1. Introduction

Optical trapping (OT) and manipulation of particles has become an essential technique for research in the fields of life, physical, material, and environmental sciences since the pioneering works by Arthur Ashkin [e.g. 1–3]. The field of OT has developed rapidly in the last few decades, and the OT-Raman spectroscopy has been extensively applied to study the complex dynamic cellular processes in single cells and spores, to observe chemical reactions, phase transitions etc. in single airborne solid particles and droplets [e.g. 4–10]. OT-cavity ringdown spectroscopy (OT-CRDS) was able to measure the absolute optical extinction of single airborne particles, inorganic or organic droplets [e.g. 11], and the OT-elastic light scattering perceived the surface roughness and orientation of single particle via subtle variations of back-scattering patterns [12]. The optical tweezers-based trapping device for studying particles’ properties has been commercially available. More widespread adoption and application of OT can still be conceived.

To date, most laser tweezers are still used to trap relatively transparent particles in relatively transparent liquid. Trapping transparent particles in air using a single-beam gradient-force did not occur until 1997 [13]. Trapping a transparent particle in air is more difficult than in liquid because of its higher relative refractive index that leads to a strong scattering force, combined with a weaker drag force, i.e. smaller damping force in air than in liquid and all these forces tend to destabilize the trapping [14]. Therefore, producing sufficient gradient force to overcome the scattering force is the key to trap transparent particles in air. In general, there are three approaches: (1) using high numerical aperture (N.A.) optics (typically > 0.95) to provide a sufficiently strong gradient force [13,14]; (2) using a focused hollow beam (even with a relatively low N.A., typically > 0.55) created with a lens [15,16] or parabolic reflector [17], to achieve stable trapping in air by reducing the scattering force; and (3) with precise alignments and more optics involved, using counter-propagating dual-beam to stably trap airborne particles by canceling the opposite scattering forces [18–22]. For absorbing airborne particles, OT can be readily realized by using a single or dual-beam with various laser intensity profiles mainly based on the strong photophoretic forces [23–24].

However, using a single laser beam or the same optical setup to trap both transparent and absorbing particles in air regardless of their properties (size, morphology, materials, etc.) remains a challenge. Yet this versatile trapping capability is essential in OT instrumentation and real-world applications, such as real-time, on-line characterization of successively arriving airborne particles that are continuously sampled from air. Furthermore, the trapping efficiency and trapping robustness is as important as the versatility for OT. Redding et al. [16] were able to focus a single shaped laser beam to produce a low-light-intensity region for photophoretic trapping of absorbing particles, while simultaneously reducing the scattering force for gradient force trapping of transparent particles. However, the relatively weak restoring force in such a configuration, as shown in Fig. 2 of Ref. [16], cannot provide high trapping efficiency for transparent particles, especially for flowing through transparent particles with high refractive indexes (n > 1.5). Although a special opto-aerodynamic design was able to trap successively arriving absorbing particles that were continuously sampled from air [25], the system failed to trap successively arriving transparent particles at a reasonable trapping efficiency (>1%). In order to trap successively arriving transparent particles with high trapping efficiency (catch and trap at least 20% of the particles from continuously sampling) and high trapping robustness, we present an advanced optical trapping method. The new optical configuration used two parabolic reflectors to form two counter-propagating conical beams from a single hollow beam to achieve unprecedented trapping ability. Our design was capable of trapping both transparent and absorbing particles with arbitrary morphology.

