Abstract

We demonstrate two-dimensional optical trapping and manipulation of 1 μm and 2.2 μm polystyrene particles in an 18 μm-thick fluidic cell at a wavelength of 1565 nm using the recently proposed Silicon-on-insulator Multimode-interference (MMI) waveguide-based ARrayed optical Tweezers (SMART) technique. The key component is a 100 μm square-core silicon waveguide with mm length. By tuning the fiber-coupling position at the MMI waveguide input facet, we demonstrate various patterns of arrayed optical tweezers that enable optical trapping and manipulation of particles. We numerically simulate the physical mechanisms involved in the arrayed trap, including the optical force, the heat transfer and the thermal-induced microfluidic flow.

©2013 Optical Society of America

1. Introduction

Optical tweezers [1] have been widely used as a laboratory tool in the biological and biomedical areas over the past two decades. One important application of optical tweezers is trapping and manipulation of micro- and nano-sized bio-particles (e.g. cells and DNA) [2, 3]. Cells with micron size can be readily manipulated by conventional single-beam optical tweezers [4,5]. DNA can be stretched and unzipped by optically manipulating microbeads binding to the ends of the DNA [6,7]. Therefore, manipulating micron-sized particles is one relevant application for optical tweezers technology [8].

Recently, optical manipulation of multiple particles by two- or three-dimensional (2D or 3D) optical beam patterns (also known as optical lattices) has been demonstrated using various approaches such as microlens array, acousto-optic deflectors and multiple-beam interference [912]. The microfabricated microlens array is reliable and cost-efficient for generation of fixed 2D optical tweezers array patterns [9]. The acousto-optic deflectors enable fast switching and modulation of multiple optical tweezers with accurate spatial- and time-domain control [10]. Among the techniques using multiple-beam interference, one notable avenue is the so-called holographic optical tweezers (HOT) using spatial light modulator (SLM) technique [1215]. When an incident light beam shines on a SLM, which is an array of electro-optic devices with individually switchable phase-sensitive elements, the reflected light beam carrying certain spatial-dependent intensity- and phase-modulations can interfere with itself to yield complex optical patterns serving as two-dimensional optical tweezers [16]. Controlled by algorithms, HOT are capable of shaping a light beam into a complex 2D or 3D optical tweezers array. Using HOT, researchers have demonstrated a host of interesting phenomena and applications in optics and the biomedical areas, such as optical vortices, microscopy and molecular kinetics [17,18]. However, HOT require free-space projection of the light beam from a sophisticated bulk optical component in order to form the holographic beam patterns, and thus make HOT less favorable for integration with fluidic chips. To our knowledge, optical tweezers array generation techniques that can potentially be miniaturized and integrated with fluidic chips for lab-on-chip applications are still not well explored.

Previously [19], we proposed and demonstrated the use of large-core square silicon-on-insulator (SOI) multimode-interference (MMI) waveguides to shape an optical beam into two-dimensional optical lattices for the trapping and manipulation of polystyrene particles. Here we term our technique as Silicon-on-insulator Multimode-interference waveguide-based ARrayed optical Tweezers (SMART). Although the generated patterns by SMART are not as complex or flexible as those demonstrated by HOT, the MMI waveguide as a key component in SMART technique can be fabricated on an optofluidic chip to potentially realize fully integrated on-chip arrayed optical tweezers.

In this paper, we systematically show two-dimensional optical trapping and manipulation of 1 μm and 2.2 μm polystyrene particles in a thin fluidic cell using SMART. We extract the optical trapping stiffness from analyzing the trapped particle trajectories. We numerically simulate the multiple physical processes involved in the particle trapping in order to decipher the respective roles of the optical trapping and the optical absorption-induced fluidic flow.

2. Principle

The optical field array number generated by a symmetric two-dimensional MMI square-core waveguide is given as [20]

N=1LNnλW2
where N is the symmetric two-dimensional integral array number (N = 1, 2,…), LN is the MMI waveguide length, λ is the propagating wavelength in free space, n is the core refractive index of the SOI MMI waveguide, and W is the square-core waveguide dimension. In this work, we fix λ = 1565 nm, n ≈3.48 and W ≈100 μm. We therefore obtain different array numbers N’s by adopting different waveguide lengths LN’s.

Figure 1 inset schematically shows the trapping of dielectric particles by the two-dimensional arrayed light beams in a thin fluidic cell. The optical trapping of particles by each light beam follows conventional single-beam optical tweezers [1]. However, the optical absorption coefficient of water in the 1550 nm wavelength range (α = 8 cm−1) is two to three orders of magnitude larger than that in the near-infrared (α = 0.043 cm−1 at 850 nm) and the visible (α = 0.0029 cm−1 at 633 nm) wavelengths [21]. In this work, we therefore do not ignore the optical absorption-induced thermal effect in water. In fact, we leverage the optical-absorption-induced thermal flow to assist the trapping and help levitate the particle [22]. Both the optical force and the fluidic drag force contribute to the particle trapping in our optical tweezers system. In the horizontal X and Y directions, the convection flow fluidic force helps collect the particles in the optical tweezers, while the optical gradient force (Fg) traps the particles. In the longitudinal Z direction, the convection flow fluidic drag force (Fc) helps lift up the particle from the cell floor, while the optical scattering force (Fs) and the optical gradient force (Fgz) depends on the particle position relative to the beam focal plane. In order to properly leverage such a flow-assisted manipulation, we need Fc to be comparable to the optical force (Fs + Fgz). In the case that Fc > Fs + Fgz + G + Fb, where G is the gravitational force and the Fb is the buoyant force in water, the particles are to be carried to the cell top [22]. It is thus critical to adopt a relatively thin fluidic cell (we adopt an 18 μm-thick cell in our experiments) in order to minimize the optical absorption and thus limit the vertical flow rate. As such, the flow only serves to help sweep the particles horizontally to the optical tweezers without raising them up to the cell top.

