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Abstract
We present an experimental study on opto-thermal oscillation and trapping of light absorbing particles. The oscillation is a three-dimensional motion in the solution. The particles at the lower substrate of the sample cell are driven towards the center of optical trap by the optical force. When the particles arrive at the location near the trap center, the laser heating on the particles results in a strong thermal gradient force that repels the particles to leave the focus spot. Next, the particles slow down under the viscous drag force. At last, the particles settle to the lower substrate of sample cell due to gravity, and restart the new oscillation process. For opto-thermal trapping of the absorbing particles, the particles are dispersed in a thin cell to compress the convention and enhance the viscous resistance. The particles can be trapped close to the spot due to the balance of optical and thermal gradient forces.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Control over mechanical motion of microparticles with laser beams is important for many fundamental investigations and practical applications. Light-to-work conversion can involve either direct transfer of optical linear and angular momentum or indirect opto-thermal effects. Optical trapping and rotation are the typical methods of direct transfer of optical momentum. Optical manipulation technology provides a driving force to deliver or trap small particles in a contactless way [1–17]. The optical tweezers can generally be regarded as the result of the balance between the optical gradient force and scattering force [18]. Optical tweezers are usually used to trap and manipulate transparent particles such as cells or colloidal particles. In recent years, there has been an explosion of interest in investigating the manipulation of absorbing particles (APs) by light [19–36]. The controlling of APs usually utilizes the opto-thermal effect, which is a two-step process [37]. The photon-surrounding and photon-APs interactions build a temperature field and drive the APs under the temperature field. It has been shown that the motion of APs is sensitive to the various factors such as the solvent composition [33], thermocapillary effect [32], photothermally induced bubbles bursting [24], and local temperature gradient [28]. By regulating these factors, the APs can be acted as rotators [25,26] or oscillators. The APs can oscillate in the solution by the synergic effect of optical forces and explosive vaporization of the cavitation bubbles [24], or under the action of light induced photophoretic force [34]. By regulating the optical and thermal forces, a Janus particle can acted as a microscale elevator [11]. Furthermore, the APs can oscillate at the water-air interface, which can be relied on the photothermal Marangoni propulsion force and restoring force tuned via surface curvature [32], or under the cooperative action of optical gradient force and thermal gradient force [28].
In the above approaches, focused laser beams were usually used to control and drive the APs. A focused beam may have the following two effects on the APs: first, the optical force, including optical gradient force and scattering force [38]. The optical gradient force points toward the laser focus center. Second, the thermal effects, mainly originating from laser heating on the APs. It is always a positive force pushing APs away from the laser focus center. By modulating the forces on the APs, different motion behaviors of the APs can be achieved. In the previous investigation [28], we have shown that the APs can oscillate at the water-air interface under the optical and thermal gradient forces. Here, we demonstrate that an AP can be controlled as an oscillator in the solution by modulating the optical force. The optical force on the APs is modulated by changing the height of the laser focus center. The APs oscillate mainly under the action of the optical force, thermal gradient force and gravity.
2. Experiment method
Our optical tweezers setup is based on a homemade microscope. A 1064-nm laser (CNI, MIL-N-1064, TEM$_{00}$, cw, Changchun, China) with the beam waist 3 mm was used as the laser trapping and heating source. The beam was expanded to fulfill the pupil of objective (8 mm) with the beam expander. The beam expander was constructed with two lens (L1 and L2, f$_{L1}$ = 30 mm, f$_{L2}$ = 100 mm). The beam was reflected by mirrors M1 and M2 into the homemade microscope, and reflected upward by a dichroic mirror to a microscope objective (LUMFLN, water immersion, 60 $\times$, NA = 1.1, Olympus, Japan) and focused into the sample cell. The sample cell was mounted at a three axial stage. The images were recorded by a CCD camera, and acquired by the movie capture software. The laser power can be changed with an adjustable power attenuation and measured at the pupil of the objective.
Fig. 1. (a) Experimental setup. Instrument layout showing optical paths for 1064 nm trapping laser and LED lamp for bright-field imaging. PA, power attenuation; BE, beam expander; M1-M2, mirrors; L, lens; MO, microscope objective; DM, dichroic mirror; (b) Schematic description of oscillation. The green dotted line is the particle motion trajectory. The arrows indicate the direction of AP movement.
The samples were a diluted suspension of APs. The APs used in the experiments were core-shell magnetic microspheres (polystyrene@Fe$_3$O$_4$, 4.0-5.0 $\mu$m in diameter, BaseLine Company). According to the TEM image of the particles in the product manual, the particle is a spherical polystyrene core, surrounded by an absorbing spherical shell (Fe$_3$O$_4$) uniformly. The beads were washed and resuspended in aqueous solution. Two sample cells were used with different thickness in the experiments. The thick sample cell was prepared using a homemade circular trough with an inner diameter of 10 mm and height of 1 mm. 200 $\mu$L diluted suspension was injected into the trough and sealed with two coverslips. The thin sample cell was without the inner. About 15 $\mu$m thick solution layer was sandwiched between two coverslips. 30 $\mu$L suspension was dropped on a coverslip and then covered with another coverslip. The suspension drop was pressed to the thin sample cell with thickness about 15 $\mu$m between the coverslips. The experiments were performed at room temperature.
