1098 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 6, MARCH 15, 2014

Multi-Dimensional Manipulation of Yeast CellsUsing a LP11 Mode Beam

Yu Zhang, Peibo Liang, Jiaojie Lei, L. Wang, Zhihai Liu, Jun Yang, and Libo Yuan

Abstract—We report a new method for constructing a singlefiber optical tweezers, which can realize multi-dimensional manip-ulation of trapped yeast cells by using a LP11 mode beam excitedin a normal communication single core optical fiber. This allowsa simple and convenient orientation control on the trapped yeastcells. The LP11 mode beam, both for generating trap and orien-tation manipulation, has been modulated by using the tension andtwisting loaded on the fiber. We present experimental results ofcontrollable deflection and orientation manipulation of the yeastcells. To the best of our knowledge, it is the first report about thetrapped yeast cells being driven by the normal single fiber opticaltweezers in multi dimensions, and it constitutes a new develop-ment for single fiber optical trapping and makes possible of morepractical applications in the biomedical research fields.

Index Terms—Controllable deflection and orientation manipu-lation, LP11 mode beam, single fiber optical trapping.

I. INTRODUCTION

O PTICAL trapping, first proposed and reported in 1986 byArthur Ashkin [1], was first demonstrated its application

for biological science fields in late 1980s [2]. And thereafterthroughout the 1990s, optical trapping began to be applied inmany different research areas, such as the atomic physics [3],micromachining [4], chemistry [5], biomedicine [6] and MEMS(Micro-Electro- Mechanical Systems) [7] researching fields,even the study of the optical trapping itself resulted in inter-esting new physics [8].

Optical fiber, as a low cost and convenient tool, has been em-ployed for optical trapping more and more. Normally the lightexiting from the fiber tip will diverge and a stable optical trapcan only be realized by balancing the gradient and the scatteringforces from two opposing fibers, therefore multi fibers need toform a single optical trap. This work is pioneered by Consta-ble [9] and applied for stretching yeast cells [10] and others [11],[12]. Then on the basis of the fiber-end micromachining tech-nology developing, the fiber tip can be molded into a special

Manuscript received October 31, 2013; revised December 17, 2013 and Jan-uary 6, 2014; accepted January 6, 2014. Date of publication January 18, 2014;date of current version January 24, 2014.

Y. Zhang, P. Liang, L. Wang, Z. Liu, and J. Yang are with theKey Lab of In-fiber Integrated Optics, Ministry Education of China,Harbin Engineering University, Harbin 150001, China (e-mail: zhangy0673@163.com; pomelocherry@126.com; erleizi-2@163.com; zhihai@vip.sina.com;yangjun141@263.net).

J. Lei and L. Yuan are with the College of Science, the Institute ofPhotonics Research Center, Harbin, China (e-mail: leijiaojie@hrbeu.edu.cn;lbyuan@vip.sina.com).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JLT.2014.2298858

tapered-shape to generate the three-dimensional optical force totrap yeast cells, which marks the emergence of the single fiberoptical tweezers [13]. The single fiber optical tweezers is muchsimple and practical to be a tool for biological cells. Up to now,it has developed many structures, such as a narrow parabola-like tapered tip fiber optical tweezers [14], [15]; a reflection-based fiber-optic tweezers [16]; axicon-tip fiber optical tweez-ers [17]; high-index fiber-optic tweezers [18], twin-core fiberoptical tweezers [19]; four-core fiber optical tweezers [20] andothers.

Although the single fiber optical tweezers, which is based onthe micro structure multi-core fiber [16], [19], [20], not onlycan trap the yeast cells but also can make the trapped yeast cellsrotation; the single fiber optical tweezers, which is based on thenormal single core fiber, is much more common and convenientfor most researchers. Compared with the multi-core single fiberoptical tweezers, the power launching [21] and distribution ratiocontrol [20] in a normal single core fiber is much easier thanmulti core fiber. However, the function of the normal singlefiber optical tweezers is single: the normal single fiber opticaltweezers just can only trap micro particle. In order to developthe normal single fiber optical tweezers new function, such asrealizing the contact-less optical trapping, we have excited theLP01 and LP11 mode beam in the normal communication fiberand control the power ratio of them, when the power of theLP01 mode beam dominates (P01 :P11 > 0.76:0.24), the trappingposition will be far away from the fiber tip and realize thecontact-less optical trapping [22]. On the basis of this, in thispaper, we go on developing the new function of the single opticaltweezers: using the LP11 mode beam as an operational tool toconstruct a novel single fiber optical tweezers to develop thesingle fiber optical tweezers new performance: realizing theyeast cells multi-dimensional manipulation, such as deflection,orientation and even rotation. To the best of our knowledge, itis the first report about the trapped yeast cells being driven bythe single fiber optical tweezers in multi dimensions.

