To identify the optimum conditions for the optical trapping of a droplet
under microgravity, we theoretically analyzed the efficiency of trapping with
counter laser beams. We found that the distance between the two foci is an
important parameter for obtaining stable trapping conditions. We also performed
an optical trapping experiment with counter laser beams under microgravity. The
experimental results correspond well to the theoretical prediction

Akihiro Isomura

Ashkin

Cizmar

Giegé

Grier

Hosokawa

Kenichi Yoshikawa

Kohira

Magome

Masahiro I. Kohira

Nobuyuki Magome

Panda

Roosen

Wrbanek

Chemical Physics Letters

English

arXiv

To identify the optimum conditions for the optical trapping of a droplet under microgravity, we theoretically analyzed the efficiency of trapping with counter laser beams. We found that the distance between the two foci is an important parameter for obtaining stable trapping conditions. We also performed an optical trapping experiment with counter laser beams under microgravity. The experimental results correspond well to the theoretical prediction

Isomura, Akihiro

Magome, Nobuyuki

Kohira, Masahiro I.

Yoshikawa, Kenichi

Kyoto University Research Information Repository

Title Toward the stable optical trapping of a droplet with counterlaser beams under microgravityAuthor(s)Isomura, Akihiro; Magome, Nobuyuki; Kohira, Masahiro I.;Yoshikawa, KenichiCitationChemical Physics Letters (2006), 429(1-3): 321-325Issue Date2006-09URL http://hdl.handle.net/2433/49165RightCopyright © 2005 Elsevier B.V. All rights reserved.Type Journal ArticleTextversionauthorKyoto UniversityToward the Stable Optical Trapping of aDroplet with Counter Laser Beams underMicrogravityAkihiro Isomura, Nobuyuki Magome 1, Masahiro I. Kohira 2,Kenichi Yoshikawa Department of Physics, Graduate School of Science, Kyoto University, Kyoto606-8502, Japan & Spatio-Temporal Project, ICORP, JST, JAPANAbstractTo identify the optimum conditions for the optical trapping of a droplet undermicrogravity, we theoretically analyzed the eciency of trapping with counter laserbeams. We found that the distance between the two foci is an important parameterfor obtaining stable trapping conditions. We also performed an optical trappingexperiment with counter laser beams under microgravity. The experimental resultscorrespond well to the theoretical prediction.1 IntroductionSince the discovery of optical trapping in 1970 by Ashkin[1], optical tweezershave been actively applied in the elds of biology, physical chemistry, con-densed matter physics and so on[2]. Up to the present era, increasing interestshave been paid for the optical trapping in the air, as the useful tool undermicrogravity in the International Space Station (ISS)[3][4]. The technique ofoptical trapping is expected to be useful on the ISS for the manipulation ofdroplets on a m to sub-mm scale, including in crystal growth by avoidingthe eect of vessels. However, as far as we know, there has been no report onthe optical trapping of a droplet under microgravity conditions in air. Corresponding author. FAX: +81 75 753 3779Email address: yoshikaw@scphys.kyoto-u.ac.jp (Kenichi Yoshikawa).1 Department of Food and Nutrition, Nagoya Bunri College, Nagoya 451-0077,Japan.2 Department of Physics, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112-8551,Japan.Preprint submitted to Chemical Physics Letters 5 July 2006xxdd<0d>0f ff fdFig. 1. Schematic illustration of the counter laser beams. f is the focus of each laserbeam and d is the distance between them. We take the sign of d as shown in thegure.Recently, we reported the optical levitation of a droplet under a linear in-crease in gravitational acceleration using a single laser[5]. To attain stableoptical trapping with a single beam, it is necessary to use a lens with a highmagnication. This means that the working distance, or the distance betweenthe lens surface and the object, is rather small; on the order of a few mm. Inview of such application on the ISS, it is important to nd the stable trappingcondition with a greater working distance. Toward this end, we adapted anoptical system with low-converged counter laser beams for optical trappingwith a long working distance.2 TheoreticalWe consider the counter laser system shown in Fig.1. In this system, the dis-tance between the foci d plays a crucial role. Although the qualitative propertyof such counter laser systems has been discussed in Ref.