3. Results and discussion
The APs are mainly exerted by the following forces: first, the optical force, including the optical gradient force and scattering force. The optical gradient force points to the laser focus center, and the optical scattering force follows the direction of light propagation. Second, the thermal gradient force close to the focus center, can be decomposed into two components. One of the thermal forces is generated by the absorption of the surrounding medium, and the another one is caused by the inhomogeneous heat absorption on the APs’ surface. The thermal gradient generated by the absorption of surroundings is much weaker than the thermal force generated by inhomogeneous absorption on the APs’ surface. The thermal gradient forces point away from the trap center. Furthermore, there is a convection current [39], which can drag the APs towards the spot center at the lower substrate. Third, the gravity. Fourth, the moving APs are dragged by the viscous drag force in the solution.
3.1 Oscillation
The density of APs is larger than that of water, so most of the APs settled to the lower substrate. If an AP feels the optical force, it will move towards the trap center. If the laser power was smaller than 200 mW, the AP will be stably trapped by the optical tweezers [28]. The stable three dimensional trapping can be attributed to that the optical gradient force was larger than the thermal gradient force at low power. For larger powers than 500 mW, the surrounding water would be heated to a superheated state. There may be bubbles forming at the APs’ surface when the APs were near the trap center. The bubbles exploding pushed the APs far away from the trap center, where the APs can no longer feel the optical trap force. The repelled AP can not move towards the trap center again. The laser power for oscillation of APs was between 200 mW and 500 mW.
The process of oscillation can be described as in Fig. 2(a). An AP moves toward the trap center under the optical force at first. As the AP approaches the trap center, the AP will be repelled by the strong thermal gradient force to leave the trap center quickly. Next, the particle is decelerated by the viscous drag force. Then, the particle slowly settles to the lower substrate of sample cell due to the gravity. The particle is propelled towards the spot center by the optical force again. The AP is repeatedly propelled, repelled and settled in the solution. One example of the oscillations is shown in Fig. 2(b) (see Visualization 1). The laser power was 200 mW, and the height of trap was 10 $\mu$m. Before the laser working, the particle was imaged obscurely at the lower substrate of sample cell. When the laser tweezers began to work, the particle gradually moved towards the trap center before it arrived at the minimum deviation displacement (R$_{in}$). Then the particle was repelled away from the trap center to the maximum deviation displacement (R$_{max}$). At last, the particle settled to the lower substrate to begin a new oscillation.
Fig. 2. Oscillation of an AP. (a) Schematic of the oscillation. An AP in the sample cell is moving along the lines (positions 1-4). The presented forces are the dominated forces at each stage of particle motion. F$_g$, gravity; F$_{op}$, optical force; F$_{drag}$, viscous drag force; F$_t$, thermal gradient force. (b)(see Visualization 1) Images of an AP at different time-points (corresponding to positions 1-4 in Fig. 1(a)). At the beginning, the AP was at the lower substrate of sample cell, which was below the imaging plane (pos. 1). The AP moved towards and then was repelled away the trap center (pos. 2). The AP slowed down until it reached pos. 3. The AP settled down to the lower substrate of sample cell again (pos. 4). The arrows indicate the motion direction. The circle indicates the focus spot. Scale bar, 5 $\mu m$. (c) Distance of the AP from trap center projecting in the imaging plane. R$_{min}$ and R$_{max}$ are the two oscillation peaks projecting in the imaging plane. T is the oscillation period. (d) The relation between the T and R$_{max}$ at laser power 200 mW.
It should be noted that the APs were not moving in, but above the imaging plane when the APs were repelled away from the spot center by the thermal gradient force. A Cartesian coordinate system is established with the focus spot center as original point. The z direction is along the laser beam propagation direction, and the imaging plane is set as the x-y plane. We employ the projected values of the APs’ location at the x-y imaging plane to investigate the property of APs’ oscillation. The deviation displacements of the AP from the trap center in x-y plane were calculated by ImageJ software. The deviation displacements has been shown in Fig. 2(c). The oscillation period T is defined as the time interval between two repulsion events. The relationship between R$_{max}$ and T is shown in Fig. 2(d) for an AP oscillation at laser power 200 mW. It can be seen that T is increased as the R$_{max}$ increases. Larger R$_{max}$ means that there is larger axial displacement, and it will spent more time to settle to the lower substrate. In addition, the increase of T also includes the time increase for the APs moving between R$_{max}$ and R$_{min}$.