2. Experimental arrangement

Figure 1 shows the schematic of the optical trapping apparatus using two focusing parabolic reflectors. Detailed alignments and dimensions of the two reflectors are shown at the top left. Either of the two reflectors was independently mounted on a stage that has the freedom for two-dimensional angle-tilting, and three-dimensional translation moving at 1 µm resolution. An expanded collimated beam (diameter = 13.0 mm) from a continuous wave (CW) laser (532 nm or 488 nm, ∼ 1 W) was formed using a pair of aspheric lenses. The beam was shaped into a collimated hollow beam with a diameter of 25.0 mm and a wall thickness of 6.5 mm using two axicon lenses. The hollow beam was directed to propagate upwards by a 45° placed mirror, then the inner part of the beam (dia. = 19.0 mm) was focused into an upward propagating (UP) hollow conical beam using parabolic reflector 1 (focal length = 2.0 mm, diameter = 12.0 mm - 19.0 mm), the beam was focused onto its optical axis at 2.5 mm above the reflector and 6.5 mm from its closest surface. Meanwhile, the outer part of the beam (dia. = 25.0 mm) was focused into a downward propagating (DP) hollow conical beam using parabolic reflector 2 (focal length = 19.0 mm, diameter = 5.0 mm – 30.0 mm). The axes of the two reflectors were aligned to overlap each other, and the two foci from the two conical beams were lined up along the optical axes of the reflectors with a vertical variable displacement ΔD ranging from −10 µm to 10 µm. A pin hole [14] or the smoke from a burning fiber was used for visualizing the alignment of the two conical beams. The two foci were positioned near the center of a containment glass chamber, which was used to minimize air turbulence near the trapping region. Both the top and bottom windows of the chamber had a circular hole of 4.0 mm in diameter. The two openings enabled particles to be introduced and removed from the chamber.

 

Fig. 1. Schematic of the optical trapping apparatus with the detailed alignments and dimensions of the two focusing parabolic reflectors. The images on the right side visualize (a) the foci of two conical beams overlapping each other; (b) a single 5-µm glass microsphere was trapped at the focal point; (c) the two foci were aligned with a displacement ΔD of ∼2 mm vertically; and (d) a single 8-µm glass microsphere was trapped at each of the two focal points.

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The images on the right side, in Fig. 1, show that two conical beams were aligned at ΔD = 0 mm (Fig. 1(a)); a single 5-µm glass microsphere trapped at the focal point (Fig. 1(b)); Fig. 1(c) shows an axial (or vertical) displacement (ΔD ∼ 2 mm) between the two foci; and Fig. 1(d) shows a 8 µm glass microsphere trapped at each of the two focal points. Reflectors 1 and 2 acted as focusing optics with an N.A. of 0.92 and 0.60, respectively. With relatively enough axial separation, as demonstrated in Fig. 1(d), either of the two reflectors is capable of forming an independent trapping for transparent airborne particles.

3. Numerical simulation

The trapping force acting on a spherical particle from one hollow conical beam (UP or DP only) or two beams with different displacement ΔD (axially) or ΔR (radially) were numerically simulated using the T-matrix method [26,27]. The trapping force is expressed in terms of the dimensionless quantity Q which is related to the actual force acting on the particle as F = QPn/c, where P is the incident laser power, n is the refractive index of the particle, and c is the speed of light [26,27]. The trapping force was first presented as the trap depth in Fig. 2, in which the colored-scale bar represented the relative strength of the trap depth. It was calculated from the axial force for different ΔD along the beam axis. The trap depth is a measurement of the minimum peak restoring force (i.e., the maximum force that can be applied to a particle in any direction before it escapes the trap). Trap depth is proportional to the trapping robustness of the setup. The method used here to estimate the trap depth only considered the axial force. This is sufficient for small displacements between the two beams (when the radial force exceeds the axial force), but for large axial (ΔD) or radial (ΔR) displacements, other methods are required for providing a more accurate estimation of the trap depth.

 

Fig. 2. Axial trap depth for the different particle sizes D at various refractive indexes n for (a–c) or at various axial displacements ΔD between the two foci for (d). (a) Only one upward propagating (UP) beam; (b) dual-beam with two foci overlapping each other; (c) dual-beam with a axial displacement ΔD = 5 µm of the two foci; and (d) at different ΔD for a particle with n = 1.5. The white shaded region bordered by the black line shows where the radial trap depth between the two traps is below 50% of the axial trap depth.

