We present the use of optical fibers to form a counter-propagating optical trap as a means of manipulating both solid and liquid aerosols. We explore the use of single and multimode fibers to achieve trapping of various particles in air, present the trapping properties of the different fiber types and compare the observed trends to those predicted by theory. Using fibers, we are able to hold suspended particles for extended periods of time and to precisely manipulate them over distances of several hundred microns. We discuss the difficulties and advantages of each fiber configuration and conclude with a demonstration that fiber based trapping offers a good candidate for studying optical binding in air.
© 2008 Optical Society of America
Since their demonstration by Arthur Ashkin , the use of optical manipulation techniques has spread into many areas of research  as a non invasive tool for the manipulation of microscopic objects. Over the last 35 years, these techniques have been refined and developed [3–5], mainly using particles suspended in a liquid medium. The ability to trap particles in air, however, also offers an additional number of interesting avenues of study. These include examining the Brownian motion of airborne particles in optical traps  as well a range of applications in atmospheric chemistry [7–9]. Creating robust traps where the particles of interest reside in the air can be difficult, mainly due to the significantly reduced buoyancy and viscosity compared to liquid based traps along with the added difficulty of populating the trapping sites in a controlled fashion.
When wishing to study the properties or dynamics of a single or small number of airborne particles, it is often essential to know their positions. By optically trapping a particle its location is fixed and its properties can be easily investigated. A stable three dimensional optical trap can only be achieved by balancing the scattering and gradient components of the light-matter interaction. This is generally achieved in one of two ways: either a high numerical aperture (NA) objective is used to tightly focus the incident beam , in which case, it is referred to as a single beam gradient trap or optical tweezers; alternatively a second equal and opposite beam is added to balance the force of the first, forming a counter-propagating trap [1,11]. Both methods have been successfully employed to optically confine aerosol particles [12,13]. Multiple single beam traps have been employed to allow several particles to be simultaneously trapped and independently manipulated using dual beam tweezers , a spatial light modulator  or an acousto-optical deflector .
Counter propagating configurations have previously been used to trap both liquid and solid particles [17–19]. Salt and sugar crystals have been trapped from solution using two counter propagating beams in a hollow core fiber using laser powers between 20mW and 1W . Much higher powers of 2.2 W per arm were used when trapping droplets between two free space beams in experiments to study ice formation . Recently, a trap formed using a dual beam trap making use of an incoming beam and retroreflected beam of 30mW has been used to study optical binding in air . All these experiments make use of free-space light beams focused through lenses. These lens-based systems are very similar to those used by Ashkin and co-workers in their early work based on radiation pressure traps. However, more recent work using systems of counter propagating beams in liquid media has seen these free beams replaced with light transmitted through optical fibers . The beam properties can then be dictated by the characteristics of the fibers chosen; potentially removing the need for any other optical components. These “fiber traps” [21–24] have several advantages over the single beam trap. They can, by providing large forces, trap a wider range of particle sizes while allowing increased optical access to the trapping area when compared to optical tweezers , making them easy to integrate with simultaneous spectroscopic analysis  and microfluidic systems . For the purpose of trapping aerosols fiber based traps also have the potential advantage of being more suitable for producing small, integrated devices (analogous to microfluidic systems), suitable for field studies.
In this paper, we demonstrate a dual beam fiber trap capable of trapping airborne particles. We compare the performance of traps using both multimode and single mode fiber and examine the possibility of studying optical binding using such configurations.
2. Theoretical model
To allow us to predict the performance of our dual beam traps, we model the optical forces present by building on existing theoretical work for liquid media [11,25,27] and apply it to aerosol trapping.
