.8 mW; (e) the AP is pulled by P2=7.6 mW; (f) the AP is pushed by P2=4.8 mW. Video of the “>” typed transport trajectory (Visualization 1).
Next, we set the p2=7.6 mW and set p1=0 mW. The AP will be pulled to move along the lower left of the negative z2-axis (see Fig. 5e). When the AP moves to the tip of the fiber probe, we set the p2=4.8 mW and keep p1=0 mW. The AP will be pushed to move upper right along the positive z2-axis and come back to zp again (see Fig. 5f). In summary, when we set the powers in two cores according to the set rules, we may perform the AP transport in the “>”-typed trajectory.
5.3 Experimental results 2: “<” type transport trajectory
Similarly, we may perform the “<” typed transport trajectory (see Visualization 2 and Fig. 6a) by changing the powers in two cores according to the set rules. Firstly, we set the power p1=p2=3.5 mW. Therefore, an AP is trapped in the position of zp (see Fig. 6b). Secondly, we set p1=0 mW and set p2=4.8 mW. The half X-typed light field will push the trapped AP to move upper right along the positive z2-axis (see Fig. 6c). When the AP moves to the far end of the X-type light field, we set the p2=7.6 mW and keep p1=0 mW. The AP will be moved along the lower left of the negative z2-axis and return to zp (see Fig. 6d). Next, we set the p1=4.8 mW and set p2=0 mW. The AP will be pushed to move along the lower right of the positive z1-axis (see Fig. 6e). When the AP moves to the far end of the X-type light field, we set the p1=7.6 mW and keep p2=0 mW. The AP will be pulled back to move along the upper left of the negative z1-axis and return to zp again (see Fig. 6f). In summary, we perform the AP transport along the “<” type trajectory.
Fig. 6. (a) The schematic diagram of the “<” type transport trajectory; (b) the image of the AP trapped by the X-typed light field; (c) the AP is pushed by P2=4.8 mW; (d) the AP is pulled by P2=7.6 mW; (e) the AP is pushed by P1=4.8 mW; (f) the AP is pulled by P1=7.6 mW. Video of the “<” typed transport trajectory (Visualization 2).
5.4 Experimental results 3: “^”type trajectory transport
We may also perform the “^” typed transport trajectory (see Visualization 3 and Fig. 7a) by using the proposed fiber probe. Firstly, we set the power p1=p2=3.5 mW. Therefore, an AP is trapped in the position of zp (see Fig. 7b). Secondly, we set the p1=4.8 mW and set p2=0 mW. The AP will be pushed to move along the lower right of positive z1-axis (see Fig. 7c). When the AP moves to the far end of the X-typed light field, we set the p1=7.6 mW and keep p2=0 mW. The AP will be pulled back to zp and moved along the upper left of the negative z1-axis (see Fig. 7d). Next, we set the p1=0 mW and set p2=7.6 mW. The half X-typed light field will pull the AP to move along the lower left of the negative z2-axis (see Fig. 7e). When the AP moves to the tip of the fiber probe, we set the p2=4.8 mW and keep p1=0 mW. The AP will be pushed to move along the upper right of the positive z2-axis and returned to zp (see Fig. 7f). In summary, when we set the powers in two cores according to the set rules, we may perform the microparticle transporting along the “^” typed trajectory.
Fig. 7. (a) The schematic diagram of the “^” type transport trajectory; (b) The image of the AP trapped by the X-type light field; (c) The AP is pushed by P1=4.8 mW; (d) The AP is pulled by P1=7.6 mW; (e) The AP is pulled by P2=7.6 mW; (f) The AP is pushed by P2=4.8 mW. Video of the “^” typed transport trajectory (Visualization 3).
6. Discussion
In the experiment, when P1=4.8 mW, the fiber probe will push the AP moving far away from the fiber tip along the z1-axis. We record the AP position along the z1-axis and the corresponding time (see Fig. 8). Therefore, the slope of the fitting line indicates the moving speed of the AP. The pushing speed is 8.2 µm/s. Similarly, when P1=7.6 mW, the fiber probe will pull the AP moving towards the fiber tip along the negative z1-axis. We also record the AP position along the z1-axis and the corresponding time (see Fig. 8). The slope of the fitting line indicates the moving speed of the AP and the fitting result of the pulling speed is 12.7 µm/s.
Fig. 8. The experimental results of the relationship between the time and the position in the z1-axis. Here FS means the fitting results.
Although the calculated results in Fig. 3e indicate that the smaller the z1, the larger the axial photophoretic force exerting on the AP, the AP performs the uniform motion. It is because that, the larger the driving force exerting on the AP, the larger driving speed of the AP, and the larger the liquid viscous drag introduced by the liquid glycerol. The formula of liquid viscous drag is Fη=6πηrv, where r is the AP radius, η is the dynamic viscosity coefficient of glycerol liquid (1.5 Pa·s at T = 300 K), v is the AP speed. The viscous drag Fη is proportional to v. Therefore, the larger the driving force, the larger the AP speed, and the larger the liquid viscous drag. With the net force of FΔα and Fη, the AP will perform the uniform motion.
Therefore, although there exist some disturbances in the speeding results in Fig. 8, in the AP transport process, the microparticle performs the uniform-like motion.
7. Conclusions
We perform reciprocating X-typed curvilinear transport of a strongly absorbing particle in pure liquid glycerol based on a dual-beam optical fiber trap. The transport manipulation is based on the strong Δα-type photophoretic forces. Our research adjusts the posture of the high-absorbing particles in pure liquid glycerol elaborately and demonstrates more details about the transport of absorbing particles. Such stable and switchable transport can be widely used in targeted drug delivery, biological sampling, and particles clearing. In addition, the manufacture of the fiber probe is simple, and the operation is convenient.
Funding
National Key R&D Program of China (2018YFC1503703); National Natural Science Foundation of China (61675053, 61705051, 61775047); 111Project (B13015); Fundamental Research Funds for Harbin Engineering University of China.
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