[6], the eect of thedistance d has not yet been discussed in detail. Here, we calculate the trap-ping force produced by counter lasers with the variables d and R (which is theradius of a spherical object).To take into account the eect of the inertia of the object, we start our dis-cussion with a motion equation. To simplify the problem, we consider motionalong the x-direction as in Fig.1.mx = Fl + Fv + Fothers (1)where m is the mass of the object, x is the acceleration of the object alongthe x-direction, Fl is the force along the optical axis induced by the convergedlaser, Fv is the viscous force, and Fothers is the other forces (including theeective acceleration force along the x-direction and random force induced byair).2As we see in the latter part, the velocity of the trapped object U is at most10 3m=s. We assume that the scale of the trapped object R is at most 10 4m,and the kinetic viscosity of air  is around 10 5m2=s. In this condition, theReynolds number is: Re = RU= ' 10 3  1 and we can apply Stokes'approximation. By calculating m = 4R3=3 and Fv = 6Rv, we can verifythe relation mv2=2 Fv x; where the radius of the trapped droplet R is onthe order of 10 m, the experimental time resolution t is 0:33 s, the velocityof the trapped droplet v = x=t, the viscosity of air  = 1:8 10 5 Pa  sand the density of the droplet  = 1:0 103kg=m3. This estimation indicatesthat the viscous force on our experimental condition is large enough to locatethe droplet at an equilibrium position in the optical potential. Therefore, underreasonable assumptions of the viscous limit, we discuss the stability of trappingdroplets through Fl and the eective optical potential.Fl is found as follows. In the case of trapping a large object(R= > 10, where is the wavelength of laser), we can calculate the trapping force with the rayoptics theory. Within the framework of ray optics, a TEM00 mode laser canbe divided into rays, which are suxed with i, and each power of the ray Piis related to the beam deviation  and lens size L Each ray hits the surfaceof the droplet at a dierent incident angle i (0  i  ), repeatedly reectsand is transmitted in the droplet until the intensity of the rays decreases tothe zero limit, and the momentum is given with a certain eciency along thex-axis, Qi = Qi(R; x;i; n1; n2):Qi = sini(Ri sin 2i   T2i [sin(2i   2ri) +Ri sin 2i]1 +R2i + 2Ri cos 2ri)+cosi(1 +Ri cos 2i   T2i [cos(2i   2ri) +Ri cos 2i]1 +R2i + 2Ri cos 2ri)(2)where i: incident angle, ri: refractive angle, Ri:reection coecient and Ti:transmission coecient. These parameters are obtained by considering the ge-ometric relation between the droplet and the direction of the beam, expressedby R; x; i;L; n1; n2 (see ref.[7]). Assuming a spherical droplet with radius Rwhose center is located at distance x from the center of the foci, we calculatethe details of the reections and transmissions for all paths of the laser beam.The total force fl isfl =Xin1PicQi =n1PcQx (3)where Qx = Qx(R; x;;L; n1; n2): trapping eciency along the optical axisand c: velocity of light. In addition, considering the distances between the3Fig. 2. Calculated potential of the counter beam lasers, deduced by a theoretical cal-culation. (a) d < 0. (b) d > 0. In the theoretical calculation, the following parameterswere used: laser power P= 150 mW, convergence angle  = 17.0 degrees, injectedratio of laser to the lens =L = 1:5, refractive index of the medium n1 = 1:00, re-fractive index of the droplet n2 = 1:35, density of the droplet  = 9:65102 kg=m3.