The oscillation of APs depends on the characters of APs, trapping depth and laser power. In the experments, the values of R$_{max}$ and T were measured at different laser powers for the same particle at the same trapping depth. One of the results is shown in Fig. 3. Each power has at least 15 oscillation events. The values of R$_{max}$ and T reduce synchronously with the laser power increasing.
Fig. 3. The property of the AP oscillation. (a) R$_{max}$ as a function of laser power. (b) T as a function of laser power.
The oscillation is affected by the absorbing layer of APs. The proportion of polystyrene core affects the optical gradient force, whereas the proportion of Fe$_3$O$_4$ shell strongly affects the thermal gradient force. The uniformity of the particles’ surface may induce the different oscillation amplitude and period at the same depth and laser power. Furthermore, the oscillation is affected by the size and weight of APs. In the experiments, two APs were adhered together, and can oscillate induced by the opto-thermal tweezers. At the same power and trapping depth, the R$_{max}$ of the two adhered-APs was significantly smaller than the amplitude of the individual APs. The reduction of R$_{max}$ can be attributed to the increase of oscillator’s weight. The repulsion impact at R$_{min}$ are almost equal for each oscillator, and the maximum deviation displacement R$_{max}$ should be reduced for the heavier particle. When the size of APs is small, the AP will be strongly disturbed by Brown motion at their settling process, and the oscillation can not be established.
If the initial position of the AP was just below the optical trap, the particle was pushed by the optical force to the optical trap center when the laser started to work. Then the particle moved backward to the lower substrate by the thermal gradient force. The oscillation of the AP became an one-dimensional motion along the z axis.
3.2 Trapping
The optical trap was generated with the tightly focused beam. When the beam was focused inside the sample cell, the irradiating area of laser beam at the lower substrate of sample cell was much larger than that of focused spot in the solution. The APs under the laser irradiating should be pushed from the lower substrate towards the trap center. However, when the trapping depth was larger than 30 $\mu$m, it was difficult to observe the oscillation. The larger trapping depth means that the AP will spent more time to arrive the location R$_{min}$. The AP obtains larger axial momentum at R$_{min}$, which induces the axial displacement at R$_{max}$. The large axial displacement exceeds the field depth of the objective, so the oscillation can not be observed.
The trapping depth should be larger than the radius of AP for oscillation. When the trapping depth is decreased down to the radius of AP, the AP should be trapped. There should be a location, where the thermal gradient force can be balanced with the optical gradient force. However, the APs can not be trapped stably in the thick sample cell. The reason can be attributed to the existence of thermal convection. The thickness of sample cell is decreased to reduce the heat convection [40]. Furthermore, the reduction of thickness of the cell can also enhance the viscous resistance [41] when the APs move to trap center by the optical force. When the thickness of sample cell is smaller than 10 $\mu$m, the opt-thermal trapping of the APs can be achieved.
The opt-thermal trapping and manipulation of an AP are shown in the Fig. 4. The laser power was 450 mW. The trapping depth was about 2 $\mu$m in Fig. 4(b), and an AP was imaged clearly. When the AP moved towards the trap center, the AP can be confined at the edge of focus spot, as shown in Fig. 4(c). The stable trapping was the result of balance of optical and thermal gradient forces. It is worth noting that unlike regular optical trapping, the AP was not confined in the trap center. There are several stable trapping location, which are distributed around the focus spot. The bright spot in Fig. 4 is the focused spot. The trapped AP can be manipulated in x-y plane. The manipulation process is shown in Figs. 4(d)–4(f). As the sample cell moved, the surrounding particles were moving with the sample cell, but the trapped AP was confined by the focus spot of laser beam. The trapped AP may change the location when there was enough viscous drag force exerted on the AP. The trap can confine multiple APs. When several APs were stably confined, they formed an ordered arrangement due to the repulsion interaction between the APs. The opt-thermal trap is a two dimensional trap. When the trapping depth increased, the stable trapping was destroyed and the APs began to oscillate.
Fig. 4. Two dimension trapping and manipulation of an AP. (a) Schematic of the trapping. An AP in thin cell moves towards and is trapped close to the trap center. (b-c) Images of trapping of an AP. The arrow indicates the particle’s moving direction. (d-f)(see Visualization 2) Video sequences showing manipulation of the trapped AP. The white arrows indicate the sample cell moving direction, which the same surrounding particle moved in the same direction. Scale bar, 10 $\mu m$.
