We present evidence that aerosol droplets, ~1-2μm in diameter, can be optically bound over a 4mm distance within a volume formed by the overlap of the central cores and rings of two counterpropagating Bessel beams. The sizes of the individual polydisperse aerosol particles can be estimated from the angular variation of the elastic light scattering. Scattered light from the two orthogonally polarized trapping beams and from a Gaussian probe beam of different wavelength can be used to provide independent estimations of size. The coalescence of two droplets was observed and characterized.
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The application of optical techniques for manipulating monodisperse particles in a condensed phase has become widespread in recent decades. More recently, there has been a growing interest in the extension of these approaches to studies of particles in the gas phase, i.e. aerosol [1,2]. Trapping polydisperse particles in air with sizes within the range observed for atmospheric particles has significant potential for advancing studies of cloud physics and chemistry by allowing detailed studies of aerosol properties to be made on a single particle basis . Other potential applications may lie in bioelectrospraying to allow manipulation of single droplets containing a single cell . In the condensed phase, optical guiding permits the transportation of particles over macroscopic distances  and optical binding provides a method of confining multiple particles to allow further study using carefully chosen beam shapes . The optical binding of multiple particles was first observed in the elongated focus of a single Gaussian beam, known as transverse optical binding , and was later observed in the form of longitudinal optical binding with the use of two counterpropagating beams . Longitudinal optical binding has since been investigated in both free space  and optical fibre geometries [10,11]. In addition, through the use of Bessel beams (BBs), the optical trapping of extended chains of particles has been achieved . These techniques could have potential for further study of aerosol particles .
BBs contain an on-axis central maximum surrounded by multiple rings of equal power that arise through the propagation of an infinite number of plane wave vectors lying along a cone shape [12,13]. The resulting interference may be considered ‘nondiffracting’ due to the propagation invariant nature of the resultant BB core over the propagation distance. The rings that act to form the BB central maximum on propagation give rise to the beam’s self-healing properties . Longitudinal optical binding can be created through the use of two beams counterpropagating in free space. If the two beams are orthogonally polarized with respect to each other, particles of a higher refractive index than the surrounding medium may induce optical binding and adopt stable equilibrium positions. On entering the beam, particles perturb the incident laser fields such that they induce trapping sites where additional particles may be optically bound . Trapping sites arise from the incident light interacting with rescattered light from particles, which allows optical binding to neighbouring particles. The use of BBs in such a setup can allow the stable confinement of many microscopic particles, dispersed in a liquid, over millimetre distances .
The distinction of our work lies in the optical trapping of microscopic aerosol particles to achieve particle chains of polydisperse aerosol droplets, <1 to 2μm radius, that have correlated motion over millimetre distances. We report an initial study of droplets optically trapped in the central cores and rings of two horizontally counterpropagating BBs. The optically trapped droplets exhibit behavior indicative of optical binding. In addition, the sizes of trapped droplets are determined through collection and analysis of the scattered light from the trapping laser. The resulting phase functions are compared for different incident polarizations from each trapping beam, the observed convolved scatter from both trapping beams, and scattering from a separate probe beam at a different wavelength. As an application of this approach for studying aerosols, we present observations of coalescence between two droplets, tracking the sizes of the droplets before and after coagulation.
2. Experimental setup
A 532nm laser wavelength (5W Verdi, Coherent) was used to create a horizontal counterpropagating BB trap in free space. At this wavelength, the water droplets to be trapped absorb only very weakly. A zeroth order BB was created using an axicon (γ = 1.5°, Eksma) and split into two arms on passing through a halfwave plate and polarization beamsplitter cube. This created two orthogonally polarized beams of equal power. Each arm passed through a lens relay to create a BB with a central core diameter of 4.5μm surrounded by over 30 concentric rings that propagated over a distance of 5mm. The arms were oriented such that the two resulting BBs were overlaid to propagate in opposing directions (defined as + z, with s polarization, and –z, with p polarization, directions in Fig. 1 ) to create the region in which droplets were confined. A CCD with x10 microscope objective (NA 0.25, Newport) was used to record images, and was aligned perpendicular to the combined BB propagation directions and in the horizontal scattering plane.
A cuvette of dimensions 1x1x10cm3 was placed central to the trapping region. A solution of sodium chloride in water at a concentration of 40g/L was nebulised (NB-02 Aerosonic Travel Nebuliser) into the trapping region of the cuvette to create polydisperse aerosol droplets. The cuvette contained water filled to approximately 2cm below the trapping region and an unsealed glass coverslip was placed over the top to maintain a sample of constant relative humidity and to reduce air current effects.