(c)Schematic illustration of the calculated potential ((a) and (b)) made by thetwo-beam lasers, considering the radius of the droplet and the disagreement be-tween the axes.foci, the total force Fl is:Fl(d; x;R) = fRightl + fLeftl (4)Under the assumption of a spherical trapped object, optical trapping exhibitsgeometrical symmetry and we can use a normalized unit of length. Eventually,the optical potential is obtained from the integration of Fl and expressed bytwo normalized parameters, d=R and x=R.We calculated potential of the counter beam lasers, using the parameters: laserpower P= 150 mW, convergence angle  = 17.0 degrees, injected ratio of laserto the lens =L = 1:5, refractive index of the medium n1 = 1:00, refractiveindex of the droplet n2 = 1:35, density of the droplet  = 9:65102 kg=m3. Theresults of the calculation for eective trapping potential are shown in Fig.2,indicating that the trapping eciency is signicantly dependent on d. Anoptical conguration with positive d is clearly preferable for optilcal trapping4Fig. 3. (a) Schematic illustration of parabolic ight (top) and the actual change ingravity with the present parabolic ight prole(bottom). (b) Schematic illustrationof the optical trapping system.under microgravity. Figure 2(c) shows the change in the potential prole asa function of d=R. As shown, not only the distance between the foci but alsothe radius of the droplet greatly aect the prole of the optical potential. Thischart is reasonable for understanding qualitative properties: if the radius Ris suciently large, the trapped object is insensitive to the distance betweenthe foci d and the sign of d become less important. In contrast, when R issuciently small, d becomes non-negligible and we must choose better settingsof d. Since we sought to dene the optimum conditions for trapping largeobjects (sub-mm scale), this diagram is applicable for designing a counterlaser trapping system. For example. if we can precisely adjust the positions ofthe foci, the setting at d=R = 4 is advantageous for trapping the object ratherthan d=R =  4. The potentiality to trap small particles is important in thegrowth of protein crystals[8][9] and liquid droplets[10].3 ExperimentalMicrogravity conditions were achieved by using a jet airplane(Mitsubishi MU-300, operated by Diamond Air Service Co., Aichi, Japan). In the experiment,the airplane ew along a parabolic ight prole, as shown in Fig.3. Duringparabolic ight, the eective gravitational acceleration g in the airplane was0.01 g0 for about 20 s, where the gravitational acceleration on the groundg0 = 9:8m=s2.The experimental setup for the optical trapping is shown in Fig.3(b). Weselected a counter laser system to press the droplets to the center of thefoci.[11][12] The laser beam from a diode pumped Nd : YVO4( = 532 nm)5was split into two beams by a half mirror, transferred via optical bers, andfocused by achromatic lenses. The convergence angle of the lenses was 17degrees, so the working distance was on the order of cm. The laser power wasset to 170 mW. We arranged two dierent optical settings, where the positionsof the laser foci are dierent, either d is positive or negative as shown in Fig.1.The droplets were injected into a glass cell (10mm 10mm 50mm) withan atomizer. The droplets, as visualized by scattering visible laser light, weremonitored with a CCD camera from the y-direction in Fig.3(b). Movies wererecorded at 30 frames per second. The experiments was carried out at arround298K.4 Results and DiscussionOn the ground in air, using the same optical trapping system, the injecteddroplets immediately fell due to the force of gravity. However, under micro-gravity in air, most of the droplets didn't fall and we could observe the mo-tions of the droplets along the laser axes. To trace the droplets' motion alongthe laser axes, we converted the movie images to a spatio-temporal diagram.Figure 4 shows the results of the optical trapping of the droplets under mi-crogravity.Figure 4 (a1) and (b1) are spatio-temporal diagrams which show the trajectoryof the droplets. Figure 4 (a2) and (b2) are snapshots of the droplets. In thesegures, the burring on the images correspond to rather fast motion of thedroplets. The small white spots are droplets that have departed from the laseraxes and are oating in front of or behind the camera foci. In contrast, atrapped droplet is a star-like object(white arrow), since a trapped droplet onthe laser axes scatter light intensively. In other words, the droplet was trappedin the setting at d=R > 0 and was not in the setting at d=R > 0.Figure 4(c) shows typical proles depicted based on the results of Fig.2(a) and(b), which are associated with the two dierent optical settings in Fig.4(a2)and (b2). The potential well in the case of d=R =  4 is deeper than that ofd=R = 4, as a whole. Whereas, near the trapping center, the gradient force inthe case of the solid arrow(d=R = 4) is much greater than that of the dashedarrow(d=R =  4). These results show that the optical setting d=R > 0 hasthe advantage over the setting d=R < 0 because of the narrow, deep potentialprole near the trapping center. It is clear that such a theoretical expectationon on the advantage of the former setting corresponds well to the experimentalresults, given in Fig.4(a2) and (b2).6(a1) (b1)(a2) (b2)2mm4sectimex−direction4secx−directionz−direction1mm2mm1mmFig. 