When the laser power was larger than 500 mW, the trapped AP began to vibrate with high frequency. We think that the temperature of the particles surface is 100 $^{\circ }$C, and there are bubbles generated at the surface of APs. The vibration may be due to the enlargement and shrinking of the generated bubbles. The trapping became unstable. The APs were repelled away from the trap center with the increasing laser power. The repulsion distance exceeded the action range of optical force, and the AP can no longer be attracted to the trap center. When the laser power was below 200 mW, the tweezers no longer confine the APs at the edge of spot in x-y plane. The optical trap became a regular three dimensional optical trap. The AP was not trapped at the geometric center of the spot, but was at the location with small deviation displacement above the geometric center in the axial direction. The APs were not burned by the focused laser beam due to the axial deviation displacement.
3.3 Force estimation and simple model
The transmittance of the objective is 60$\%$ at wavelength of 1064 nm, so laser power on the particle is 120 mW when the laser power is 200 mW at the pupil of objective. According to the previous result [28], the transverse optical stiffness $k_x$ is about 0.08 $pN/(\mu m\cdot mW)$. It can be estimated that the optical gradient force and the thermal gradient force are both about 0.2 pN/mW. When the laser power is 200 mW at the pupil, the thermal gradient force is about 24 pN. The axial optical stiffness $k_z$ is about 1/3.6$\times k_x$ = 0.02 $pN/(\mu m\cdot mW)$ according to the measurements of the optical trap stiffness [23]. When the power is less than 200mW at the pupil, the optical trap can stably trap the APs, and the axial deviation is about 1 $\mu m$ from the focus venter, so the optical scattering force $F_{sc}$ is about 2.4 pN. According to the parameters of the AP, the radius (r) is 2.5 $\mu m$, the effective density ($\rho$) of the AP is 1.463 $g/cm^3$, the volume of the AP is v=$4\pi r^3/3=65 \mu m^3$, so the gravity $F_g=\rho \texttt {v}g$=0.9 pN. The optical scattering force is larger than gravity, so the APs can be pushed by the scattering force toward the focus center. The thermal gradient force is larger than the scattering force, so the APs will be pushed away from the optical trap when they reach the focus center.
Due to the good thermal conductivity of water, the thermal gradient force generated by the light absorption is small and can be neglected when the deviation displacement of particle is larger than the range of thermal gradient force (R$_{t}$). However, the optical force at R$_{t}$ can not be neglected, so we assume the range of the optical trapping force (R$_{o}$) is larger than R$_{t}$. It can be seen that the optical gradient force and the thermal gradient force were balanced at x = 2.5 $\mu m$ in Fig. 4. Therefore, we think that the critical range of thermal gradient force R$_{t}$ is about 2.5 $\mu m$. However, the action range of optical gradient force is much larger than the radius of the microsphere [42,43], so the critical range of the optical trap gradient force R$_{o}$ is greater than R$_{t}$. The APs are no longer exerted by the thermal gradient force after the APs leave R$_{t}$, but are still exerted by the optical trapping force before they arrive R$_{o}$. The APs are exerted by the optical trapping force except the dominated viscous drag force during the deceleration to R$_{max}$. The decrease of R$_{max}$ can be attributed to the enhancement of optical trapping force with increasing laser power. According to the previous analysis at laser power 200 mW, T is decreased with the decreasing R$_{max}$, so T decreases when the laser power is increasing in Fig. 3. The precise model is highly complicated. The heating is not a continuous one but accidental only when the particle will approach the beam waist. If more displacement information and velocity are obtained, and the thermal gradient are measured, the precise model may be established based on thermo-osmotic flows at boundary [44,45].
4. Conclusion
In conclusion, we present the opto-thermal oscillation and trapping of light absorbing particles in this letter. It is different from the oscillation of the APs at the two-dimensional interface, the oscillation of the APs in the solution is a three-dimensional motion. The APs at the lower substrate of the sample cell are driven by the optical scattering force and the optical gradient force to move towards the trap center. Due to the drastic enhancement of the light intensity at the location near the trap center, the asymmetric heat absorption on both sides of the particles induced a great temperature gradient, which repels the APs away the trap rapidly. The movement speed of the APs slows down to zero under the action of the optical gradient force and the viscous drag force. Then, the APs slowly settle to the lower substrate of the sample cell due to gravity and restart a new oscillation process. The period and amplitude of the APs oscillation are depended to the laser power and the trapping depth. Furthermore, two-dimensional trapping of APs can be achieved when the thickness of the sample cell is smaller than 10 $\mu$m. The particles are trapped in the x-y imaging plane with the trapping location at the edge of the trap center. The oscillation and trapping of APs were observed at laser power 200-500 mW. When the laser power is smaller than 200 mW, the optical tweezers can stably trap the APs in three dimensions, and the trapping position is above the focused spot center. When the laser power is larger than 500 mW, the two-dimensional trapping of the APs become very unstable due to the expanding and shrinking of generated bubbles at the surface of the APs under the laser irradiation. The results in this letter are useful for controlling the light absorbing particles, which may enable further studying behaviors of the light driven motors.
Funding
National Natural Science Foundation of China (11874138).
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