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In the simulation, the point matching method was used to calculate the vector spherical wave function representation of the conical hollow beams. When the two beams are aligned, the phase of both beams was assumed to be uniform and equal. When the upper beam is displaced vertically, an additional phase correction was added corresponding to the difference in the path length of moving the upper reflector 2. For horizontal displacements, no additional phase change was added. This assumption is only valid for small angles/displacements.

Figures 2(a-c) presents the calculated axial trap depth for different particle sizes (0.5–10 µm in diameter) with varying refractive indexes (n = 1.01 – 2.0). Where the force was from (a) only one upward propagating (UP) beam; (b) dual-beam with two foci overlapping each other; (c) dual-beam with ΔD = 5 µm; while Fig. 2(d) shows the axial trap depth for displacements ΔD from –15 µm to + 15 µm for a particle with refractive index of 1.5 and diameters from 0.5 µm to 10 µm. Here the trapping laser power in a single beam is the same as the total power in the dual-beam trapping. The white shaded region shows where the radial trap depth between the two traps is below 50% of the axial trap depth.

These simulations revealed that (1) dual beam trapping (Figs. 2(b-c)) can improve axial trap depth and extend the size and refractive index range of particles that can be trapped as compared to single beam trapping (Fig. 2(a)). Such a feature also means that dual-beam trapping with lower laser power can supply the same strength of restoring forces as single beam trapping with higher power; (2) The hollow beam trapping here (by both single- and dual-beam) works better for big particles (2-10 µm) than for small particles (0.5-2 µm); (3) Dual-beam trapping with a perfect alignment (ΔD = 0 µm in Fig. 2(b)) gives a similar force pattern as single-beam trapping (Fig. 2(a)). The main differences are: an extended range of particles that can be trapped by the dual-beam configuration, particularly for higher refractive index particles; and additional fringes due to the interference between the two beams. By adding a small phase difference between the upper and lower beam (e.g., by displacing the upper beam by a small distance), the trap depth can be optimized for a particular particle. (4) Single beam trapping is more favorable for low refractive index particles with n∼1.1-1.5, and dual-beam provides stronger trapping depth and extends the trapping to cover particles with refractive indexes n∼1.1-1.9. (5) When there is a small displacement between the two foci, the force pattern is shifted and benefits trapping particles with an even higher refractive indexes (around 1.2-2.0), and a small gap between the two foci (+ΔD) improves trap depth as shown in Fig. 2(d). Once the two foci are separated by more than the particle diameter, the radial trap depth starts to reduce. This configuration is similar to trapping large particles with dual beam holographic optical tweezers. Once the two foci are displaced in the opposite direction (so that the two foci overlapped at a -ΔD), the axial trap depth decreases, and in some cases particles are no longer trapped.

Figure 3 shows how the forces act on a spherical particle with dia. = 5 µm and n = 1.5 at different positions near the focal point using a single beam or dual-beam trapping. The length of the arrow indicates the relative strength of the force, and the arrow head points to the force direction. For such a particle, the UP beam (Fig. 3(a)) and DP beam (Fig. 3(b)) separately provide strong radial forces and strong axial forces in the beam propagation direction. However, the particle could not be strongly trapped as the force opposite to the beam propagation direction is relatively weak. The simulation illustrated how a single-beam trap only produce a weak axial restoring force even for relatively high N.A. focusing (0.92 max. for the UP beam), but barely noticeable restoring force for lower N.A. (0.6 max. for the DP beam). This drawback of using one trapping beam is overcome by using the dual-beam trapping configuration. Figures 3(c-i) shows the optical forces at different alignments with the same total power as Fig. 3(a) and 3 (b) but being split between the UP and DP beams. Figures 3(d-f) first explored the effects of different axial displacements between the two beams; while Figs. 3(g) and 3(h) demonstrated the results with different radial displacements; and finally Fig. 3(i) showed a combined displacement in both directions. It seems that the small positive axial displacements have negligible influence on the force strengths and directions, except for the extended force distribution along the axis (Figs. 3(d-e)). In contrast, a negative axial displacement resulted in a very small axial trap depth, as shown in Fig. 3(f). The force field distributions were very sensitive to the radial displacements, even it was as tiny as ΔR = 1.0 µm (Fig. 3(g)) or ΔR = 2.0 µm (Figs. 3(h-i)). It is apparent that the force was strongly asymmetrically distributed for the radial misalignment, and resulted in lower trapping efficiency. These results were also consistent with our experimental trials that a perfect radial alignment (ΔR = 0 µm) is more critical than the axial alignment. For trapping absorbing particles, the alignment between the two beams is not so critical, as they can always be readily trapped at some relatively low intensity regions by one of the two beams or the interference area of the two beams with any spatial intensity profiles mainly by the strong photophoretic forces, but the trapped positions could be slightly different for particular particles.