4. Spatio-temporal diagrams of droplets under microgravity conditions togetherwith selected representations of traces. The optics are (a1) d > 0. (b1) d < 0. (a2)and (b2) are the 1 sec accumulation of the video frames, indicating the existenceof a trapped particle in the former, whereas no particle was xed in the latter.(c) Schematic illustration to explain the dierence between trapped and untrappeddroplets. The solid line is the potential prole in the case of d=R = 4 and the brokenline is that in the case of d=R =  4.5 ConclusionWe performed the optical trapping of a water droplet with a counter laserin air under microgravity and investigated the properties of the counter lasertrapping system. We showed that the position of the laser foci strongly af-fected the trapping eciency. A theoretical calculation based on ray optics7reproduced the experimental trend. The working distance of our trapping sys-tem is on the order of cm, so it has the advantages of trapping large objects.The working distance of our trapping system was on the order of cm, indi-cating the signicant advantage compared to the single-laser trapping. Thepresent results may contribute to the design of a manipulation system on theInternational Space Station (ISS), including experiments on protein crystalgrowth and a container-less micro-reactor.6 AcknowledgementThe authors thank Mr. S. Watanabe, Mr. Y. Sumino, and N. Matsuda fortheir helpful suggestions and Ms. Hayata and Messrs. Fujii, Kawakatsu, andTakahashi for their technical assistance. This research was supported in part bya Grant-in Aid from the Ministry of Education, Science, Sports and Culture ofJapan, the Grant-in-Aid for the 21st Century COE“Center for Diversity andUniversality in Physics” from the Ministry of Education, Culture, Sports,Science and Technology (MEXT) of Japan, and“Ground-based ResearchAnnouncement for Space Utilization”promoted by the Japan Space Forum.References[1] A. Ashkin, Acceleration and trapping of particles by radiation pressure, Phys.Rev. Lett. 24 (1970) 156.[2] D. G. Grier, A revolution in optical manipulation, Nature 424 (2003) 810.[3] J. Panda, C. R. Gomez, Setting up a rayleigh scattering based ow measuringsystem in a large nozzle testing facility, NASA/TM (2002) 211985.[4] S. Y. Wrbanek, K. E. Weiland, Optical levitation of micro-scale particles in air,NASA/TM (2004) 212889.[5] M. I. Kohira, A. Isomura, N. Magome, S. Mukai, K. Yoshikawa, Opticallevitation of a droplet under a linear increase in gravitational acceleration,Chem. Phys. Lett. 414 (2005) 389.[6] G. Roosen, A theoretical and experimental study of the stable equilibriumpositions of spheres levitated by two horizontal laser beams, Opt. Comm. 21(1977) 189.[7] A. Ashkin, Forces of a single-beam gradient laser trap on a dielectric sphere inthe ray optics regime, Biophys. J. 61 (1992) 569.8[8] R. Giege, J. Drenth, A. Ducruix, A. McPherson, W. Saenger, Study of theaerodynamic trap for containerless laser materials processing in microgravity,Prog. Cryst. Growth Charact. Mater. 30 (1995) 237.[9] Y. Hosokawa, S. Matsumura, H. Masuhara, K. Ikeda, A. Shimo-oka, H. Mori,Laser trapping and patterning of protein microcrystals: Toward highlyintegrated protein microarrays, J. Appl. Phys. 96 (2004) 2945.[10] N. Magome, M. I. Kohira, E. Hayata, S. Mukai, K. Yoshikawa, Optical trappingof a growing water droplet in air, J. Phys. Chem. B 107 (2003) 3988.[11] G. Roosen, C. Imbert, Optical levitation by means of two horizontal laser beams:A theoretical and experimental study, Phys. Lett. 59A (1976) 6.[12] T. Cizmar, V. Garces-Chavez, K. Dholakia, P. Zemanek, Optical conveyor beltfor ddelivery of submicron objects, Appl. Phys. Lett. 86 (2005) 17401.9

Toward the stable optical trapping of a droplet with counter laser beams under microgravity

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