1. Introduction

The ability of trapping and migration of nano/microscopic particles and biomolecules precisely is particularly important in the fields of biomedicine and physical chemistry. Optical tweezers, which were first introduced by Ashkin [1], have been widely used in such fields [2,3] due to the targeted and noninvasive nature [4]. Conventional optical tweezers trap objects near the focus of a laser beam. Therefore, dielectric particles [5], metallic particles [6], cells [7], and biomolecules [8] can be trapped to a designated position with the assistance of optical tweezers. However, since the optical force of optical tweezers is usually a few or tens of pN, while the trapping range is a few microns [9], it is hard to trap and/or migrate particles in a larger range with large number. Photophoresis, which is caused by the uneven heat distribution in the particle radiated by light [10], can also be used for particles manipulation. Particles with high absorptivity move away from light irradiation (positive photophoresis), while those with low absorptivity move toward light irradiation (negative photophoresis) [11]. Compared to conventional optical force (gradient force), photophoretic force is usually orders of magnitude larger [12,13], and thus can be used for large number of particles trapping and migration [14–16]. Besides the uneven heat distribution in the inner part of a single particle, uneven temperature distribution in a bulk medium can also result in the migration of particles. When particles are suspended in such a medium, they can be migrated along temperature gradient, typically from hot to cold. This effect is called thermophoresis [17]. Since its early introduction, thermophoresis has been widely used for particles trapping/migration and biomolecules research [18–20]. However, the setups used in these approaches consist of a chamber and an objective to focus a laser beam as a heat source, which may face challenges when trapping and migrating objects in narrow spaces. Since an optical fiber can be easily fabricated to a designed shape, it is an excellent tool for particles manipulation [21]. Recently, by combining photophoresis and temperature gradient, an optical fiber-ring was used for larger number particles trapping and migration [22]. However, the trapping capability is strongly dependent on the size and shape of the ring. In this work, we report a method for massive dielectric particles trapping and migration by a tapered optical fiber with the assistance of negative photophoresis and temperature gradient.

2. Experiment

2.1. Experimental setup

Figure 1a shows the experimental setup. A personal computer (PC) interfaced microscope with a charge coupled device (CCD) is used for real-time monitoring and image capture. A glass slide is mounted on a translation stage. A tapered fiber (3.1-µm in diameter, Fig. 1b) was fabricated from a commercial single-mode optical fiber by flame heated technique and fixed by a microstage. The fiber taper is immersed in a sample suspension which is hemisphere shape with an average diameter of 3.2 cm and a maximum thickness of 2.5 mm, while the other end is connected to a 1.55-µm wavelength laser through an erbium-doped fiber amplifier (EDFA). The suspension was prepared by diluting 2.08-µm diameter silica particles into deionized water (volume ratio of particles to water ~1:1,000) with the assistance of ultrasonic.

 

Fig. 1 Schematic of the experimental setup and the optical microscope image of the tapered optical fiber. (a) Experimental setup. The fiber is fixed by a microstage with the taper immersed in a water suspension of silica particles and the other end connected to a 1.55-µm laser through an EDFA. The images and videos can be captured by the computer connected CCD. (b) The optical microscope image of the tapered optical fiber. The diameter of the tapered fiber is D = 3.1 µm.

