1. Introduction

Many fields of research require the manipulation and sorting of particles that are much larger than single cells, including: small nematodes (C. elegans) and fly larvae (D. melanogaster) to obtain genetic variants [1], large cellular constructs such as tumor microspheroids to understand the tumor microenvironment [2,3], and ‘one-bead one-compound libraries’ for analysis of molecular interactions which are typically synthesized on microspheres greater than 100 µm in diameter [4]. For these applications current manipulation technologies limit the sorting rates to approximately 100/s at best down to a few particles/min at worst. This low sort rate is due to the inability to use conventional charge-based droplet-sorting approaches that require orifices large enough to prevent clogging (typically 5 times the particle diameter). These larger orifices suffer from turbulence that detrimentally affects droplet break off points [3,5–7]. These requirements significantly limit sorting particles greater than about 70 µm in diameter [7] and have led to the development of alternative sorting systems that use jets of air to divert a flowing stream which contains particles of interest hundreds of µm in diameter at rates of 5 particles/s [8]. While the particle size is impressive, the throughput remains low, preventing the sorting of very large particle populations. A ‘one bead one compound library’ can easily consist of several hundred thousand elements for example, which would require many days to sort using current technologies. A particle manipulation approach that can easily and selectively divert particles hundreds of µm in diameter at rates orders of magnitude faster than what is possible using current approaches is therefore needed.

For this reason we explore the limits of optical sorting techniques which have been previously based on scanning laser optical trapping [9] and holographic optical trapping [10] and limited to standard cell-sized particles (< 10 µm). To overcome this limitation, we instead employ diode laser bar optical trapping, a simple and inexpensive optical manipulation approach that is easily adapted to flowing particles [11,12]. These traps are created using linear, 1 µm wide, single laser emitters that range in length from 25 µm to 1 mm with output powers in the 10’s of watts. In this technique, the laser is focused into the sample in a manner that preserves the line shape, creating a long and linear trapping area over which particles can be manipulated. This approach has been effectively modeled for particle sizes up to 16 µm [13]; however, these traps can be up to 1 mm in length and it is expected that these can be employed to control much larger particles than possible using traditional, point optical trapping [11,12].

In this work, we mathematically model and demonstrate the expansion of diode laser bar optical trapping and manipulation into particle sizes up to 200 µm, an order of magnitude greater than previously demonstrated. Our expanded model predicts future modifications that will enable the manipulation of particles as large as 500 µm, which could eventually be used as the basis of fluorescence activated cell sorting (FACS). Additionally, this system could be used as a large particle passive sorter similar to microfluidic [14] and optical sieves [15] where much smaller particles (~2 µm) have been continuously deflected.

2. System schematic

Figure 1 illustrates the large particle diode laser bar optical trapping system. In this, the 5 W diode laser bar emitter (Laser Diode Incorporated, CW 5000-CM-00) is 460 µm by 1 µm and centered at a wavelength of 808 nm. The emitter output is collected and collimated by a singlet asphere (Thorlabs, C240TME-A) and focused into a 1 mm inner diameter square, glass capillary using a matching singlet asphere, preserving the beam size and shape. The sample consisting of the large particle solution is imaged through a 4x 0.10 NA DIN (or 10x 0.25 NA JIS) objective lens into a camcorder with IR filters used to block any high intensity laser light.

 

Fig. 1 Schematic of large particle diode laser bar trapping system

Download Full Size | PDF

3. Mathematical trapping force model extension

To model the diode laser bar optical trapping forces on large particles we expand upon previously published calculations [13] that are modified from the classic Mie ray-optics approach [16,17]. This model determines the total force on the particle by treating the laser light source as an infinite number of incident rays, parallel to the vertical axis, with the field modeled as a Gaussian of tunable size and focal position [13]. Calculation results for larger particles can be seen in Fig. 2 where the trapping force plateaus as particle size increases as expected due to the decreasing particle curvature relative to the fixed width of the focused laser spot line. As the particle size increases it encounters more light but the surface is flatter, lessening the refraction and the force imparted on the particle. This suggests that wider laser line widths can impart higher forces by extending illumination over a larger portion of the curved surface.