II. FIBER PROBE FABRICATION

The LP11 mode beam is excited by splicing conventional980-nm single mode fiber (ClearLite R©980 Photonic Fibers,OFS) to a normal single mode fiber (Corning R© SMF-28) with adefined offset (∼2 μm). The two-step method [22] is employedto fabricate the tapered-shape fiber tip, and the images of thefiber tip are shown in Fig. 1. Unlike the fiber tip fabricated bythe normal chemical etching [17] or heating fused tapered tech-nology [14], [19], the fiber tip here is fabricated by using theselective chemical etching and discharge current fusion moldingprocedure. In step one, the fiber tip is molded to be a cone shape

0733-8724 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

ZHANG et al.: MULTI-DIMENSIONAL MANIPULATION OF YEAST CELLS USING A LP1 1 MODE BEAM 1099

Fig. 1. (a) Image of the fiber tapered-tip fabricated after step one. (b) Imageof the final fiber tapered-tip, fabricated after step two, where 2R is the diameterof the fiber core. (c) Magnified image of the final fiber tapered-tip, where r isthe radius of the half-lens tip.

Fig. 2. (a) Simulation results of the LP11 mode beam output optical fielddistribution. (b) Image of far field profile distribution of the LP11 mode beamwith two lobes.

structure with the cone angle of 30◦ [see Fig. 1(a)]; after moldedby the step two, the fiber tip can be regarded as a truncated conewith cone angle of 60◦ and a half-lens with radius r = 1.0 μm[see Fig. 1(b) and (c)].

According to Fig. 2(a), the LP11 mode beam propagates in thecore, totally internal reflects on the fiber tip side, then convergesinside of the fiber tip, and finally refracts out of fiber from thetip. The converging position of the LP11 mode beam is inside ofthe fiber tip, where the light field gradient distribution is large,therefore the yeast cells outside of the fiber tip will be drawnand moving towards the fiber tip. The beam propagation method(BeamPROP R©, RSoft) is employed to simulate the output lightfield distribution. Simulation condition: light source wavelengthis 980 nm; the fiber core diameter is 8.2 μm. The refractive indexof the fiber core and the surrounding medium (water) are 1.4676and 1.33 respectively.

III. METHORD AND EXPERIMENTIAL SETUP

Although the fiber probe presented above is the same as thatin [22], the optical tweezers function, manipulation and controlmethod are much different.

A. Method of Varying Power Distribution Ratio in Two Lobes

For the normal communication fiber, whose core is circular,we just need consider one polarized direction (for example, x-polarized modes). Therefore the light field of the LP01 and LP11modes can be expressed as [23]

ψ01 (r, z) = A01ϕ01 (r) exp [−j (β01z + α01)] (1)

ψ11 (r, z) = A11ϕ11 (r) exp [−j (β11z + α11)] (2)

Fig. 3. Interference patterns (the fiber operated at Δα = 0 and normalizedfrequency V = 3.212). (a) ΔβΔL = 0; (b) ΔβΔL = π/4; (c) ΔβΔL = π/2;(d) ΔβΔL = 3π/4; (e) ΔβΔL = π .

Fig. 4. Images of the light field patterns with different ΔL. (the normalizedfrequency V = 3.212) (a) ΔL = 0 μm; (b) ΔL = 40 μm; (c) ΔL = 80 μm;(d) ΔL = 120 μm; (e) ΔL = 160 μm.

where ϕ01(r) and ϕ11(r) are the scalar field functions of LP01and LP11 beam respectively, A01 and A11 are the amplitudecoefficients of the modes, β01 and β11 are longitudinal propa-gation constants of the modes, and α01 and α11 are the initialphase difference between modes.