We consider two horizontally aligned optical fibers centered along the z-axis, separated by a distance s. At the midpoint between these fibers we place a lossless dielectric particle of radius r 0, which is offset from the optical axis by a distance d along the x-axis. This particle is illuminated by a Gaussian beam emerging from each fiber with a minimum beam waist of ω 0. Note that as we are only considering Gaussian beams this model is only valid for single mode fiber and not multimode fiber. By considering a ray incident on the particle at point P, at an angle θ to the optical axis, and following a geometrical force calculation the two main results of Sidick’s work can be obtained [28, Eqs. 9(a) and 9(b)] which give the trapping efficiencies in the x and z directions due to a single beam as:
where qs, qg, are the fractions of momentum transferred to the parallel and perpendicular directions of the incident ray respectively. Both of these functions are dependent on the transmittance and reflectance of the particle and hence the trapping efficiencies Qx, Qz are dependent on the ratio of the refractive index of the particle and medium, N. Rc is the radius of curvature of the ray, which when projected onto the z-axis gives Rz. r and ω are the beam radius and beam waist at a given position along the z-axis, γ is the half apex angle of the beam and a is the separation between the rays’ source and particle centre. The portion of the particle illuminated by the incident beam is defined by the boundary θmax at which the angle of incidence=π/2. All of these variables are defined in greater detail in . Note that for the case of an on-axis beam (d=0) the Qz component can be simplified significantly and will become independent of φ. It is also important to note that due to symmetry, an on-axis particle will experience no force in the x-direction. Equally a particle positioned at the centre of the two fibers will not experience a force along z, assuming equal power in each arm. The trapping efficiency relates to the force from a fiber via the constant (n1P)/c where n1 is the refractive index of the medium, P is the laser power coming out of the fiber and c is the speed of light giving:
Equations 1 and 2 define the trapping efficiencies due to a single beam. To find the total force experienced by a particle trapped using a counter-propagating setup the force from each fiber, given by equation 3, must be summed. Along the x-axis, the forces act to reinforce one another, making the restoring force across the x-axis greater than that along the z. We concentrate on forces due to displacements along the x-axis for the remainder of this section. In our experimental configuration we are limited in the number of variables we can control: primarily we cannot control the size of the particles falling into the trap (unlike most liquid based traps where the particle size is well known). The size of the particle trapped has a direct effect on the magnitude of the optical force it experiences in the trap as can be seen in Fig. 1.
While we may not be able to accurately control the particle sizes, two things that can be controlled are the type of substance trapped and the fiber separation. In the former case the larger the index ratio between particle and medium the stronger the trapping will be, making trapping in air more effective than trapping in water. This can be seen in Fig. 2(a) where the theoretical force and axial offsets are shown for all the materials experimentally trapped in air, and for reference for a silica particle trapped in water (N=1.08).
In our experimental work we looked at trapping achieved with fiber separation of 170 and 240µm. The theoretical force curves for these separations can be seen in Fig. 2(b). Together Figsures 1 and 2 demonstrate the effect that any combination of changes to the fiber system such as a larger, higher refractive index or a particle trapped at a decreased fiber separation would have on the restoring force that balances gravity.
Using the theoretical model it is possible to consider the maximum sized particle that could be stably trapped at a given power. This is done by finding particles whose weight is equal to the maximum restoring optical force. Doing this for even the lowest experimental powers produces values far larger than any trapped droplet observed. While this would seem a contradiction, this process assumes that the particles have no initial kinetic energy and ignores any effects due to air currents. As the particles are actively introduced into the trapping cell during the experiment, the model allows us to safely state that the particles we trap are well within the theoretical limits of the system.
3. Experimental setup
The experimental setup is shown in Fig. 3. We found that using connectorised fibers as opposed to fibers with bare ends within the trapping cell made the system more mechanically robust. Alignment was achieved and maintained by fixing one arm in place and mounting the other on an adjustable linear motion stage. 1.27cm diameter lens tubes were used to hold the fibers in place and to make room for a long working distance objective (Mitutoyo OBJ PLAN NIR 50X) through which the system was observed. A custom piece of glassware was used to create a trapping cell into which the aerosol could be sprayed while minimizing the effect of air currents. The aerosols were produced using an ultrasonic nebuliser (Omron U22(NE-U22-E)), which when used with pure water produces aerosols with a mass median aerodynamic diameter of between 3 and 5 microns . It should be noted that as water droplets are not able to exist in a non saturated environment, salt (NaCl) was added to the water before being nebulised. Salt reduces the vapour pressure and allows stable droplets to be formed. The concentration of salt also affects the size of droplets  produced from the nebuliser, with higher concentrations producing larger drops.