The polarization of the scattered light by droplets from either BB can be assumed to be the same as that of the incident light as the droplets are spherical. Thus, a Polaroid was placed in front of the CCD to allow selection of scattering from either the s polarized beam (polarized along the y-axis) or the p polarized beam (polarized along the x-axis) or the combined polarization of both arms (s + p linear polarization). A 633nm probe beam (Helium Neon laser, Spectra Physics), gently focused to illuminate a single optically bound droplet from above with s polarization along the z-axis, was also used to characterize the size of particles, with the scattered light collected using the same CCD system. In this case a long pass filter at 550nm and a coloured glass filter were placed in front of the CCD to reduce scattered light from the trapping beams.
3. Optical trapping of aerosol droplets
A total beam power of 340mW was measured before the final optic, providing a maximum power of 11mW in the BB beam core. Particle chains are created by the gravitational settling of droplets into the trapping region or through additional droplets being guided into the proximity of others and adopting stable trapping positions. As new droplets join a particle chain, the array adjusts to form a new equilibrium configuration, which is accompanied by a change in chain length and inter-particle separation. New droplets entering the trap can also lead to instability in the chain configuration resulting in droplet coalescence, forced ejection or replacement of a droplet already resident in the trap. The disruption caused to the array can result in full or partial collapse of the droplet chain. These observed inter-particle dynamics are indicative of optical binding . Further evidence for optical binding comes from the observation of what occurs when the power equilibrium between the two trapping beams is changed. The array of droplets undergoes collective motion over a short distance on brief interruption of one beam. Immediate reintroduction of the beam causes the array to return to the original position where a similar stable configuration is again achieved. BB reformation distances  for the particle sizes trapped are very much lower than the inter-particle separations observed.
Long range optical trapping of particles was achieved in the central core of the BB over a distance of 4mm, as shown in Fig. 1(a). Droplets optically trapped over this long range could be stably confined for over 4 hours (similar to the findings presented in ). Smaller groups of particles were also observed to trap closely together over a shorter range in the BB core and rings, as seen in Fig. 1(b). This arrangement of trapped droplets had a short residence time (up to 30 mins) compared to the longer particle chains (as was reported by Karasek et al.  for particles in a liquid medium). A change in power did not affect the droplet separation, but a lower power was observed to lead to less stable trapping and a reduction in the residence time in the trap.
Work on optical binding in the condensed phase has mainly considered monodisperse particles that create very regular inter-particle spacing. Our use of polydisperse droplets requires consideration of droplet sizes, which are likely to introduce variation in the inter-particle separations. Discussion of droplet sizes and inter-droplet separations is deferred to later, where we size the three optically trapped droplets shown in Fig. 1(b).
We note that this system of two counterpropagating beams allows the optical guiding and transportation of droplets in either direction over millimetre distances, as determined by the BB propagation distance. This can allow droplets to be confined and characterized through optical binding and, on removing one trapping beam, allows the sorting of groups of droplets.
4. Sizing of particles from the phase function
The phase function (PF) was obtained from individual optically bound droplets and compared to Mie theory calculations to determine droplet size [2,15]. The scattering has an angular dependence that is dependent on droplet size, refractive index, composition, incident wavelength, and incident light polarization, and has an angular range determined by the collection optics. For Mie theory to hold true formally requires plane wave illumination of spherical and homogeneous droplets. Scattering from a gently focused 633nm laser beam with Gaussian profile (with paraxial approximation) was therefore compared to the Bessel intensity scattering profile of the trapping beams. By exploiting the nature of the optical trap we can independently size optically bound particles by sequential selection of the scattered light from the two orthogonal polarizations. This provides us with three possible polarizations of s, p or a combination of s + p polarizations. Scattering patterns from optically bound droplets were compared to Mie theory in a similar approach to Meresman et al. . The two orthogonal polarizations of the trapping beams were used along with the combined s + p polarization and the s polarized probe beam to independently size each droplet. In determining the PF, the beam traveling in the + z direction scatters light in an angular pattern equivalent to 180-0° from left to right in the image. The angular collection range is between 66.6 and 112.3°. The PF image of the -z direction beam is inverted in angle for correct comparison with Mie theory calculations. When the combined scatter from both beams is viewed, the observations must be compared with simulations that convolve the appropriate backward-forward scattering components of the two polarizations. An example of the PFs obtained for a droplet using the four methods is shown in Fig. 2 .