The intensity pattern due to the interference of LP01 and LP11modes is given by

I (r, z) = ψ201 + ψ2

11 + 2ψ01ψ11 cos (Δβz + Δα) (3)

where Δβ = β01 − β11 ,Δα = α01 − α11 .When the fiber is stretched by ΔL in axial strain, the intensity

pattern due to the interference of LP01 and LP11 modes is givenby

I (r, z) = ψ201 + ψ2

11 + 2ψ01ψ11 cos [Δβ (z + ΔL) + Δα] .(4)

The MATLAB R© calculation is employed to obtain the fieldpattern oscillation distributions as shown in Fig. 3, where thefiber length varies from z to z + ΔL. The simulation condition:n1 = 1.4676, Δ = (n1 − n2)/n1 = 0.003, A11 = 1, A01 /A11 =0.5, and λ = 980 nm.

In our experiment, the Δβ and the Δα are independent onthe axial strain, when we stretch the fiber and cause the fiberlength varying from z to z + ΔL, the two lobes of the outputintensity generate energy exchange and oscillation responded tothe varying of ΔL as shown in Fig. 4.

B. Method of Varying Field Pattern Orientation of Two Lobes

The LP11 mode has a field pattern consisting of two lobesdistributed symmetrically around the fiber center. Generally,when a fiber is being twisted, its field pattern will be affectedsimultaneously by both a geometric effect, and an opto-elasticeffect [24]. The geometric effect rotates the field pattern inthe same direction as the applied external rotation of the fiber.The opto-elastic effect applies an additional counter rotationeffect to the field pattern through a change in the mode field byrefractive index perturbation. Therefore, combining geometricalrotation with opto-elastic effects, the LP11 mode field patternwill rotate around the fiber geometric center with the rotationangle linearly proportional to the fiber twist angle [25]. Fig. 5

1100 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 6, MARCH 15, 2014

Fig. 5. Images of the light field patterns with different fiber twisting angle.Here θ is the LP11 mode beam field pattern rotation angle; α is the twistingangle loaded on the fiber. And from the experimental results above, the linearlyrelation between the θ and α is θ ≈ 0.9α.

Fig. 6. Configuration of the experimental set-up of the single fiber tweezerswith LP11 mode beam. Here the mode selector is used to control the powerratio between the LP01 and LP11 mode beam [22]; the tension loading unit isemployed to load the tension on the fiber to stretch the fiber and change thepower distribution in two lobes of the LP11 mode beam, and the fiber lengthfixed between P1 and P2 is ∼1 m; the twist loading unit is employed to twistthe fiber and making the two lobes rotating around the fiber axis. PC, personalcomputer; CCD, charge coupled device.

gives the experiment results of the two lobes rotation with thetwisting loaded on the fiber.

C. Experimental Set-Up

The configuration of the single fiber optical tweezers withLP11 mode beam is described in Fig. 6. A 980-nm laser lightsource with power adjusting range of 0 to 110 mW is employed.The cores of 980-nm light source pigtail and the normal SMFare spliced with a defined offset to excite the LP11 mode beampropagation. The tension loading unit is employed to produceand control the power oscillation distribution in the two lobesof the LP11 mode beam. The twist loading unit is employed tocontrol the rotation of the LP11 mode beam field pattern.

IV. MULTI-DIMENSIONAL MANIPULATION

The multi-dimensional manipulation of the yeast cells drivenby the single fiber optical tweezers with the LP11 mode beam canbe classified into three classifications: one is the manipulationin the x−z plane (see Fig. 7), the yeast cells deflecting or orien-tating about the fiber tip; the second one is the manipulation in

Fig. 7. Schematic diagram of the LP11 mode beam trapping an ellipsoidalyeast cell, whose radiuses are ra , rb and rc (ra �= rb �= rc ). The most stabletrapping state meets the condition of ra < rb < rc . (a) The structure of theellipsoidal yeast cell. (b) The long axis of the cell is along the z axis. (c) Thelong axis of the cell is along the y axis. (d) The long axis of the cell is along thex axis.

Fig. 8. Video images of the manually controlled rotation (around the fiber tip)of a yeast cell manipulated by the LP11 mode beam. Here σ is the rotation angleof the yeast cell.

the x−y plane, the yeast cells deflecting or orientating about thefiber main axis; the third one is the combination manipulationof above two, which is the manipulation exerting on the yeastcells in the x−y−z space, realizing the truly multi-dimensionalcontrollable arbitrary orientation manipulation.