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2.2. Massive trapping

To get a high trapping efficiency, the output power of the 1.55-µm laser was amplified to 170 mW by the EDFA and then injected into the fiber. Once the 170-mW laser was injected into the fiber, light will be outputted from the tapered end of the fiber and a light intensity distribution region will be formed in water. The distribution will affect particles, which were randomly suspended in water, in a large region. Therefore, particles move toward the light intensity region because of negative photophoresis and accumulated at the center of the region where the negative photophoretic force (F _P) and temperature gradient force (F _T) achieve equilibrium. The temperature gradient force was induced by the strong absorption of 1.55-µm wavelength light by water. The detailed discussion will be given in section 3. The inset of Fig. 2a shows the optical microscope image of the tapered fiber in water with laser on for t = 0′00″. Figure 2a shows the optical microscope image with laser injected for 5 s. It can be seen that, particles move toward the region, which is hundreds of micrometers to the end of the fiber. After 2 mins, about 2100 particles were trapped, forming a spindle-shaped assembly region (Fig. 2b). Detailed trapping process is shown in Media 1 (from t = 4′20″ to 4′35″). As time goes by, more and more particles were trapped, and thus the spindle-shaped region became larger. At t = 5′00″, about 5150 particles were trapped (Fig. 2c). As more and more particles were trapped to the spindle-shaped region, particles outside the assembly region became fewer and fewer, and particles velocity became lower and lower. When t = 15′00″, the trapping process achieved a saturation state as shown in Fig. 2d. There are about 10,150 particles assembled in the spindle-shaped region (the maximum diameter is a = 290 µm, while the minimum one is b = 100 µm). There were only a few particles outside the spindle-shaped region. Compared with the situation of Figs. 2a-c, the water outside the assembly region in Fig. 2d was much cleaner. The inset of Fig. 2d shows the image for t = 15′05″ with a 50× objective, showing that the distance between the center of the spindled-shaped region and the end of the fiber is d = 380 µm.

 

Fig. 2 Optical microscope images for different massive trapping process, detailed process is shown in Media 1 (from t = 4′20″ to 4′35″). (a) Image with laser (1.55 µm, 170 mW) launched into the fiber for t = 0′05″, particles begin to be trapped. The inset shows the image with laser for t = 0′00″ (the fiber included), no particles trapped. The red arrow in the inset indicates the propagation direction of 1.55-µm wavelength of light. (b) Image with laser for t = 2′00″, about 2,100 particles trapped, forming a spindle-shaped region. (c) Image with laser for t = 5′00″, about 5,150 particles trapped. (d) Image with laser for t = 15′00″, about 10,150 particles trapped. Trapping process is almost saturated. The dashed curve shows the spindle-shaped trapping region, and the white dashed arrows indicate the maximum diameter of the spindle-shaped region with a = 290 µm and the minimum one b = 100 µm. The inset shows the image for t = 15′05″ with a 50× objective, showing that the distance between the center of the trapping region and the end of the fiber is d = 380 µm. The red arrow in the inset indicates the propagation direction of 1.55-µm wavelength of light.

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2.3. Results

The average moving velocity of particles was obtained from the video records of the experiments. Figure 3 shows the average velocity (V) of individual particles moving toward the assembly region in y direction (transverse, as shown in the inset of Fig. 3) versus operating distance (d, from the particles to the center of the spindle-shaped region). It can be seen that, for a given time t, as d decreases, V increases first, and then decreases. V achieves a maximum value (denoted as V _m) at a certain d (denoted as d _m). This is because far from the assembly region, the main force exerted on particles is F _P, which is directed towards the assembly region and speeds up the particles. While near the assembly region, a strong temperature gradient appears due to the strong absorption of light by water which generates another force (F _T) directed outside the assembly region, and works against F _P. So particles gradually slow down. Figure 3 shows that V _m decreases from 20.5 to 9.8 µm/s when t increases from 1′00″ to 7′00″, while d _m decreases from 188.3 to 159.2 µm. This is because the area of the assembly region increases as t increases, and the assembled particles gradually reduce the extension of light. Thus, the F _P exerted on the particles reduces, and consequently, particle velocity and d _m decrease. In the experiment, we further found that the moving velocity of particles in both side of the assembly region with the same distance to the center along y axis is almost the same. This is because the light distribution in both sides of the axis along the fiber is symmetric. While in the sides along x axis, the intensity of light gradually decreases, so the velocity in the left side is lower than that of the right side, and consequently, the left tail of the spindle-shaped assembly region is longer than that of the right as shown in Fig. 2 and the inset of Fig. 4 . However, we cannot obtain the complete velocity distribution along x axis due to the limitation of the microscope’s visual field (320 µm × 240 µm for a 200× objective).