 figure: Fig. 1

Fig. 1 Schematic of the experimental setup. Inset: Schematic of optical trapping and manipulation of particles in a thin fluidic cell using SMART. Fg: the optical gradient force exerted on the particle in the horizontal directions, Fgz: the optical gradient force exerted on the particle in the Z direction, Fs: the optical scattering force exerted on the particle in the Z direction, G: the gravitational force exerted on the particle, Fb: the buoyant force in water, Fc: the convection flow fluidic drag force exerted on the particle in the Z direction. Black solid arrows: the force exerted on the particle. Blue dashed arrows: the absorption-induced fluidic flow. Red solid curves: the light beam intensity distributions in the horizontal and longitudinal directions. Red dashed arrows: beam focal plane.

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3. Experiment

3.1 Experimental setup

Figure 1 schematically shows our experimental setup. The continuous-wave (cw) laser in the 1550nm wavelength range is amplified by a 33dBm erbium-doped fiber amplifier (EDFA) and is end-fired into a SOI square-core MMI waveguide through a butt-coupled single-mode fiber (SMF). The SMF launching position is controlled by the X-Y translation stages. The light spots array from the MMI output facet is projected to a thin fluidic cell of polystyrene particle colloidal solution diluted by deionized (DI) water (~1.6 × 108 particles/ml for 1 μm particles, ~1.3 × 107 particles/ml for 2.2 μm particles). We fabricate the fluidic cell using two glass slides separated and sealed by gel with 18 μm particles. We use a 10× microscope objective (MO) to collect and collimate the light output from the MMI, and use a 20× MO (numerical aperture (NA) = 0.4) to focus the pattern array to a ~50 μm pattern inside the cell. The laser power is ~500 mW measured after the SMF, ~130 mW after the MMI waveguide, and ~100 mW after the 20× MO. We thus estimate the laser power to be approximately or slightly less than 100 mW inside the fluidic cell, given the reflective loss of the focused beam at the glass cell substrate and the scattering loss inside the substrate glass. We use a 50× long-working-distance MO to image the particles onto a charge-coupled device (CCD) camera.

3.2 Device fabrication and MMI patterns generation

We adopt from a previous work 100 μm square-core MMI waveguides on a SOI wafer with a 100 μm silicon layer and a 2 μm buried oxide layer [23]. Figure 2(a) shows the scanning electron micrograph (SEM) of the MMI waveguide cross-section. The waveguide was defined by standard photolithography and etched by plasma reactive ion from the silicon layer to the oxide layer. The waveguide sidewall was smoothed by tetramethyl ammonium hydroxide (TMAH) solution. An oxide upper-cladding layer was formed on the entire waveguide using plasma-enhanced chemical vapor deposition. The cladding thickness is around 2 μm on the top and 0.5 μm on the sidewall. The fabricated waveguides were cleaved to desired lengths and the end-facets were polished.

 figure: Fig. 2

Fig. 2 Imaged light beam array patterns of the MMI waveguides. (a) SEM of the fabricated SOI MMI waveguide featuring the end-facet. (b)-(e) NIR images (in gray scale) of the array patterns from the MMI waveguides of various lengths: (b) 11 mm, (c) 5.5 mm, (d) 4.5 mm and (e) 3 mm. (f) Imaged 7 × 7 array light intensity profile (in gray scale shown in false colors) of the MMI waveguide with 3mm length. Inset of (f): schematic of the relative position between the butt-coupled SMF and the MMI waveguide facet. (g)-(j) Imaged light intensity profiles (in gray scale shown in false colors) with the corresponding SMF core offsets from the MMI waveguide facet center.

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Figures 2(b) to 2(e) show the imaged array patterns from the MMI waveguides of various lengths end-fired at 1565 nm and captured by a near-infrared (NIR) camera after a neutral-density (ND) filter. The array patterns exhibit N = 2 for LN = 11 mm, N = 4 for LN = 5.5 mm, N = 5 for LN = 4.5 mm and N = 7 for LN = 3 mm, which are consistent with Eq. (1). The array patterns are slightly non-uniform due to fabrication imperfections and the surface roughness on the MMI and SMF end-faces.

Figure 2(f) shows the imaged 7 × 7 array pattern from a 3mm-long MMI waveguide. The inset schematically shows the alignment of the end-firing SMF and the MMI waveguide facet. As the SMF cladding diameter of 125 μm is similar to the MMI waveguide width of 100 μm, while the SMF core diameter is only 9 μm, aligning the SMF and the MMI is readily done by aligning the SMF cladding with the MMI waveguide.

We vary the SMF end-firing position from the MMI waveguide center to tailor the output pattern array size and shape [24]. In order to clearly label the SMF end-firing position, we define a coordinate (X’ μm, Y’ μm) relative to the MMI waveguide center. Figure 2(g) shows the imaged 7 × 7 array pattern transforms to a 7 × 3 pattern (columns × rows) as the SMF end-firing position is tuned to (0 μm, −20 μm). Figures 2(h) and 2(i) show that by further offsetting the SMF to (0 μm, −25 μm) and (0 μm, −30 μm), we tune the imaged array patterns to 7 × 2 and 7 × 1, respectively. Figure 2(j) shows the imaged array pattern only appearing from one quarter of the MMI waveguide facet in the case that the SMF is end-firing near the waveguide corner position (20 μm, −20 μm). We remark that for this 3mm-long MMI waveguide the non-symmetric array pattern offset directions are consistent with the SMF offset directions. For MMI waveguides of different lengths, the non-symmetric array pattern offset directions can be opposite to the SMF offset directions.