A. Manipulation in X−Z Plane

According to the Fig. 7, for an ellipsoidal yeast cell, thethree radii in the Cartesian coordinate system are ra , rb and rc

respectively [see Fig. 7(a)], which are unequal to each other.The probable trapping states caused by the LP11 mode beam arein three forms, as shown in Fig. 7(b), (c) and (d) (labeled with“A”, “B” and “C”).

The state “A”, whose potential energy is the lowest, is themost stable trapping state [26], therefore the trapping realizedby the LP11 mode beam will be in this form. When we vary thelight power distribution ratio in the two lobes of the LP11 modebeam, the trapped yeast cells will correspondingly deflect aboutthe fiber tip in x−z plane as shown in Figs. 8(a)–(l).

Since the yeast cell size (∼several μm) and the laser wave-length (∼1 μm) have the same order of magnitude, the numericalalgorithm is employed to calculate the optical forces exerting onthe yeast cells. Here the finite difference time domain (FDTD )method, as a normal numerical algorithm, is selected. The 3-DFDTD method requires a huge computer memory and the LP11beam mode field distribution is symmetric about the fiber mainaxis in the x−z plane, therefore the 2-D FDTD algorithm [27]is employed to simulate and verify the deflection manipulationmechanism presented above, and the results are shown in Fig. 9.FDTD simulation conditions: the light source wavelength is980 nm; the diameter of fiber core is 8.2 μm, the long and shortdiameters of the yeast cell are 6 and 4 μm respectively. The re-fractive index of the fiber core, yeast cells, and the surrounding

ZHANG et al.: MULTI-DIMENSIONAL MANIPULATION OF YEAST CELLS USING A LP1 1 MODE BEAM 1101

Fig. 9. (a) Simulation model and light field distribution with unequal powerin two lobes of LP11 mode beam. Here σ is the angle between the long-axisof the yeast cells and the fiber main axis (z axis). (b) Simulation results oftorques generated by the LP11 mode beam with different power ratio in twolobes. Where PL means the power in the left lobe and PR means the powerin the right lobe. Here we define the torque positive direction is clockwise. (c)Original partial magnification of (b) as labeled by the black circle with dashedlines.

medium (water) are 1.4676, 1.40 and 1.33 respectively. The gridstep is chosen as 0.05 μm.

According to the Fig. 9(b), for σ = 0◦ (labeled by “�”), whenthe power in left lobe is larger than the power in the right one,the torque is larger than zero, which means the LP11 mode beamdrives the yeast cells to rotate clockwise; when the power in leftlobe is less than the power in the right one, the torque is less thanzero, which means the LP11 mode beam drives the yeast cells torotate counterclockwise; when the power in right lobe is equalto the power in the left lobe, the torque is zero, which meansthe yeast cell is trapped without rotation. For σ = 30◦ (labeledby “♦−”), when the power distribution is in the range of −0.09< log(PL /PR ) < 0 [see Fig. 9(c)], where the power in left lobeis less than the power in the right lobe, but the torque is largerthan zero, which means the yeast cells will rotate clockwiseeven though the power in right lobe is larger than the left lobe,which is caused by the initial deflection of the yeast cells. Thecondition of σ = 60◦ (labeled by “�”) has the similar results,when the power distribution is in the range of 0 < log (PL /PR )< 0.08, where the power in the left lobe is larger than the powerin the right one, but the torque is less than zero, which means theyeast cells will rotate counterclockwise caused by the relativelarger initial deflection angle of the yeast cells.

B. Manipulation in X−Y Plane

In order to demonstrate clearly the LP11 mode beam drives thetrapped yeast cells deflecting about the fiber main axis in x−yplane, the micro particle with two-body structure [see Fig. 10(a)]is employed. Similarly with the ellipsoidal yeast cells, the prob-able trapping states of this two-body micro particle are shownin Fig. 10(b), (c) and (d). Unlike the ellipsoidal yeast cells, thestate “B” is the most stable trapping state. Therefore the trappingrealized by the LP11 mode beam will be in the form of state “B”(see Fig. 11). Actually this two-body structure micro particleis constructed by two yeast cells which are connected by theliquid adhesion in the solution. When we adjust the output lightfield pattern distribution of the LP11 mode beam, the trapped

Fig. 10. Schematic diagram of LP11 mode beam trapping a micro particlewith the two-body structure. (a) the structure of the two-body micro particle; (b)the connecting line of the two cells center is along the z axis; (c) the connectingline of the two cells center is along the y axis; (d) the connecting line of the twocells center is along the x axis.