A 532nm laser (Quantum Finesse 4W) was used for all of the work. The same setup was used with both multimode fiber (MMF) and single mode fiber (SMF) by simply replacing the fibers with those of the desired properties. The MMF used was 0.22-NA 50µm Core Multimode Vis-IR Fiber (Thorlabs part# AFS50/125Y), while the single mode fiber (Thorlabs part# 460HP) had a mode field diameter of 3.5±0.5µm@515nm and both were used with ST connectors. When using MMF with equal power down each arm and with the variable neutral desnity (ND) filters set to ND=0, 27% of the total laser output could be transmitted down each arm. Due to the small core size of the SMF fibers, mechanical drift in the launching stages produced significant and random power fluctuations in the transmitted power. Approximately 5–8% total laser power could be transferred using SMF. To account for this, the power down each arm was measured directly using a power meter, before and after each trapping sequence. By keeping the trapping sequences to around 5 minutes no change in transmitted power was observed. As the power remained constant over this period any effects that might result from salt or other particles building up on the exposed fiber ends can also be neglected. However, to minimise any effect this might have, the fiber ends were cleaned thoroughly before the start of each sequence. The trap was positioned horizontally so that the gradient force is balancing gravity.
4. Multimode fiber trapping
Due to their larger core size, multimode fibers (MMF) are much easier to couple into providing greater power with which to trap, and are simpler to align. This makes the multimode system relatively easy to set up. However, being multimode they produce a complex intensity pattern as can be seen in Fig. 4. While Fig. 1 showed the optical force to be dependent on particle size, using MMF makes this behaviour more complex. Sufficiently large droplets will straddle the peaks and troughs of the optical field and experience an average field emitted from each fiber. Smaller droplets, however, experience a local force dependent on their exact position in the overall overlapping mode patterns.
Due to the complex nature of this overlapping field any number of stable local trapping sites can be created, each with a different power, up to and including the total output of the fiber. This makes trapping very unpredictable. We were able to simultaneously trap anywhere up to 10 water droplets. The local nature of the trapping field is again emphasised when the power balance between each fiber is adjusted. The trapped particles then move independently of one another according to the change in their particular local field. Hence while some particles will move a large distance, others may not move at all, as can be seen in the Fig. 5.
For our work with multimode fibers we concentrated on trapping water. As previously mentioned the amount of salt added to the water used in the nebuliser will affect the size of the droplets produced, with higher concentrations producing larger drops. Figure 6 shows how this affects trapping behaviour, with an increase in average trapped droplet size at a given power if the salt concentration is higher. Maximum droplet sizes were determined visually using a custom LabView program.
5. Single mode fiber trapping
The output from a single mode fiber (SMF) generally results in only one stable equilibrium position [25,27]. While being harder to align, the trapping position and behaviour of these fibers is much more predictable. By adjusting the power down each arm the particle position can be fully controlled as is shown in Fig. 7
The optical force experienced by an aerosol is dependent, amongst other things, on the fiber separation and power, as shown in equations 1–3. To establish the trapping ability of the fibers, shown in Fig. 8, droplet sizes were measured at a range of powers at fiber separations of 170 and 240µm. At separations greater than these trapping became less reliable while closer separations impeded the flow of particles. The aerosol used was water doped with NaCl at 50g/L.