In addition to the pattern array number variation, the center-to-center spacing of the adjacent light spots also varies from around 5 μm in the 7 × 7 array pattern to around 10 μm in the 7 × 2 array pattern. We note that the 7 × 7 array pattern is captured with the same optical power attenuation (after the same ND filter) as the non-symmetric array patterns, and thus the captured images (Figs. 2(f)2(j)) show that the intensities of the array patterns vary with the SMF end-firing position.

3.3 Microparticle trapping

Figure 3(a) shows twenty 2.2 μm polystyrene particles trapped by the 7 × 7 light spots array. The 49 positions of the array are, however, not fully filled by the particles, because the diluted colloidal solution limits the particle number density near the trapping array. We label the particles by the position coordinates (X, Y), where X and Y correspond to the column number from the left of the array and the row number from the bottom, respectively. There is almost one particle at each position in the observed 5 × 4 rectangular array, except that there are two particles at (4, 3) labeled by a dotted-line circle and no particle at (1, 1) labeled by a dashed-line circle. The center-to-center spacing between the adjacent particles in the X direction is ~5 μm, while the spacing in the Y direction is ~7 μm, suggesting a slight distortion of the array due to the focusing optics. We note that the imaging plane is near the fluidic cell bottom suggesting that the 2.2 μm polystyrene particles are in close proximity to and possibly in contact with the glass substrate (as illustrated in Fig. 1).

 figure: Fig. 3

Fig. 3 Optical trapping arrays of 2.2 μm and 1 μm polystyrene particles in DI water. (a) Optical photograph of the trapped 2.2 μm particles. (b) Trajectories of the trapped particles taken from a 1-minute video. (c) Histogram of the particle displacements from the trapping center position. (d) Trajectories of three untrapped 2.2 μm particles under Brownian motion. (e) Optical photograph of the trapped 1 μm particles. (f) Trajectories of the trapped particles taken from a 40-second video. (g) Histogram of the particle displacements from the trapping center position. (h) Trajectories of three untrapped 1 μm particles under Brownian motion.

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We analyze the trapping stiffness at each trapping site by tracing the particle positions from a ~60-second video with a rate of 30 frames per second [25]. Figure 3(b) shows multiple particle trapping trajectories extracted from all ~1,800 frames. All the particles are localized in a position corresponding to the light spots array pattern. Figure 3(d) shows the trajectories of three untrapped 2.2 μm particles in Brownian motion extracted from the same video clip.

Figure 3(c) shows the histogram of the displacement r away from the center position in 0.2 μm intervals of a representative trapped particle at (1, 3) (labeled by a dashed-line circle in Fig. 3(b)). We assume a linear trapping stiffness defined as [26,27]

k=kBTr2P
where kB is the Boltzmann constant (1.38 × 10−23 m2 kg s−2 K−1), T is the absolute temperature in the system, r2 is the variance of the displacement and P is the optical power at each light spot. As the estimated ~100mW optical power in the fluidic cell is divided into an array of 7 × 7 spots, the average estimated power is ~2 mW for each light spot assuming a uniform array. We assume T to be at room temperature (300 K) for the fluidic cell as a whole, although the temperature in the light spots array region could be few tens of degrees higher than 300 K due to the optical absorption of water, according to our numerical simulations to be discussed below. We therefore estimate the trapping stiffness of the single particle trap at (1, 3) is ~18.2 pN/μm/W, according to Eq. (2).

We also trap 1 μm particles. Figure 3(e) shows 1 μm polystyrene particles trapped by the 3 × 3 light spots array from a 7-mm-length waveguide. Because the particle size is smaller than the individual beam spot size, each beam traps more than one particle and the trapped particles are clustered. The imaging plane is away from the substrate indicating that the 1 μm polystyrene particles are levitated in water. We extract the clustered particle trajectories from the video, as shown in Fig. 3(f). Figure 3(g) shows the histogram of the displacement r away from the center position in 0.2 μm intervals of a single trapped particle at (2, 1) (labeled by a dashed-line circle in Fig. 3(f)). We estimate the trapping stiffness of this single particle trap to be ~3.4 pN/μm/W (according to Eq. (2)), which is smaller than the value estimated for 2.2 μm particles. The measured trapping stiffness values are smaller than typical traditional optical tweezers [25,26] partly due to the fact that we use a relatively low NA objective lens in order to have a relatively large trapping area. The unfocused SMF mode-field diameter of ~9-10 μm for the input-coupling also limits the array spot size in the fluidic cell and thus the trapping stiffness, which could be improved by using a lensed SMF with a tightly focused spot size for the input-coupling. Figure 3(h) shows the trajectories of three untrapped 1 μm particles (not clusters) in Brownian motion extracted from the same video clip.

Table 1 compares the displacement variances and trapping stiffness of 1 μm and 2.2 μm particles in SMART. The variances for the trapped 1 μm particle clusters are in the range of 0.052 to 0.35 μm2, which are time-independent. While the untrapped 1 μm particles under Brownian motion exhibit position variances of ~1 to 24 μm2, which increase with time after the particles are released from the traps [28]. For 2.2 μm particles, the trapped particles also show orders of magnitude smaller variances (0.095 to 0.15 μm2) than the untrapped ones (~1 to 4 μm2). The trapping stiffness of 2.2 μm particles (13.5 to 21.8 pN/μm/W) is generally larger than that of 1 μm particle clusters (1.2 to 7.9 pN/μm/W). During a similar time period of 1 minute, the untrapped 2.2 μm particles exhibit smaller variances in Brownian motion than 1 μm particles. We note that for the analysis of 2.2 μm particles trapping, we exclude some particles with extremely large stiffness (the two-particle cluster at (4, 3) and the single particle at (2, 1)), which we attribute to the possible scenario that those particles are in contact with the substrate. In our experiments (not shown here), we have also trapped 0.8 μm and 3 μm polystyrene particles using 3 × 3 and 5 × 5 arrays, respectively. This is about the same particle size range compares to conventional optical traps.