Fig. 11. Video images of the manually controlled rotation (around the fiberaxis) of a two-body structure yeast cells trapped by the LP11 mode beam. Thetop images of (a)–(e) show the yeast cells with two-body structure rotate aroundthe fiber axis. The bottom images of (a)–(e) are the schematic diagrams of thetransverse light field rotation distributions. (f) Shows the coordinate system inthe top images; and (g) shows the coordinate system in the bottom images.

Fig. 12. Video images of the manually controlled combination rotation(around the fiber axis and tip) exerting on the yeast cell. (a)–(d) show thetrapped yeast cell rotates around the fiber tip in the xoz plane with the rotationangle increasing; (d)–(f) show the yeast cell rotates around the fiber tip in thexoz plane with the rotation angle decreasing. (g)–(h) show the same yeast cellrotates around the z axis about 90◦ and then rotation around the fiber tip; (i)shows the same yeast cell deflects along the +y direction; (j) shows the sameyeast cell turns back with no deflection along the y direction; (k) shows thesame yeast cell deflects along the −y direction; (l) shows the yeast cell turnsback to the initial state: the cell long-axis coincides with the z axis.(m) Videoof the multi-dimensional manipulation exerting on the yeast cell (Media 1).

yeast cells with two-body structure will rotate correspondinglyas shown in Fig. 11(a)–(e).

When the two lobes distribute symmetrically with the x axis(see Fig. 11(a, bottom)), the trapping realized by the LP11 modebeam will be in the state of two bodies symmetrically with yaxis as seen in Fig. 11(a, top). When we rotate the field patternof the output light field, the trapping state of the two-body yeastcells will rotate correspondingly [see Fig. 11(b), (c), (d) and(e)]. This rotation manipulation is just like that we clamp theyeast cells and then rotate the clamper to realize the rotation ofthe yeast cells.

C. Combination Manipulation

The combination manipulation drives the trapped yeast cellsrotating around the fiber main axis while rotating around thefiber tip (see Fig. 12). Actually the combination rotation is thecommon form for the LP11 mode beam to drive the trappedyeast cells rotating.

1102 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 32, NO. 6, MARCH 15, 2014

V. CONCLUSION

We have successfully demonstrated a single fiber opticaltweezers with the LP11 mode beam as a powerful tool for themulti-dimensional manipulation of yeast cells. This single fiberoptical tweezers employ the LP11 mode beam guided by a nor-mal single core fiber for both trapping and deflection, orientationeven rotation of the trapped yeast cells. By varying the light fielddistribution of LP11 mode beam (transverse light field distribu-tion direction and the power ratio of two lobes), the deflectionand the orientation of the yeast cells could be realized andcontrolled.

This technique can be extended to the biochemical analysisand manipulation. Since this single fiber optical tweezers couldbe easily integrated with other micro optical device platform,the proposed configuration can find potential applications inlab-on-a-chip devices.

REFERENCES

[1] A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of asingle-beam gradient force optical trap for dielectric particles,” Opt. Lett.,vol. 11, no. 5, pp. 288–290, May. 1986.

[2] A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation ofviruses and bacteria,” Science, vol. 235, no. 4795, pp. 1517–1520, Mar.1987.

[3] J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Obser-vation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett., vol. 41, no. 20, pp. 1361–1364, Nov.1978.

[4] R. C. Gauthier, “Optical trapping: a tool to assist optical machining,” Opt.Laser Technol., vol. 29, no. 7, pp. 389–399, Oct. 1997.

[5] J. C. Crocker and D. G. Grier, “When like charges attract: The effects ofgeometrical confinement on long-range colloidal interactions,” Phys. Rev.Lett., vol. 77, no. 9, pp. 1897–1900, Aug. 1996.