4. Results and discussions

A number of different types of dry particles, spherical or non-spherical, absorbing or non-absorbing (transparent), in the size range from one to a few tens microns were tested in this dual-beam trap. The tested particles were silica glass microspheres (Cospheric, n = 1.46); NIST-traceable borosilicate glass microspheres (Duke Scientific, n = 1.56); NIST-traceable polystyrene microspheres (Thermo Scientific, n = 1.59); Johnson grass spores (Greer, n∼1.55); volcanic ash collected from Eyjafjallajökull (n∼1.4-1.6); Bacillus subtilis (BG) spores (n∼1.55); Ragweed pollen (Geer); Fly ash (Particle information service, Inc.); Ground Ammonium sulfate (Sigma); Ground sugar (sucrose); and Arizona road dust (Powder Tech., Inc.). All particles were easily caught and trapped with high trapping efficiency (>50%) and strong trapping robustness. Figure 4 shows that particles with different sizes in the range of 1-30 µm in diameter were stably trapped.

 

Fig. 3. Two-dimensional force distributions on a spherical particle (dia. = 5 µm, n = 1.5) near the focal point using (a) the UP beam only; (b) the DP beam only; (c-f) dual-beam trapping with a displacement ΔD; (g-h) dual-beam trapping with a displacement ΔR; and (i) with a displacement in both ΔD and ΔR.

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Fig. 4. Various non-absorbing and absorbing particles with spherical or non-spherical shapes were trapped in air. (a) 1 µm silica glass spheres (dia. = 0.961 ± 0.030 µm), (b) ∼1 µm fly ash, (c) glass microsphere (dia. = 2 ± 0.5 µm dia.), (d) ∼5 µm ground sugar (sucrose), (e) glass microsphere (dia. = 5 ± 0.5 µm), (f) glass microsphere (dia. = 7.9 ± 0.8 µm), (g) ∼10 µm Arizona road dust, (h) ∼10 µm ground ammonium sulfate, (i) ∼10 µm volcanic ash, (j) glass microsphere (dia. = 10.9 ± 1.1 µm), (k) ∼20 µm single ragweed pollen, and (l) ∼30 µm dia. aggregate of Bacillus subtilis (BG) spores.

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In the experiment, we found that the trapping efficiency was very sensitive to the alignment of the two foci. A small axial displacement either positive (more effective) or negative helped particle trapping. This axial displacement ΔD (a few microns) is more favourable for trapping a larger particle (e.g., >5 µm). Once the dual-beam trapping was in an optimized alignment, which is defined as a perfect overlap of the two optical axes of the reflectors with no radial displacement (ΔR = 0 µm), there was almost always a particle being trapped once particles were dusted into the trapping area; however, the trapping efficiency dropped dramatically once the alignment of the two optical axes was off (ΔR ≠ 0). Using the definition of average trapping efficiency as a ratio of a successful trapping event over the number of attempts [23], the trapping efficiency in the current design can reach higher than 50% for transparent particles (2-10 µm), this is about 10 times higher than the single hollow beam trapping scheme using a relatively low N.A. (∼0.55) optical focusing [16]. This efficiency for trapping transparent particles is comparable to those in trapping absorbing particles in air, which relies on the much stronger photophoretic force, using dual-beam or confocal beam configurations [23]. The efficiency of the present method for trapping absorbing particles is nearly 100%.