Tables Icon

Table 1. Variances and trapping stiffness of untrapped (Brownian motion) and trapped 1 μm and 2.2 μm particles in DI water

3.4 Microparticle manipulation

In addition to trapping particles in a two-dimensional array form, we also demonstrate particle manipulation. Figure 4 shows the optical manipulation of thirteen 2.2 μm particles by 2 × 2 array patterns from an 11mm-long MMI waveguide. The top row shows the images of the trapped particles, the middle row shows the imaged light array patterns for these trapping configurations and the third row schematically depicts the corresponding SMF end-firing positions. The MMI output pattern evolves from (a) a single light spot with the SMF at (20 μm, 20 μm), to (b) a 2 × 1 array pattern with the SMF at (0 μm, 20 μm), to (c) a 2 × 2 array pattern with the SMF at (0 μm, 0 μm), to (d) a 1 × 2 array pattern with the SMF at (20 μm, 0 μm), and finally returns to (e) a single output spot with the SMF returns to (20 μm, 20 μm). The manipulation of the particles follow the MMI output patterns accordingly forming (a) a single cluster, (b) splitting into two parts in the X-direction, (c) further splitting in the Y-direction giving a total of four parts, (d) recombining to two clusters in the Y-direction, and (e) finally returning to one cluster of thirteen particles. No particle is lost during the 1-minute interval.

 figure: Fig. 4

Fig. 4 Optical manipulation of 2.2 μm polystyrene particles (Media 1, 5× speed). (a) A cluster of 13 trapped particles at 0 s. (b) The cluster is split in the X direction at 14 s. (c) The cluster is further split in the Y direction into four parts at 26 s. (d) The split groups of particles are recombined in the X direction back to two clusters at 45 s. (e) The remaining split groups of particles are recombined in the Y direction back to a single cluster at 58 s. White dashed arrows: the cluster transport directions. First row (from the top): images of the trapped particles; second row: the corresponding imaged MMI output patterns; third row: schematics of the corresponding SMF end-firing positions. Black dashed arrows: the SMF offset directions.

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4. Numerical simulations

We adopt a commercial finite-element method (FEM) based two-dimensional numerical simulation tool (COMSOL Multiphysics) in order to quantitatively analyze the optical force and the absorption-induced fluidic drag force exerted on particles by the arrayed beams. Our numerical modeling strategy follows [29]. We consider an array of Gaussian light beams propagating in a thin fluidic cell. We calculate the steady-state electromagnetic field distributions of the light beams scattered by particles, and the temperature distribution and the fluidic flow due to optical absorption in water (α = 8 cm−1).

Figure 5(a) shows the simulated electric-field amplitude distribution of three 10mW incident Gaussian beams with 10 μm spacing, as in our 1 μm particle trapping experiment using a 3 × 3 array (Figs. 3(e)–(g)). We assume the beam is focused with NA of 0.4 at 2 μm above the bottom of a 20 μm-thick fluidic cell with open boundaries in the horizontal directions [30]. We account for Fresnel reflections and refractions from the fluidic cell bottom- and top-water-glass interfaces. Figure 5(b) shows the simulated light-scattering electric-field amplitude distribution of the Gaussian beams assuming one 1 μm polystyrene particle is located at the center of the beam waist for each beam. As such, our simulations account for the coherent light scattering due to multiple beams and multiple particles. Using the simulated multiple-beam-multiple-particle light-scattering electric-field amplitude distribution, we calculate the optical force exerted on the particle by the light beam array based on the Maxwell stress tensor T integral on the particle surface S as follows [31, 32]

F=TndS=12ε0E2(n22-n12)dS
where E is the position-dependent light-scattering electric-field amplitude, n is the outward-directed unit normal vector of the particle surface S, n1 = 1.33 is the index of refraction of water (real part only) and n2 = 1.55 is the index of refraction of polystyrene particles. As the optical force depends on the particle relative position to the beam, we simulate the optical force exerted on a single particle by displacing the particle in the lateral and longitudinal directions from the center of the beam waist, while keeping the other particles fixed at the beam waist centers. The calculated maximum optical gradient force in the horizontal directions is ~15 fN for 1 μm particles with a 0.5 μm lateral offset from the beam waist center. Assuming a linear recoiling force near the beam focus, we estimate the corresponding trapping stiffness to be ~3 pN/μm/W (according to Eq. (2)), which is consistent with our measurements (~1.2 - ~7.9 pN/μm/W).

 figure: Fig. 5

Fig. 5 FEM-based simulations of the physical mechanisms involved in the multiple-beam optical tweezers. (a) Electric-field amplitude profile of three incident Gaussian beams. (b) Electric-field amplitude profile of the three incident Gaussian beams scattered by three 1 μm particles located at the beam waist centers. (c) Temperature distribution of the fluidic cell of water illuminated by the three Gaussian beams. (d) Flow velocity distribution of the absorption-induced fluidic flow. (e) Electric-field amplitude profile of seven incident Gaussian beams. (f) Electric-field amplitude profile of the seven incident Gaussian beams scattered by seven 2.2 μm particles located at the beam waist centers. (g) Temperature distribution of the fluidic cell of water illuminated by the seven Gaussian beams. (h) Flow velocity distribution of the absorption-induced fluidic flow.

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As the multiple particle scattering only alters the electric field amplitude distribution at the wavelength scale and does not significantly reduce the field amplitude, as shown in Figs. 5(a) and 5(b), in the thermal and fluidic flow simulations we only simulate the thermal and fluidic flow distributions induced by the water absorption of the arrayed Gaussian beams without particles. We also assume that the particles’ perturbations to the thermal and fluidic flow distributions are negligible due to their small sizes.

Figure 5(c) shows the simulated temperature distribution in the thin cell of water upon the arrayed Gaussian beam illumination without particles. The calculated peak temperature in the fluidic cell is ~30 K above the room temperature. The calculated total electromagnetic energy absorption is ~2% of the total input power (30 mW).

Figure 5(d) shows the simulated absorption-induced convection flow in the thin cell of water, with a maximum velocity of ~150 nm/s in the horizontal directions toward the multiple beam region from the cell floor and outward from the multiple beam region in the cell top. Within the multiple beam region the fluidic flow is dominated by the upward flow with a velocity of ~100 nm/s. The calculated fluidic force exerted on a 1 μm particle by the upward flow is ~0.9 fN, taken into account the pressure distribution. The calculated fluidic force is consistent with the Stokes fluidic force assuming an upward flow of ~100 nm/s. For 1 μm polystyrene particles, the gravitational force is 0.36 fN after accounting for the buoyant force in water. According to our simulations, we find that the 1 μm particle equilibrium position is at ~0.4 μm above the beam focal plane (~2.4 μm above the cell floor), with the calculated total optical force (scattering force and gradient force) of ~0.55 fN pointing downward in the longitudinal direction balancing the fluidic, gravitational and buoyant force. Our simulations thus suggest that a 1 μm polystyrene particle is levitated away from the cell floor, which is in qualitative agreement with our experimental observation (Sec. 3.3).

Figures 5(e) to 5(h) show the numerical simulations of the electric field amplitude, temperature and absorption-induced flow distributions of an array of seven Gaussian beams in a fluidic cell. We assume the individual beam power is 2 mW and the beam spacing is 5 μm, as in our 2.2 μm particle trapping experiment using a 7 × 7 array (Figs. 3(a)3(c)). Figure 5(f) shows the calculated light-scattering electric field amplitude distributions of the seven Gaussian beams with seven 2.2 μm particles located at the beam waist centers. The calculated maximum optical gradient force exerted on the particle in the horizontal directions is ~28 fN at 1 μm offset from the beam waist center. The corresponding trapping stiffness of ~14 pN/μm/W (according to Eq. (2)) is consistent with our measurements (~13.5 - ~21.8 pN/μm/W). The calculated peak temperature in the fluidic cell is ~20 K above the room temperature (assuming no particles), upon a calculated total electromagnetic energy absorption of ~2% of the total input power (14 mW). The convection flow spans the whole beam array region, with a maximum velocity of ~80 nm/s in the horizontal directions and a upward flow velocity of ~40 nm/s. The calculated fluidic force exerted on a 2.2 μm particle by the upward flow is ~1.1 fN. For 2.2 μm polystyrene particles, the gravitational force is 2.9 fN after accounting for the buoyant force in water. According to our simulations, we find that the 2.2 μm particle equilibrium position is at ~0.5 μm below the beam focal plane (~1.5 μm above the cell floor), with the calculated total optical force (scattering force and gradient force) of ~2 fN pointing upward in the longitudinal direction balancing the fluidic, gravitational and buoyant force. Our simulations thus suggest that a 2.2 μm polystyrene particle is situated in close proximity to the cell floor, which is in qualitative agreement with our experimental observation (Sec. 3.3).

5. Conclusion

We demonstrated a two-dimensional optical tweezers using arrayed light beam patterns from SOI-based 100 μm-sized square-core MMI waveguides. We observed in a thin fluidic cell optical trapping and manipulation of arrays of 1 μm and 2.2 μm polystyrene particles. Based on the trapped particle trajectories, we estimated the optical tweezers trapping stiffness for 1 μm and 2.2 μm polystyrene particles. We numerically simulated the particle interactions with the arrayed light beams, the optical absorption-induced heat transfer of the arrayed light beams and the resulting convection flow, and the associated optical force and fluidic drag force. Our SMART technique promises future integration of on-chip arrayed optical tweezers on a silicon substrate for more sophisticated lab-on-chip applications, such as parallel trapping and manipulation of an array of (bio) particles.

Acknowledgments

We acknowledge Dr. Hui Chen (now at Sun Yat Sen University, Guangzhou, China) for the prior work on the two-dimensional MMI waveguides fabrication and characterization.

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18. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011). [CrossRef]  

19. T. Lei and A. W. Poon, “Silicon-on-insulator 100µm-core multimode interferometer waveguides for two-dimensional microparticle trapping and manipulation,” in 2012 IEEE 9th International Conference on Group IV Photonics (IEEE, 2012), pp. 66–68.

20. S. L. He, X. Y. Ao, and V. Romanov, “General properties of N x M self-images in a strongly confined rectangular waveguide,” Appl. Opt. 42(24), 4855–4859 (2003). [CrossRef]   [PubMed]  

21. G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-microm wavelength region,” Appl. Opt. 12(3), 555–563 (1973). [CrossRef]   [PubMed]  

22. Y. Y. Liu and A. W. Poon, “Flow-assisted single-beam optothermal manipulation of microparticles,” Opt. Express 18(17), 18483–18491 (2010). [CrossRef]   [PubMed]  

23. H. Chen and D. T. K. Tong, “Two-dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005). [CrossRef]  

24. L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices based on self-imaging - Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]  

25. A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95(16), 168102 (2005). [CrossRef]   [PubMed]  

26. N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214(1–6), 15–24 (2002). [CrossRef]  

27. R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70(4), 1813–1822 (1996). [CrossRef]   [PubMed]  

28. D. D. Jia, J. Hamilton, L. M. Zaman, and A. Goonewardene, “The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres,” Am. J. Phys. 75(2), 111–115 (2007). [CrossRef]  

29. J. S. Donner, G. Baffou, D. McCloskey, and R. Quidant, “Plasmon-assisted optofluidics,” ACS Nano 5(7), 5457–5462 (2011). [CrossRef]   [PubMed]  

30. S. Rancourt-Grenier, M. T. Wei, J. J. Bai, A. Chiou, P. P. Bareil, P. L. Duval, and Y. L. Sheng, “Dynamic deformation of red blood cell in dual-trap optical tweezers,” Opt. Express 18(10), 10462–10472 (2010). [CrossRef]   [PubMed]  

31. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

32. S. Gaugiran, S. Gétin, J. M. Fedeli, G. Colas, A. Fuchs, F. Chatelain, and J. Dérouard, “Optical manipulation of microparticles and cells on silicon nitride waveguides,” Opt. Express 13(18), 6956–6963 (2005). [CrossRef]   [PubMed]  

References

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
    [Crossref] [PubMed]
  2. C. Butler, S. Fardad, A. Sincore, M. Vangheluwe, M. Baudelet, and M. Richardson, “Multispectral optical tweezers for molecular diagnostics of single biological cells,” Proc. SPIE 8225, 82250C (2012).
    [Crossref]
  3. E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
    [Crossref] [PubMed]
  4. H. Zhang and K. K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008).
    [Crossref] [PubMed]
  5. P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005).
    [Crossref] [PubMed]
  6. M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
    [Crossref] [PubMed]
  7. U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, “Unzipping DNA with optical tweezers: high sequence sensitivity and force flips,” Biophys. J. 82(3), 1537–1553 (2002).
    [Crossref] [PubMed]
  8. J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
    [Crossref] [PubMed]
  9. Y. Y. Sun, L. S. Ong, and X. C. Yuan, “Composite-microlens-array-enabled microfluidic sorting,” Appl. Phys. Lett. 89(14), 141108 (2006).
    [Crossref]
  10. K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
    [Crossref]
  11. M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
    [Crossref] [PubMed]
  12. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
    [Crossref] [PubMed]
  13. M. Padgett and R. Di Leonardo, “Holographic optical tweezers and their relevance to lab on chip devices,” Lab Chip 11(7), 1196–1205 (2011).
    [Crossref] [PubMed]
  14. K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
    [Crossref] [PubMed]
  15. R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
    [Crossref] [PubMed]
  16. T. Čižmár and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19(20), 18871–18884 (2011).
    [Crossref] [PubMed]
  17. J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
    [Crossref]
  18. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
    [Crossref]
  19. T. Lei and A. W. Poon, “Silicon-on-insulator 100µm-core multimode interferometer waveguides for two-dimensional microparticle trapping and manipulation,” in 2012 IEEE 9th International Conference on Group IV Photonics (IEEE, 2012), pp. 66–68.
  20. S. L. He, X. Y. Ao, and V. Romanov, “General properties of N x M self-images in a strongly confined rectangular waveguide,” Appl. Opt. 42(24), 4855–4859 (2003).
    [Crossref] [PubMed]
  21. G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-microm wavelength region,” Appl. Opt. 12(3), 555–563 (1973).
    [Crossref] [PubMed]
  22. Y. Y. Liu and A. W. Poon, “Flow-assisted single-beam optothermal manipulation of microparticles,” Opt. Express 18(17), 18483–18491 (2010).
    [Crossref] [PubMed]
  23. H. Chen and D. T. K. Tong, “Two-dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005).
    [Crossref]
  24. L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices based on self-imaging - Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
    [Crossref]
  25. A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95(16), 168102 (2005).
    [Crossref] [PubMed]
  26. N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214(1–6), 15–24 (2002).
    [Crossref]
  27. R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70(4), 1813–1822 (1996).
    [Crossref] [PubMed]
  28. D. D. Jia, J. Hamilton, L. M. Zaman, and A. Goonewardene, “The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres,” Am. J. Phys. 75(2), 111–115 (2007).
    [Crossref]
  29. J. S. Donner, G. Baffou, D. McCloskey, and R. Quidant, “Plasmon-assisted optofluidics,” ACS Nano 5(7), 5457–5462 (2011).
    [Crossref] [PubMed]
  30. S. Rancourt-Grenier, M. T. Wei, J. J. Bai, A. Chiou, P. P. Bareil, P. L. Duval, and Y. L. Sheng, “Dynamic deformation of red blood cell in dual-trap optical tweezers,” Opt. Express 18(10), 10462–10472 (2010).
    [Crossref] [PubMed]
  31. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  32. S. Gaugiran, S. Gétin, J. M. Fedeli, G. Colas, A. Fuchs, F. Chatelain, and J. Dérouard, “Optical manipulation of microparticles and cells on silicon nitride waveguides,” Opt. Express 13(18), 6956–6963 (2005).
    [Crossref] [PubMed]

2012 (1)

C. Butler, S. Fardad, A. Sincore, M. Vangheluwe, M. Baudelet, and M. Richardson, “Multispectral optical tweezers for molecular diagnostics of single biological cells,” Proc. SPIE 8225, 82250C (2012).
[Crossref]

2011 (4)

M. Padgett and R. Di Leonardo, “Holographic optical tweezers and their relevance to lab on chip devices,” Lab Chip 11(7), 1196–1205 (2011).
[Crossref] [PubMed]

T. Čižmár and K. Dholakia, “Shaping the light transmission through a multimode optical fibre: complex transformation analysis and applications in biophotonics,” Opt. Express 19(20), 18871–18884 (2011).
[Crossref] [PubMed]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

J. S. Donner, G. Baffou, D. McCloskey, and R. Quidant, “Plasmon-assisted optofluidics,” ACS Nano 5(7), 5457–5462 (2011).
[Crossref] [PubMed]

2010 (3)

S. Rancourt-Grenier, M. T. Wei, J. J. Bai, A. Chiou, P. P. Bareil, P. L. Duval, and Y. L. Sheng, “Dynamic deformation of red blood cell in dual-trap optical tweezers,” Opt. Express 18(10), 10462–10472 (2010).
[Crossref] [PubMed]

Y. Y. Liu and A. W. Poon, “Flow-assisted single-beam optothermal manipulation of microparticles,” Opt. Express 18(17), 18483–18491 (2010).
[Crossref] [PubMed]

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

2009 (1)

K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
[Crossref] [PubMed]

2008 (2)

H. Zhang and K. K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

2007 (2)

R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
[Crossref] [PubMed]

D. D. Jia, J. Hamilton, L. M. Zaman, and A. Goonewardene, “The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres,” Am. J. Phys. 75(2), 111–115 (2007).
[Crossref]

2006 (1)

Y. Y. Sun, L. S. Ong, and X. C. Yuan, “Composite-microlens-array-enabled microfluidic sorting,” Appl. Phys. Lett. 89(14), 141108 (2006).
[Crossref]

2005 (4)

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005).
[Crossref] [PubMed]

S. Gaugiran, S. Gétin, J. M. Fedeli, G. Colas, A. Fuchs, F. Chatelain, and J. Dérouard, “Optical manipulation of microparticles and cells on silicon nitride waveguides,” Opt. Express 13(18), 6956–6963 (2005).
[Crossref] [PubMed]

H. Chen and D. T. K. Tong, “Two-dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005).
[Crossref]

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95(16), 168102 (2005).
[Crossref] [PubMed]

2003 (3)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

S. L. He, X. Y. Ao, and V. Romanov, “General properties of N x M self-images in a strongly confined rectangular waveguide,” Appl. Opt. 42(24), 4855–4859 (2003).
[Crossref] [PubMed]

2002 (3)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, “Unzipping DNA with optical tweezers: high sequence sensitivity and force flips,” Biophys. J. 82(3), 1537–1553 (2002).
[Crossref] [PubMed]

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214(1–6), 15–24 (2002).
[Crossref]

1997 (1)

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

1996 (2)

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[Crossref]

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70(4), 1813–1822 (1996).
[Crossref] [PubMed]

1995 (1)

L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices based on self-imaging - Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

1986 (1)

1973 (1)

Ao, X. Y.

Arimondo, E.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214(1–6), 15–24 (2002).
[Crossref]

Ashkin, A.

Baffou, G.

J. S. Donner, G. Baffou, D. McCloskey, and R. Quidant, “Plasmon-assisted optofluidics,” ACS Nano 5(7), 5457–5462 (2011).
[Crossref] [PubMed]

Bai, J. J.

Bareil, P. P.

Baudelet, M.

C. Butler, S. Fardad, A. Sincore, M. Vangheluwe, M. Baudelet, and M. Richardson, “Multispectral optical tweezers for molecular diagnostics of single biological cells,” Proc. SPIE 8225, 82250C (2012).
[Crossref]

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

Bjorkholm, J. E.

Block, S. M.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[Crossref]

Bockelmann, U.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, “Unzipping DNA with optical tweezers: high sequence sensitivity and force flips,” Biophys. J. 82(3), 1537–1553 (2002).
[Crossref] [PubMed]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Butler, C.

C. Butler, S. Fardad, A. Sincore, M. Vangheluwe, M. Baudelet, and M. Richardson, “Multispectral optical tweezers for molecular diagnostics of single biological cells,” Proc. SPIE 8225, 82250C (2012).
[Crossref]

Chatelain, F.

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Chen, H.

H. Chen and D. T. K. Tong, “Two-dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005).
[Crossref]

Chiou, A.

Chiou, P. Y.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005).
[Crossref] [PubMed]

Chu, S.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70(4), 1813–1822 (1996).
[Crossref] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
[Crossref] [PubMed]

Cižmár, T.

Clemen, A. E. M.

K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
[Crossref] [PubMed]

Colas, G.

Curtis, J. E.

K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
[Crossref] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Dérouard, J.

Dholakia, K.

Di Leonardo, R.

M. Padgett and R. Di Leonardo, “Holographic optical tweezers and their relevance to lab on chip devices,” Lab Chip 11(7), 1196–1205 (2011).
[Crossref] [PubMed]

R. Di Leonardo, F. Ianni, and G. Ruocco, “Computer generation of optimal holograms for optical trap arrays,” Opt. Express 15(4), 1913–1922 (2007).
[Crossref] [PubMed]

Donner, J. S.

J. S. Donner, G. Baffou, D. McCloskey, and R. Quidant, “Plasmon-assisted optofluidics,” ACS Nano 5(7), 5457–5462 (2011).
[Crossref] [PubMed]

Duval, P. L.

Dziedzic, J. M.

Eriksson, E.

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

Essevaz-Roulet, B.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, “Unzipping DNA with optical tweezers: high sequence sensitivity and force flips,” Biophys. J. 82(3), 1537–1553 (2002).
[Crossref] [PubMed]

Fardad, S.

C. Butler, S. Fardad, A. Sincore, M. Vangheluwe, M. Baudelet, and M. Richardson, “Multispectral optical tweezers for molecular diagnostics of single biological cells,” Proc. SPIE 8225, 82250C (2012).
[Crossref]

Fedeli, J. M.