[6] M. W. Saurabh Raj and D. Petrov, “Absorption spectroscopy of single redblood cells in the presence of mechanical deformations induced by opticaltraps,” J. Biomed. Opt., vol. 17, no. 9, p. 097006, Sep. 2012.

[7] B. Landenberger, H. Hofemann, S. Wadle, and A. Rohrbach, “Microfluidicsorting of arbitrary cells with dynamic optical tweezers,” Lab Chip, vol. 12,pp. 3177–3183, May 2012.

[8] K. Onda and F. Arai, “Multi-beam bilateral teleoperation of holographicoptical tweezers,” Opt. Exp., vol. 20, no. 4, pp. 3633–3641, Feb. 2012.

[9] A. Constable, J. Kim, J. Mervis, F. Zarinetchi, and M. Prentiss, “Demon-stration of a fiber-optical light-force trap,” Opt. Lett., vol. 18, no. 21,pp. 1867–1869, Nov. 1993.

[10] J. Guck, R. Ananthakrishnan, T. J. Moon, C. C. Cunningham, and J. Kas,“Optical deformability of soft biological dielectrics,” Phys. Rev. Lett.,vol. 84, no. 23, pp. 5451–5454, Jun. 2000.

[11] J. Guck, S. Schinkinger, B. Lincoln, F. Wottawah, S. Ebert, M. Romeyke,D. Lenz, H. M. Erickson, R. Ananthakrishnan, D. Mitchell, J. Kas,S. Ulvick, and C. Bilbyet, “Optical deformability as an inherent cellmarker for testing malignant transformation and metastatic competence,”J. Biomed. Opt., vol. 88, no. 5, pp. 3689–3698, May. 2005.

[12] R. W. Applegate, J. Squier, T. Vestad, J. Oakey, and D. W. M. Marr,“Fiber-focused diode bar optical trapping for microfluidic flow manip-ulation,” Appl. Phys. Lett., vol. 92, no. 1, pp. 0139041–0139043, Jan.2008.

[13] R. S. Taylor and C. Hnatovsky, “Particle trapping in 3-D using a singlefiber probe with an annular light distribution,” Opt. Exp., vol. 11, no. 21,pp. 2775–2782, Oct. 2003.

[14] Z. H. Liu, C. K. Guo, J. Yang, and L. B. Yuan, “Tapered fiber opticaltweezers for microscopic particle trapping: fabrication and application,”Opt. Exp., vol. 14, no. 25, pp. 12510–12516, Dec. 2006.

[15] L. B. Yuan, Z. H. Liu, and J. Yang, “Measurement approach of brownianmotion force by an abrupt tapered fiber optic tweezers,” Appl. Phys. Lett.,vol. 91, no. 5, pp. 0541011–0541013, Jul. 2007.

[16] C. Liberale, P. Minzioni, F. Bragheri, F. D. Angelis, E. D. Fabrizio, andI. Cristiani, “Miniaturized all-fibre probe for three-dimensional optical

trapping and manipulation,” Nature Photon., no. 1, pp. 723–727, Nov.2007.

[17] S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Manipulation of mam-malian cells using a single-fiber optical microbeam,” J. Biomed. Opt.,vol. 13, no. 5, p. 054049, Oct. 2008.

[18] K. Sarwar, C. Kerbage, A. Fernandez-Nieves, and D. A. Weitz, “Opticalmanipulation and rotation of liquid crystal drops using high-index fiber-optic tweezers,” Appl. Phys. Lett., vol. 91, no. 9, pp. 0911191–0911193,Aug. 2007.

[19] L. B. Yuan, Z. H. Liu, J. Yang, and C. Y. Guan, “Twin-core fiber opticaltweezers,” Opt. Exp., vol. 16, no. 7, pp. 4559–4566, Mar. 2008.

[20] Y. Zhang, Z. H. Liu, J. Yang, and L. B. Yuan, “Four–core optical fibermicro–hand,” J. Lightw. Technol., vol. 30, no. 10, pp. 1487–1491, May2012.

[21] L. B. Yuan, Z. H. Liu, and J. Yang, “Coupling characteristics betweensingle-core fiber and multicore fiber,” Opt. Lett., vol. 31, no. 22, pp. 3237–3039, Nov. 2006.