 

Fig. 2 Graph of calculated, resultant deflection forces for different line orientations and net gravity/buoyancy force vs. particle diameter for polystyrene particles. Points are discreet numerical calculations. Lines are smoothed curves that follow the numerical calculated model values.

Download Full Size | PDF

Unlike previous studies which used smaller particles to determine a ‘failure velocity’ in flow [12], we are exploring the use of a variety of large particles (>100 µm diameter) that rapidly settle out of aqueous solution. To create predictable velocities, we instead align our channels vertically and let particles settle through the solution due to the net forces of gravity and buoyancy acting on the particles. Different particle sizes result in different velocities and different forces required to trap the particles. Here, we define a breaking force, which is the optical restoring force normal to the trap long axis required to balance the gravitational force on the particle. In the simplest example with the laser perpendicular to the direction of particle travel, the breaking force equals the net gravitational force on the particle. If this net force exceeds that of the maximum effective trapping force however, the particle simply passes through the laser trap. By plotting both the expected net gravitational force and the trapping force as a function of particle size, particles that will be effectively trapped can be predicted (Fig. 2). Under the conditions we model in this example, we expect to efficiently trap particles less than ~120 µm.

As the laser line is rotated toward the particle flow direction, it does not directly oppose the particle flow. In this case, we consider the net force as the sum of two components, the breaking force perpendicular to the laser, and the transverse force parallel to the laser line. Here, the force balancing the net gravitational force, used for trapping particles, decreases as the trap angle increases. If however, the trapping forces remain greater than the net gravitational forces, the particles translate along the long axis of the laser and are moved like a conveyor belt, down the laser line as far as it extends. This predicted reduction of the breaking force can be seen in Fig. 2 where the calculated trapping force as a function of particle size is presented. Using polystyrene particles we model the gravitational forces to get a single curve opposing the laser trapping force, both of which are a function of particle size.

To test our model experimentally, we drop polystyrene particles of known size and composition through water and view them with a camera to determine which sizes trap and which do not. The failure point described by the model is the situation in which the laser will not trap nor deflect the particle of a particular size, at a specific angle. According to our predictions, placing the laser line at 0° would allow particles up to ~120 µm in diameter to be trapped. This was verified experimentally by dropping 100 µm particles and watching them trap, while larger, 200 µm particles did not. Placing the laser at 45° instead allows larger particles, up to 136 µm diameter, to be deflected by the laser. Again, because optical trapping occurs due to gradients in the optical field intensity, using a line optical trap instead of a round spot only traps particles along the short axis of the focal line, allowing them to move freely along the length of the line [11]. Thus we are exploiting the vector nature of the force and are able to deflect larger particles than in the perpendicular laser line orientation, which prevents particle translation.

Although various polystyrene particle sizes (10 µm, 42 µm, 55 µm, 100 µm, 134 µm, and 200 µm) were dropped through water in the glass capillary, the 134 µm diameter particle sample (Spherotech, Lake Forest, IL) was of particular interest. Consistent with our predictions, the 10 µm, 42 µm, 55 µm, and 100 µm particles all trapped easily and the 200 µm particles fell straight through the 0° laser line focus. Since the coefficient of variation (CV) of the 134 µm particle sample was 16%, they ranged in size from ~110 µm to ~160 µm diameter, encompassing the intersection of the 0° laser trap force and gravitational force as well as the 45° trapping force and the gravitational force. Using this sample very few particles trap at 0° (~1 in 10), while at the 45° angle, nearly all the particles were diverted. Additionally, the model suggests that orienting the laser at 75° would allow diverting of some of the 200 µm particles, while no other angle orientation attempted would. This was verified experimentally shown below, further confirming the model’s accuracy.

4. Optical trapping and manipulation of large particles

4.1 Stationary particles

The first account of optical trapping of particles larger than previously attempted (>> 20 µm) is shown below. We performed this experiment by creating a small parafilm well on a glass slide into which we placed 100 µm polystyrene particles and water, which quickly settled to the bottom of the well due to their size. The laser was then focused into the well, while the sample was moved, resulting in the translation of two, 100 µm particles within the trap (Fig. 3 ).

 

Fig. 3 (Media 1) Movie of 100 µm particles traversing through water by diode laser bar trapping imaged with 10x objective. The laser is left stationary while the sample is moved.