Based on the aspects of simplicity, robustness, flexibility, and efficiency, which have been used to evaluate the optical trapping quality and performance of the different optical-trapping schemes [23], this new design holds all the advantages of simplicity, flexibility, and high trapping efficiency. In order to quantitatively analyze the trapping robustness as defined [23], a series of small amount of disturbing air was puffed into the chamber to test how robust the trapping was. The robustness was roughly estimated by gradually increasing the strength and puffing frequency of the air turbulence to check how far the particle could be pushed away and still be drawn back to the original position and stably trapped by the restoring force. Figure 5 (with Visualization 1) showed one typical test in which a particle was stably trapped initially, later it started to vibrate by a relatively weak air disturbance, then it was pushed away a few tens micron by the increasing disturbance but was still able to return back to its trapping position. Comparing with the other optical configurations using single hollow beam trapping [16,24], or dual-beam trapping using focused Gaussian beams with low N.A. optics [e.g. 17], this dual-beam trapping arrangement greatly increased the trapping robustness to be very strong. As the absorbing particles are trapped mainly by the strong photophoretic forces, the corresponding trapping robustness is also much stronger than the transparent particles.

 

Fig. 5. The moving behavior of a trapped particle under air disturbance (see Visualization 1).

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Here, the two parabolic reflectors were selected as the focusing optics instead of expensive microscope objectives (commonly used for OT), because they cannot only achieve a large N.A., but also can focus the beam far away from surfaces of all optical components (≥ 6.5 mm in this configuration) to minimize the possible sample contamination of the optics, while the working distance for high N.A. microscopic objective (>0.95) is only a few microns. In addition, a parabolic reflector can be arranged to focus light either forward as a lens (Reflector 1), or backward as a mirror (Reflector 2), such special features of the parabolic reflectors allowed us to create such dual counter-propagating conical beams from a single collimated hollow beam, without using any other optics as otherwise needed in typical dual-beam trapping setups for forming two beams. Contrasting to the most common dual-beam configurations, which focus two horizontally counter-propagating beams for trapping, this upward and downward counter-propagating arrangement took the advantage of the strong scattering force along the optical axis of the reflectors to balance the gravitational force, increasing the axial trapping robustness yet supplying low power trapping that benefits especially for studying live biological samples [19]. Meanwhile, introducing particles along the optical axis of the beams (from the conical opening) greatly increases the contact cross-section for catching particles [26] to the laser beam, which significantly improved the particle trapping efficiency. As the particle is trapped far away from the optical surfaces (or at a longer working distance), the system offers sufficient space and flexibility to be integrated with other laser spectroscopic techniques, such as Raman spectroscopy, for on-line trapping-enabled particle characterization.

5. Summary

In summary, an advanced optical trapping method was developed to trap both transparent and absorbing particles with arbitrary morphology. The inner and outer parts of the single hollow laser beam, were reflected, respectively, by parabolic reflectors to form two counter-propagating (upward and downward) conical beams and focus to a focal point. The usage of a single beam enabled relatively simple alignment and without the usage of optics for forming dual-beams, while it holds the advantages of dual-beam trapping with high efficiency and strong robustness. The vertical arrangement also allowed to introduce particles along the hollow focusing cone to increase the particle capturing rate. The parabolic reflector was also able to supply a large N.A. focusing while trapping particles at a far distance to minimize sample contamination, and more importantly to enable easy integration with other optical characterization spectroscopic techniques. Numerical simulations helped confirm the design of the optical arrangement and better understand the trapping force field that is particularly advantageous for highly efficient trapping of transparent particles in air. Experimental results demonstrated a good agreement with the simulations and further supported the following arguments: