APPLIED PHYSICS LETTERS 92, 161110 共2008兲
Static optical sorting in a laser interference field Petr Jákl, Tomáš Čižmár, Mojmír Šerý, and Pavel Zemáneka兲 Institute of Scientific Instruments of the ASCR, v.v.i., Academy of Sciences of the Czech Republic, Královopolská 147, 612 64 Brno, Czech Republic
共Received 17 January 2008; accepted 3 April 2008; published online 24 April 2008兲 We present a unique technique for optical sorting of heterogeneous suspensions of microparticles, which does not require the flow of the immersion medium. The method employs the size-dependent response of suspended dielectric particles to the optical field of three intersecting beams that form a fringelike interference pattern. We experimentally demonstrate sorting of a polydisperse suspension of polystyrene beads of diameters 1, 2, and 5.2 m and living yeast cells. © 2008 American Institute of Physics. 关DOI: 10.1063/1.2913759兴 Optical micromanipulation techniques have been attracting increasing attention in recent years especially due to the growing list of their various applications.1 Among them, light-based separation of micro-objects—termed optical sorting2,3—occupies a prominent position. There exist several classes of optical sorting techniques. The so-called active methods require external recognition of particle properties 共e.g., fluorescence兲 and subsequently, one applies an optical force 共optical tweezers or controlled radiation pressure兲 to deviate the particles into separate channels.4–6 On the other hand, passive sorting is based on one or more intrinsic physical properties 共e.g., size, and refractive index兲 that, in turn, results in a different behavior of such particles placed within an optical field without any active recognition step involved. For example, optical chromatography employs counteracting forces coming from the fluid flow and laser radiation pressure, which both differently depend on the particles’ properties. Thus, different particles have different equilibrium positions and a spatial separation of suspension components is achieved.7,8 The so-called cross-type optical chromatography uses a laser beam perpendicular to the fluid flow.9 More complex passive sorting arrangements utilize a static optical potential landscape 共so-called optical lattice兲 frequently combined with fluid flow.10–13 The size and/or material 共refractive index兲 of objects drifting in the fluid flow strongly influences the trajectories of the objects through the optical lattice. Since the optical lattice sorting relies on the mutual motion of the objects and fluid, a traveling optical lattice in a static fluid 共so-called static sorting兲 also sorts micro-objects and even submicrometer objects.14,15 The combination of fluid flow and dynamic optical lattice minimizes the limitations coming from the particle-particle interactions.16 Recently, it was demonstrated that due to the thermal motion of micro-objects in the fluid, objects of different properties can be still sorted even if both the fluid and the optical lattice are static.17 In this paper, we present a separation method that also takes advantage of a simple arrangement of both a static fluid and a static optical lattice, but instead of thermal motion, radiation pressure is used to differentially propel the objects and, thus, sort them. Our method is based on the imbalance between optical forces acting on particles of different sizes and/or refractive indices placed within an interference field created by three a兲
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beams. Two of the beams copropagate and create interference fringes on the top surface of the sample-filled cuvette where they overlap 共see Fig. 1兲. The behavior of suspended particles in the direction perpendicular to the fringes is similar to the well studied configuration of a particle placed within a standing wave.15,18,19 The particles settle with their centers in the fringe maximum or minimum according to their sizes, but there also exist intermediate particle sizes that feel no force coming from the intensity modulation across the interference fringes. Along the fringes, the particles are pushed by the radiation pressure exerted by both beams. This force significantly varies with the particle size and refractive index and it also
FIG. 1. Experimental configuration. Linearly polarized laser beams from laser Verdi V5 共Coherent, 5.5 W, 0 = 532 nm兲 are focused with lenses into the optical glass cuvette 共23/G/5, Starna Cells兲. The white arrows and dots mark beam polarizations that are controlled by polarizing beamsplitters with half-wave plates. All three beams overlap on the top surface of the cuvette and form a sorting region of size 40⫻ 60 m2 elongated along the z axis. The distance between the interference fringes L is adjusted by changing the distance ⌬ between the two beams coming from the left and is given by L = / 共2 sin ␣ cos 兲, where is the laser wavelength in the medium and angles ␣ and  are defined in the figure. The Roman numbers I–IV in the inset indicate four different types of object behavior, which is further described in Fig. 2.
0003-6951/2008/92共16兲/161110/3/$23.00 92, 161110-1 © 2008 American Institute of Physics Downloaded 15 May 2008 to 195.178.70.247. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
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FIG. 2. Calculated optical forces as a function of particle diameter d in the arrangement of three incident plane waves with  = 42° and L = 2.6 m 共top兲 or L = 5 m 共bottom兲. The intensities of both copropagating beams correspond to the experimental values 0.7 mW/ m2 and the intensity of the third beam is 2 cos共␣兲⫻ higher. Fxextr 共thick curves兲 corresponds to the extremal optical force across the fringes 共positive for equilibrium position xeq located at the fringe intensity maximum兲. Fz共xeq兲 共thin curves兲 corresponds to the optical force along the fringes for the object placed at fringe intensity maximum 共regions I and II兲 or minimum 共regions III and IV兲. The ripples come from Mie scattering resonances. The refractive indices of polystyrene and water were npolyst = 1.5878+ i0.0004 and nw = 1.335.
strongly depends on the transversal equilibrium location of the particle 共i.e., if the particle settles in the fringe intensity maximum or minimum兲. Therefore, particles of different properties move with different velocities along the fringes. In order to achieve particle sorting, we use a third beam that counter propagates with respect to the above two beams and the polarization of which is perpendicular to them to minimize any interference effects with them. Its intensity is tuned so that the subsequent radiation pressure force results in a reversal of the motion of the slower particles. This results in the static optical sorting of two types of microparticles to opposite directions by the radiation pressure, without any fluid flow or fringe movement 共compare behaviors I–IV in Fig. 1兲. Up until now, only planar configurations with three beams have been both theoretically20–23 and experimentally studied.24 However, our experiments revealed that the planar configurations are not convenient due to the jamming of particles in the sorting region. Therefore, we have designed a three-dimensional configuration wherein the sorting region is placed on the top surface of a cuvette filled with a heterogeneous suspension of particles. Laser beams coming from the bottom of the cuvette propel the micro-objects to the region
Appl. Phys. Lett. 92, 161110 共2008兲
FIG. 4. Sorting of polystyrene microspheres of types I and II of diameters 2 m 共Duke Scientific 4K-02, 1.998⫾ 0.022 m兲 and 5.2 m 共Duke Scientific 240, 5.2⫾ 0.5 m兲 placed into intensity maxima of interference fringes of width 5 m. For the sake of clarity, one selected particle is marked with a cross and the fast motion of two smaller ones is followed with the arrows.
where the beams overlap and where the particle sorting takes place 共see Fig. 1兲. Figure 2 illustrates how the particle diameter influences the optical forces Fextr and Fz共xeq兲. Their shapes reveal the x origin of particles behavior for four different particle sizes in Fig. 1. A sign reversal of Fz occurs either for particles of different sizes placed all within fringe intensity maxima 共I, II兲 or minima 共III, IV兲 or if one size is localized in intensity maximum 共I or II兲 and the other in minimum 共IV or III兲. This behavior leads to particle sorting demonstrated below. Figure 3 confirms the optical sorting of the binary suspension of 1 m 共type I兲 and 5.2 m 共type IV兲 particles. In agreement with the theoretical predictions in Fig. 2, the sorted particles are pushed in opposite directions along the fringes. As illustrated by Fig. 4, even when objects of both sizes are drawn to the fringe maximum 共types I and II兲, they can still be propelled to opposite directions 共and, thus, sorted兲 for the appropriate intensity of the counterpropagating beam. Figure 4 also clearly demonstrates particles arriving at the top of the cuvette from the bulk solution underneath. When located further from the top cuvette surface, the particles are out of focus 共see the black arrows in the figure兲, whereas at the level of the surface, they are in focus. Figure 5 demonstrates the successful application of our method to the sorting of biological objects of different sizes, namely, yeast cell spores 共smaller size兲 and living yeast cells suspended in water. In this paper, we have introduced an experimental method for sorting of micro-objects 共including living cells兲 according to their size in a static geometry of three laser
FIG. 3. Sorting of polystyrene microspheres of diameters 1 m 共Duke FIG. 5. Sorting of living yeast cells and spores. The smaller objects are Scientific 5100A, 1.07⫾ 0.01 m兲 and 5.2 m 共Duke Scientific 240, 5.2⫾ 0.5 m兲 placed into interference fringes of width 2.6 m and vertiyeast spores; they settle in the fringe maxima and are pushed along the cally oriented in the figure. Smaller particles settle in the fringe intensity positive direction of the z axis while the larger objects 共cells兲 are drawn to maximum 共type I兲 and the bigger ones in intensity minimum 共type IV兲. The the intensity minima and subsequently pushed in negative z axis direction. time scale in seconds is denoted above the figure. The width of the fringes was set to 5 m. Downloaded 15 May 2008 to 195.178.70.247. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
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beams. The proposed technique does not require the flow of the immersion medium. Its main advantage is that the sorted particles or cells need not be stained or modified and is, thus, passive in nature. The experimentally tested throughput of this method is about 0.5–5 particles per second. The presented experimental results are in very good agreement with the theoretical predictions even though the calculations are based on a simplified description of the incident beams as plane waves. The theoretical model suggests that the method can be also applied to sort micro-objects of similar sizes with respect to their refractive indices 共not experimentally demonstrated in this paper兲. The sorted particles can be extracted through, for example, a microfluidic output in the top part of the cuvette. A possible combination of our method with fluid flow or interference fringe movement could increase the throughput and number of sorted sizes and result in optical fractionation. The authors are obliged to Professor K. Dholakia and Doctor A. Jonáš for their critical comments and we acknowledge support from the GA AS CR 共KJB100650601兲, ISI IRP 共AV0 Z20650511兲, MEYS CR 共LC06007兲 and EC 6FP NEST ADVENTURE Activity 共Project ATOM-3D, No. 508952兲. M. J. Lang and S. M. Block, Am. J. Phys. 71, 201 共2003兲. B. S. Zhao, Y.-M. Koo, and D. S. Chung, Anal. Chim. Acta 556, 97 共2006兲. 3 K. Dholakia, M. P. MacDonald, P. Zemánek, and T. Čižmár, Methods Cell Biol. 82, 467 共2007兲. 4 T. N. Buican, M. J. Smyth, H. A. Crissman, G. C. Salzman, C. C. Stewart, and J. Martin, Appl. Opt. 26, 5311 共1987兲. 1 2
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