[22] Z. H. Liu, L. Wang, P. B. Liang, Y. Zhang, J. Yang, and L. B. Yuan,“Mode division multiplexing technology for single-fiber optical trappingaxial-position adjustment,” Opt. Lett., vol. 38, no. 14, pp. 2617–2620, Jul.2013.

[23] A. W. Snyder and J. D. Love, Optical Waveguide Theory. London, U.K.:Chapman & Hall, 1983, Ch. 13, pp. 281–300.

[24] R. Ulrich and A. Simon, “Polarization optics of twisted single-modefibers,” Appl. Opt., vol. 18, no. 13, pp. 2241–2251, Jul. 1979.

[25] Y. F. Yuan, G. Wu, X. Li, Y. Q. Fan, and X. K. Wu, “Effects of twisting andbending on LP21 mode propagation in optical fiber,” Opt. Lett., vol. 36,no. 21, pp. 4248–4250, Nov. 2011.

[26] M. Ikeda, K. Tanaka, M. Kittaka, M. Tanaka, and T. Shohata, “Rotationalmanipulation of a symmetrical plastic micro-object using fiber optic trap-ping,” Opt. Commun., vol. 239, no. 1–3, pp. 103–108, Sep. 2004.

[27] H. Yang, G. Y. Feng, S. H. Zhou, and H. Y. Ding, “A new method basedon conservation momentum to calculate the trapping force using FDTDalgorithm,” Proc. Symp. Photon. Optoelectron., pp. 1–4, 2010.

Yu Zhang received the B.S. degree in physics education, the M.S. degree in bio-physics, and the Ph.D. degree in photonics from Harbin Engineering University,Harbin, China, in 2003, 2006, and 2012, respectively. She is currently with thePhotonics Research Center, College of Science, Harbin Engineering University.Her research interests include fiber optic trapping and its applications. She is theauthor or coauthor of more than ten papers published in various internationaljournals.

Peibo Liang received the B.S. degree in physics and the M.S. degree in opticalengineering from Harbin Engineering University, Harbin, China, in 2009 and2012, respectively. She is currently working toward the Ph.D. degree with thePhotonics Research Center, College of Science, Harbin Engineering University.His research interests include waveguide theory and optical fiber trapping.

Jiaojie Lei received the B.S. degree in photonics from Harbin Engineering Uni-versity, Harbin, China, in 2011. She is currently working toward the M.S. degreewith the Photonics Research Center, College of Science, Harbin EngineeringUniversity. Her research interests include waveguide theory and optical fibertrapping.

L. Wang, biography not available at the time of publication.

Zhihai Liu received the B.S. degree in optoelectronics, the M.S. degree in op-tical engineering, and the Ph.D. degree in photonics from Harbin EngineeringUniversity, Harbin, China, in 1999, 2003, and 2006, respectively. He is currentlywith the Photonics Research Center, College of Science, Harbin EngineeringUniversity. His research interests include fiber optic trapping and its applica-tions. He is the author or coauthor of more than 30 papers published in variousinternational journals.

ZHANG et al.: MULTI-DIMENSIONAL MANIPULATION OF YEAST CELLS USING A LP1 1 MODE BEAM 1103

Jun Yang received the B.S. degree in optoelectronics, the M.S. degree in opticalengineering, and the Ph.D. degree in photonics from Harbin Engineering Uni-versity, Harbin, China, in 1999, 2002, and 2005, respectively. He is currently aProfessor in the Photonics Research Center, College of Science, Harbin Engi-neering University. His research interests include fiber optic sensors and opticinterferometers. He is the author or coauthor of more than 60 papers publishedin various international journals.

Libo Yuan received the B.S. degree in physics from Heilongjiang University,Harbin, China, in 1984, the M.Eng. degree in communication and electronicsystem from Harbin Shipbuilding Engineering Institute, Harbin, in 1990, andthe Ph.D. degree in photonics from The Hong Kong Polytechnic University,Kowloon, Hong Kong, in 2003. He is currently a Professor in the PhotonicsResearch Center, Harbin Engineering University. His research interests includemicrostructured fiber-based in-fiber integrated optics, fiber optic devices andcomponents, and fiber optic sensors and its applications. He is the author orcoauthor of more than two book, four book chapters, and 280 of his researchpapers. He is the holder of 25 patents.