We also trapped a number of other substances in air, including ethanol, glycerol (20% in water), and 3.01µm solid silica particles using nebulization. The ethanol evaporated too quickly to get any useful sizing data. Fig. 9 shows data for glycerol trapped at a fiber separation of 170µm. We were able to trap solid particles, loading them into the trap by placing them into solution with ethanol, which quickly evaporated leaving behind the silica particle . The solid particle was stably trapped for in excess of half an hour.
6. Optical binding
Optical trapping occurs as a result of a particle being held in an equilibrium position due to a balance in both the gradient and scattering components of the matter-light interaction. The presence of this particle, will also distort the optical field slightly, for example by refocusing light from each fiber to a point on the opposite side of the particle. Given the correct conditions, this refocusing can result in another stable trapping position being formed. Were a particle to be trapped at this new equilibrium point, it would have a similar distorting effect on the light field experienced by the first particle. As a result, the position of each individual particle is dependent on the position of all of the others, creating a self-sustaining system where optical forces create arrays of trapped particles, an effect referred to as optical binding.
While these systems have been extensively investigated using liquid media [24,30,31], there may be advantages in carrying out experiments in air, including the ability to increase the relative refractive index of the particles and media and the possibility of seeing dynamics such as breathing modes.
During the course of our investigation into trapping single particles, we recorded many examples of optical binding using the single mode fiber trap. A separate, detailed study of optically-bound systems is required, but this falls outside the scope of the present work. However, examples of optical binding of water and, separately, glycerol can be seen in Fig. 10. It is interesting to note that the bound arrays always seem to have a large particle in the presence of much smaller particles.
7. Discussion and summary
As can be seen in Figs. 5 and 7, fiber based trapping of aerosol particles can be achieved using both single and multimode systems. Using MMF allows for easy coupling, alignment and for multiple particles to be trapped simultaneously, however, due to the complex nature of the light field a quantitative study of the trap is difficult and the trap behaviour is unpredictable. Using SMF the coupling and alignment becomes more critical but the trap behaviour is more predictable and lower laser powers are required to trap. Using both types of fibers we were able to manipulate particles over distances of several hundred microns. With SMF the range of motion extends fully from one side of the trap to the other, which is often not the case using MMF due to the more complex nature of the optical field.
We find, as might be expected, that increased power allows larger particles to be trapped. This behaviour is supported by the linear relation between optical force and power as stated in equation 1.3. The general trends shown in Figs. 1 and 2 can be seen in the experimental data of Fig. 8 with larger separations reducing the optical force and thus the size of particle that can be held. Regardless of power the smaller sized particles can still be trapped. This feature contrasts with the behaviour of particles in a single beam trap, where the size of the smallest trappable drop increases with power . We have been limited in our investigation of trapping size by our ability to produce a very wide range of droplet sizes. The nebuliser used produces polydisperse pure water particles of between 3–5µm in diameter. The addition of salt has the effect of increasing particle size, explaining why liquid particles smaller than 4µm were not observed. Particles as large as 20µm were trapped, created through droplet coagulation in the ambient cloud. In addition due to the stiffness of the trap it was possible to grow a trapped particle in size by repeated addition of aerosols. We believe that this size of ~20µm represents the upper limit of particle sizes we are able to produce. It is therefore probable, based on the theory, that the fiber trap can be used to hold much larger particles but we were unable to experimentally verify this.
One obvious advantage of using a fiber trap is the ability to trap larger particles than with a single beam gradient trap, an indication of the larger optical forces present when using a counter propagating configuration. The combination of the large trapping forces, the large trapping area and the possible compactness of a fibre trap system, when compared to a normal optical tweezers make the system an attractive option for developing robust field based devices. In addition, the fiber trap concept opens up analogues to microfluidic systems for aerosols. One can imagine integrated light sources combined with covered microchannels in which aerosols can flow and be manipulated and analysed.
This work was funded by a Royal Society Joint Project award and the UK EPSRC. CL-M and JCG-V acknowledge financial support from CONACyT México and from Tecnológico de Monterrey grant CAT141. DM is a Royal Society University Research Fellow.
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