The droplet radius was estimated to be 1.19μm, 1.12μm and 1.15μm using the 532nm trapping laser with p, s, and s + p polarizations respectively, and 1.21μm for the s polarized 633nm probe beam. This gives an average determined droplet radius of 1.17μm with standard deviation 0.05μm. The associated error for one Mie calculation is less than ± 0.09μm, but this can be significantly improved by comparing all four methods. The absolute uncertainty associated with the particle size estimated from one, three or all four PFs, do not appear to systematically change with droplet size. We have therefore demonstrated that the droplet radii can be obtained from analysis of combined polarizations of the scattering from the two trapping beams. The PFs obtained from particles deviated from Mie theory because of the scattered light pixel coverage associated with the CCD collection angle. All PFs for a single droplet for each polarization and wavelength were taken within 20 seconds of each other to allow changing of filters and the Polaroid.
Thirty six droplets were studied ranging from 0.55 to 1.74μm in radius, with an average particle size of (0.99 ± 0.04)μm. The smallest particle optically bound and characterized in this study was (0.55 ± 0.03)μm in radius. This is close to the limit for estimating the size from Mie theory  and a larger error is associated with particle sizing. The use of multiple sizing methods becomes important as smaller droplets are studied. The ability to distinguish particle radius using a single scattering pattern becomes more difficult because of the increasingly featureless nature of the PF with decreasing particle size.
We note that reflected light from top and bottom surfaces of the optically bound droplets, known as glare spots , were easily observed. The glare spots were obtained and used to determine droplet sizes through brightfield illumination, and the outcomes were in agreement with PF sizing.
To explore the nature of the optical binding within a particle array, it is necessary to determine the sizes of the individual droplets and the inter-particle separations. The PF recorded for determination of particle size requires that a reduced field of view be imaged (shown in the observed droplet image in Fig. 2). For cases where many droplets form a chain, the elastically scattered interference patterns from neighbouring droplets may overlap and be unresolved. To avoid this we consider the three droplets trapped in the core shown in Fig. 1(b). A time of 2 s elapsed between droplet separation and measurement of the size images seen in the figure. The relative inter-particle spacing of the three droplets were determined to be approximately 136μm (spacing of droplets 1 → 2) and 241μm (spacing of droplets 2 → 3). Droplet radii were determined from the PFs obtained from the combined s + p polarisation and were estimated to be (1.4 ± 0.1)μm, (1.0 ± 0.1)μm and (1.2 ± 0.1)μm for droplets 1, 2 and 3, respectively. The BB reformation distance  for these particle sizes is approximately 20μm, which is considerably less than any of the observed particle separation distances, and therefore consistent with optical binding as opposed to independent trapping of several particles. The polydispersity of the aerosol sample adds considerably to the complexity of the analysis and any modelling approach, and a more rigorous discussion is beyond the scope of this present paper.
5. Droplet coalescence
Nebulised droplets fall into the trapping region under gravity and can interact with optically bound droplets. Through the study of droplet-droplet interactions we can observe the coalescence of two droplets . Such an event is shown in Fig. 3 , with data taken at a total beam power of 83mW measured before the final optic. Note: the trapping power used here, a core power of < 3mW, is very much lower than that required to optically trap in the condensed phase. The two interacting droplets are sized before and after coalescence using the PF from the combined s + p polarization of the trapping beams. When coalescence between two droplets occurs, the array of particles can become unstable. Particles either readjust to adopt new trapping positions or, more often, are ejected from the trap leading to partial or entire array collapse.
In Fig. 3, scattering from droplets A and B was measured immediately before coalescence occurs, with the corresponding PF intensity profiles shown in Fig. (a) and (b) respectively. Droplet A enters the trapping region and is guided towards a stable trapping position where droplet B is optically bound. The droplets coalesce to form droplet C with a corresponding PF shown in Fig. 3(c). Before coalescence, droplets A and B were found to have radii of 0.84μm and 1.59μm, respectively, and after coalescence droplet C had a radius of 1.70μm. From the respective droplet volumes for A and B, the expected resultant droplet radius would be 1.66μm which is in good agreement with the value determined for droplet C and within the ± 0.09μm uncertainty described above for sizing from a single scattering method.
The application of longitudinal optical trapping to polydisperse aerosol droplets has been shown. Single droplets were trapped over an extended (4mm) region and characterized. We are able to use the combined polarization of the trapping beams to size droplets. Clear evidence is presented for optical binding of polydisperse particles in counterpropagating BBs, together with a direct study of aerosol dynamics for particles of radius ~1μm. In addition, we have demonstrated that particle manipulation can be combined with characterization. Future work will include coupling the system with cavity ring down spectroscopy to allow detailed characterization of optically confined droplets, and a flow system will be coupled with the trapping region for particle delivery . Development of a model is needed for a full understanding of the binding mechanism for polydisperse droplets and to describe the particle behavior observed.
The authors thank Natural Environment Research Council for funding this research. We are grateful to J. B. Wills for helpful discussions and assistance with Labview.
References and links
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