 

Fig. 3 The average velocity of individual particles in the transverse direction (y direction) at different time of the laser injected with the distance d to the center of the trapping region. The inset shows the image for t = 4′00″, indicating the center of the trapping region, x and y direction.

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Fig. 4 (a) Histogram of trapped particles number versus the time of the laser injected with different optical power. (b) The assembling speed at different time of the laser injected with different optical power.

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To test the trapping capability, different optical powers (1.55-µm wavelength light) were injected into the suspension through the same tapered fiber. Experiments indicate that lower input power can also trap particles. However, since the area radiated by light with a lower power is relatively smaller, so fewer particles can experience the photothermal effect induced by the light. As a result, the trapping efficiency is relatively lower compared to a higher input power. The numbers of trapped particles were counted for the experiments with different input powers (obtained from the video records of the experiments). Figure 4a shows the histogram of the number with the time of optical power applied. The trapping process achieves saturation in 15.0, 13.5, and 11.5 mins for the situation of 170, 150, and 100 mW input power, respectively. Corresponding trapped particles are about 10,150, 6,550 and 2,600. Further experiment results show that very high input power can result in an obvious convection which will interfere with the trapping process, and thus cannot be used to massive particles trapping. We have also calculated the assembly speed (the number of particles assembled in the spindle-shaped region per second) of particles at different time of optical power applied (Fig. 4b). Higher input power can result in a higher assembly speed. The assembly speed reaches a maximum value at t = 3.1, 5.1, and 5.5 mins for the input powers of 170, 150, and 100 mW, respectively. The corresponding maximum assembly speeds are 22.1, 14.8, and 7.4 ind./s. When the trapping process has tended to saturation, the assembly speed tended to zero.

2.4. Massive migration

After the trapping and assembly of particles, a particularly important process is the migration of the assembled particles. This process can be realized by moving the tapered fiber through tuning the microstage showed in Fig. 1a. Figure 5a shows the original saturated state of the trapping process (the same as the inset of Fig. 2d) with the input power of 170 mW. When the fiber was shifted to a new location with a distance of 112 µm along –y direction (Fig. 5b) while remaining the optical power unchanged, a new equilibrium location for F _P and F _T was formed on the extension line of the tapered fiber. As a result, the assembled particles were migrated to a new location. Figure 5b shows the image of t _m = 0′07″, where t _m denotes the duration of particle migration. When t _m = 0′20″ and 0′40″, about 60% (Fig. 5c) and 90% (Fig. 5d) of the assembled particles were migrated to the new location, respectively. When t _m = 1′05″, almost all of the assembled particles were migrated to the new location (Fig. 5e), with only an extremely small part left in the original location (the residual particles shown in Fig. 5d). The whole migration process took 65 s. The detailed migration process is shown in Media 2 (from t _m = 0′02″ to 0′22″). It is noted that there is a trace left at the original location of the assembled particles (shown in Fig. 5f). This is because the assembled particles were deposited on the glass slide due to gravity as time goes by, and a few of the particles were adhered and residual on the slide during the migration. To realize a high migration efficiency and the opposite direction migration at the same time, the fiber was moved to another new location with a distance of 172 µm along the +y direction. Figure 5f shows the image of t _m = 1′10″. When t _m = 1′35″, 2′05″, and 2′45″, about 20% (Fig. 5g), 60% (Fig. 5h), and 95% (Fig. 5i) particles were migrated to the new location, respectively. When t _m = 3′25″, almost all of the assembled particles were migrated to the new location (Fig. 5j). The detailed process of the second migration is shown in Media 3(from t _m = 1′05″ to 1′25″). The migration distance is much larger and the efficiency is much higher than that reported previously in Ref. [20]. These experiments indicate that a tapered fiber can be used for massive particles trapping and migration with high flexibility and efficiency.