Download Full Size | PDF

4.2 Gravity opposition

Due to the predictable settling of large particles in water, we are able to verify our line optical trapping model by calculating terminal velocities for these particles of known density in a surrounding water medium. Particle settling velocities are 360 µm/s, 460 µm/s, and 1086 µm/s for the 115 µm, 130 µm, and 200 µm particles respectively. The model is then verified against the gravity and buoyancy force calculations.

In Fig. 4 a large particle, approximately 115 µm, is shown falling due to the force of gravity. The diode laser bar is left on, and when the large polystyrene particle encounters the laser it is immediately pulled into the trap and held stationary. When tested, 200 µm polystyrene particles (not shown in the figure) instead fell directly through the trap line, just as the model predicted.

 

Fig. 4 (Media 2) Movie of 115 µm particle falling and then being trapped by a diode laser bar against gravity imaged with 10x objective.

Download Full Size | PDF

4.3 Deflection for sorting

Since line traps hold particles in the short axis of the laser focus but allow them to move freely along the long axis, we can take advantage of the diode laser bar trap to sort falling large particles. Figure 5 shows a large particle (~130 µm) falling and being deflected across the capillary where, by simply turning the laser on or off, the sorting of large particles by deflecting particles into different outputs could be performed. Figure 6 further verifies the accuracy of the large particle deflection model, showing a 200 µm polystyrene particle being deflected by the laser trap line oriented at 75°.

 

Fig. 5 (Media 3) Movie of 130 µm particle being deflected across streamlines in 45° diode laser bar trap imaged with 4x objective.

Download Full Size | PDF

 

Fig. 6 (Media 4) Movie of 200 µm particle being deflected across streamlines in 75° diode laser bar trap imaged with 4x objective.

Download Full Size | PDF

4.4 Flowing particle predictions

Sorting however, can also be accomplished with flowing rather than settling particles and we include predicted flow rate limitations for various particle sizes and laser oriented at 75°. Figure 7 shows the velocities at which the laser can be used to deflect particles along with the laser force. This demonstrates that a 500 µm particle could be deflected at 75° across even a 500 µm/s flow.

 

Fig. 7 Optical trapping model force (triangles) and 75° drag forces vs particle size for different particle velocities.

Download Full Size | PDF

5. Conclusion

A model for diode laser bar optical trapping has been expanded and verified for particle size ranges significantly larger than previously attempted. This ability to optically deflect particles much larger than traditional single cell sizes is possible due to the long, linear shape of the laser focus. The optical deflection model implies that one can extrapolate the high-end particle size limitations of diode laser bar optical trapping methods. Particles over 100 µm in diameter are trapped and held within fluid, and particles up to 200 µm are deflected across a capillary demonstrating the potential ability to sort.

For sorting, simple trigonometry shows how far the particle can be translated across capillaries into desired outputs. Using our 460 µm diode laser bar oriented at 75° in the settling scenario, a 200 µm particle would be translated 119 µm. This is enough to sort, but for ease of design one may want to translate a particle one full diameter across streamlines. This could be accomplished either by using two 460 µm diode laser bars or a single 1150 µm, 10 W emitter (RPMC #LDX-4103-808). The theoretical throughput limits of such a system can be predicted by the settling rates of the particles and the size of the laser. Assuming the particles must be separated by a full laser distance to eliminate coincidence and for a 200 µm particle with a settling velocity of approximately 1 mm/s and a laser length of 500 µm, we predict sorting at 2 particles/s for a single sorting channel under ideal conditions without Poisson statistical limitations in particle arrival times. Flowing particle scenarios imply that with a single laser we would be able to sort one 500 µm particle/s, again keeping them spaced one diameter apart to avoid coincidence. Parallelizing this system with 5 lasers would be enough to sort 5 particles/s, and match what is currently commercially available [8]. In addition, the optical trapping technique has the advantage that it does not create aerosols, which present many safety concerns especially when dealing with biological samples. This technique could lead to a parallel sorting device using multiple, inexpensive, powerful lasers capable of high throughput particle sorting up to 500 µm for combinatorial chemistry, tumor microspheroid analysis, and many other applications. This would make a useful alternative, with abilities to sort particles over 70 µm compared to traditional droplet based sorters.