 

Fig. 5 Optical microscope images for different massive migration process (input power kept at 170 mW). (a-e) Migration along –y direction, detailed process is shown in Media 2 (from t _m = 0′02″ to 0′22″). (a) Image for migration time t _m = 0′00″, trapped particle and the fiber are at their original locations. (b) For t _m = 0′07″, the fiber was moved with a distance of 112 µm, the white dashed line indicates the original location of the fiber while the white arrow indicates migration direction. (c) For t _m = 0′20″. (d) For t _m = 0′40″. (e) For t _m = 1′05″, particles migrated with a distance of 112 µm, dashed spindle-shaped region indicates the original location of the trapped particles. (f-j) Migration along the +y direction; the detailed process is shown in Media 3 (from t _m = 1′05″ to 1′25″). (f) Image for t _m = 1′10″, the fiber was moved with a distance of 172 µm, blue dashed line indicates the original location of the fiber while the blue arrow indicates migration direction. (g) For t _m = 1′35″. (h) For t _m = 2′05″. (i) For t _m = 2′45″. (j) For t _m = 3′25″, particles migrated to the new location (172 µm to the original location), the blue dashed spindle-shaped region indicates the location of the trapped particles at the beginning of the second migration.

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3. Discussion and explanation

To explain the massive trapping process, a schematic illustration is given in Fig. 6 . Light outputted from the tapered end of the fiber will propagate in the water with a long distance and a large diverged area, and thus affect the particles in a large region. Besides, part of the light propagated along the tapered region will also be leaked outside from the fiber, thus, particles around the fiber will also be affected. The light intensity distribution is schematically shown with different color in Fig. 6. The radiated silica particles (nearly transparent to 1.55-µm wavelength of light) will experience a negative photophoretic force (F _p, blue arrows). Meanwhile, due to the strong absorption of the 1.55-µm light by water (absorption coefficient α = 10.9 cm⁻¹ [23]), the temperature of water will increase a different value due to the different light intensity distribution, and thus, a temperature gradient will occur in water. This temperature gradient will generate a force (F _T, black arrows) [17,18]. F _T works on particles against F _p, which leaves a resultant force (F, pink arrows) exerted on particles. Far away from the fiber, the temperature gradient is not obvious, and the main force exerted on particles is F _P, which traps particles to the stronger region. As light becomes stronger, the temperature gradient becomes more obvious and F _T becomes stronger. In region I and IV indicated in Fig. 6, F gradually changes its magnitude and direction, and consequently, particles in these regions move toward Axis (the gray dashed line) in a curved trajectory (the white dashed curved arrow), which is consistent with our experiment results. Once particles are trapped around the Axis, F _T and F _P are almost in a line but in the opposite direction. In the region near the end of the fiber (region II), F _T is larger than F _P, so F is directed away from the fiber, and thus, particles moves to the left and are trapped where F _P and F _T achieve equilibrium (denoted as Position E). While far away from the fiber end (region III), F _P is larger than F _T, and particles moves to the right till trapped in Position E. Particles aside Position E vertical to the axis (y axis direction) move directly to the location since F _P is directed to it while F _P is directed opposite to it. As a result, particles in the entire light radiated region are trapped to Position E, and finally assembled at Position E.

 

Fig. 6 Schematic illustration of the trapping process. The color bar represents the intensity of light from the tapered fiber, the blue arrows represent F _P, and the black arrows represent F _T, while the pink arrows represent the resultant force F exerted on particles. The white dashed curve represents the trajectory of some particles, and I−IV indicates different regions with particles.

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To understand and explain the experimental observations better, a theoretical model has been given with a two-dimensional finite element simulation (COMSOL Multiphysics 3.5a). The refractive indices of the water and the tapered fiber are set to be 1.33 and 1.44, respectively. Figure 7a shows the simulated electric field distribution at a power of 170 mW which was injected into the 3.1-µm diameter tapered fiber. It can be seen that the light outputted from the fiber focuses a little first (the focal spot is 180 µm away from the fiber tip), then diverges to a large area and becomes weaker gradually. The light in the large diverged area can affect the motion of the particles in water. Once the light radiated on the silica particles which has a low absorption for the 1.55-µm wavelength of light, each particle acts as a microlens and focuses the radiation to the rear side of the particles as shown in Fig. 7b, leaving a part of hotter surface and resulting in a negative photophoretic force (F _p). The force F _p is 5 orders of magnitude larger than the optical pressure force with the same radiated power [13]. Compared with F _p, the optical pressure force exerted on particles can actually be neglected. Thus each particle will be trapped towards the stronger light region as schematically shown in Fig. 6. Since light far from the fiber tip is attenuated a lot as shown in Fig. 7a, thus the optical force and thermal response are very weak in this region. However, since the photophoretic force is much stronger than optical force, weak light existing at about 600 µm to the fiber tip can also generate a negative photophoretic force, which is large enough to trap the silica particles far from the fiber tip towards the light intensity region, forming the localized trapping and assembly.

 

Fig. 7 Two-dimensional simulation results of light distribution and estimated temperature variation. (a) Electric field distribution of the 1.55-µm wavelength of light outputted from the 3.1-µm diameter tapered fiber. (b) Electric filed distribution of the 1.55-µm light radiated on a single silica particle (2.08 µm in diameter) suspended in water. (c) Power flow S and estimated temperature variation ΔT, the zero point of x axis is set at the focal spot (not fiber tip).

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Due to the strong absorption of the 1.55-µm light by water, a different temperature increment will be appeared in water due to the different distribution of light intensity. This temperature increment can be approximated to be [22]

where

The temperature variation (ΔT) along the Axis is also shown in Fig. 7c. It can be seen from Fig. 7c that the temperature variation far from the focal spot is small, but weak light still exits (Fig. 7a), so the dominate force exerted on particles is F _p. While near the strong light distribution region, the temperature variation is large. The large temperature gradient (as large as 0.11 K/µm) generates a force F _T [17,18] working against F _p, thus particles gradually slow down, and at last stopped (trapped) at the Position E (shown in Fig. 6). Since the strong light distribution forms a spindle-shaped region as shown in Fig. 7a indicated by dark dashed line, therefore assembly region of particles is a spindle-shaped region. This is consistent with the experimental results shown in Figs. 2 and 5. It should be noted that since the simulation is carrier out without particles in water, while in the experiment, particles in water can scatter light to a farther region, thus the simulated distance between the assembly region and the fiber tip (about 280 µm) is less than that of the experiment (380µm).

It should be further noted that though the sample is in an open structure. Since the sample size we used is much larger (a hemisphere shape, average diameter: 3.2 cm, maximum thickness: 2.5 mm) than that of the tapered fiber (diameter: 3.1 µm), and the experimental time is less than 20 minutes, so the effect of convection and evaporation is much weaker than that of the photophoresis and temperature gradient. Therefore, the massive trapping and migration process was induced by photophoresis and temperature gradient.

4. Conclusion

We have experimentally demonstrated a method of massive photothermal trapping and migration of dielectric particles with high flexibility and efficiency. With the help of negative photophoretic force and temperature gradient force generated by the light outputted from a tapered fiber, particles suspended in water were trapped with a highest moving velocity of 20.5 µm/s, and a maximum assembly speed of 22.1 ind./s. The number of assembled particles has increased by four orders of magnitude in 15 mins with an input power of 170 mW. By simply shift the fiber through tuning a microstage, almost all of the assembled particles can be migrated with a distance of 172 µm in 140 s. The experiment was based on 2.08-µm silica particles (nearly transparent to 1.55-µm wavelength of light), but this method is applicable to other particles, bacteria, or biological samples with low absorption coefficients to 1.55-µm wavelength of light. This technique can be easily used for accumulation and transportation of microscale particles or biological samples with little harm to the biophysical circumstances, and further be used for massive trapping and removal of particles or bacteria from water. Beside, since particles with different diameters and different refractive index have different photophoretic forces and velocities, this technique can be used as a particle massive sorting tool. Since the magnitude of the viscous drag forces under “flow” conditions may limit the applicability of this concept, thus this technique may face challenge in applying in a condition with a strong flow.