Finer, J. T.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70(4), 1813–1822 (1996).
[Crossref] [PubMed]

Fuchs, A.

Gaugiran, S.

Gelles, J.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

Gétin, S.

Goksör, M.

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

Goonewardene, A.

D. D. Jia, J. Hamilton, L. M. Zaman, and A. Goonewardene, “The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres,” Am. J. Phys. 75(2), 111–115 (2007).
[Crossref]

Granéli, A.

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[Crossref]

Hale, G. M.

Hamilton, J.

D. D. Jia, J. Hamilton, L. M. Zaman, and A. Goonewardene, “The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres,” Am. J. Phys. 75(2), 111–115 (2007).
[Crossref]

Hanstorp, D.

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

Haraszti, T.

K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
[Crossref] [PubMed]

He, S. L.

Heslot, F.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, “Unzipping DNA with optical tweezers: high sequence sensitivity and force flips,” Biophys. J. 82(3), 1537–1553 (2002).
[Crossref] [PubMed]

Ianni, F.

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

Jia, D. D.

D. D. Jia, J. Hamilton, L. M. Zaman, and A. Goonewardene, “The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres,” Am. J. Phys. 75(2), 111–115 (2007).
[Crossref]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Kurre, R.

K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
[Crossref] [PubMed]

Landick, R.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

Liu, K. K.

H. Zhang and K. K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008).
[Crossref] [PubMed]

Liu, Y. Y.

Lundqvist, F.

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Malagnino, N.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214(1–6), 15–24 (2002).
[Crossref]

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

McCloskey, D.

J. S. Donner, G. Baffou, D. McCloskey, and R. Quidant, “Plasmon-assisted optofluidics,” ACS Nano 5(7), 5457–5462 (2011).
[Crossref] [PubMed]

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Ohta, A. T.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005).
[Crossref] [PubMed]

Ong, L. S.

Y. Y. Sun, L. S. Ong, and X. C. Yuan, “Composite-microlens-array-enabled microfluidic sorting,” Appl. Phys. Lett. 89(14), 141108 (2006).
[Crossref]

Padgett, M.

M. Padgett and R. Di Leonardo, “Holographic optical tweezers and their relevance to lab on chip devices,” Lab Chip 11(7), 1196–1205 (2011).
[Crossref] [PubMed]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices based on self-imaging - Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

Pesce, G.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214(1–6), 15–24 (2002).
[Crossref]

Poon, A. W.

Querry, M. R.

Quidant, R.

J. S. Donner, G. Baffou, D. McCloskey, and R. Quidant, “Plasmon-assisted optofluidics,” ACS Nano 5(7), 5457–5462 (2011).
[Crossref] [PubMed]

Rancourt-Grenier, S.

Richardson, M.

C. Butler, S. Fardad, A. Sincore, M. Vangheluwe, M. Baudelet, and M. Richardson, “Multispectral optical tweezers for molecular diagnostics of single biological cells,” Proc. SPIE 8225, 82250C (2012).
[Crossref]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

Rohrbach, A.

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95(16), 168102 (2005).
[Crossref] [PubMed]

Romanov, V.

Ruocco, G.

Sasso, A.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214(1–6), 15–24 (2002).
[Crossref]

Schmitz, C.

K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
[Crossref] [PubMed]

Scrimgeour, J.

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

Sheng, Y. L.

Simmons, R. M.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70(4), 1813–1822 (1996).
[Crossref] [PubMed]

Sincore, A.

C. Butler, S. Fardad, A. Sincore, M. Vangheluwe, M. Baudelet, and M. Richardson, “Multispectral optical tweezers for molecular diagnostics of single biological cells,” Proc. SPIE 8225, 82250C (2012).
[Crossref]

Smith, S. B.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices based on self-imaging - Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

Sott, K.

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Spatz, J. P.

K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
[Crossref] [PubMed]

Spudich, J. A.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70(4), 1813–1822 (1996).
[Crossref] [PubMed]

Sun, Y. Y.

Y. Y. Sun, L. S. Ong, and X. C. Yuan, “Composite-microlens-array-enabled microfluidic sorting,” Appl. Phys. Lett. 89(14), 141108 (2006).
[Crossref]

Sveningsson, M.

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

Thomen, P.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, “Unzipping DNA with optical tweezers: high sequence sensitivity and force flips,” Biophys. J. 82(3), 1537–1553 (2002).
[Crossref] [PubMed]

Tong, D. T. K.

H. Chen and D. T. K. Tong, “Two-dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005).
[Crossref]

Uhrig, K.

K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
[Crossref] [PubMed]

Vangheluwe, M.

C. Butler, S. Fardad, A. Sincore, M. Vangheluwe, M. Baudelet, and M. Richardson, “Multispectral optical tweezers for molecular diagnostics of single biological cells,” Proc. SPIE 8225, 82250C (2012).
[Crossref]

Viasnoff, V.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, “Unzipping DNA with optical tweezers: high sequence sensitivity and force flips,” Biophys. J. 82(3), 1537–1553 (2002).
[Crossref] [PubMed]

Visscher, K.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[Crossref]

Wang, M. D.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

Wei, M. T.

Wu, M. C.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005).
[Crossref] [PubMed]

Yin, H.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

Yuan, X. C.

Y. Y. Sun, L. S. Ong, and X. C. Yuan, “Composite-microlens-array-enabled microfluidic sorting,” Appl. Phys. Lett. 89(14), 141108 (2006).
[Crossref]

Zaman, L. M.

D. D. Jia, J. Hamilton, L. M. Zaman, and A. Goonewardene, “The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres,” Am. J. Phys. 75(2), 111–115 (2007).
[Crossref]

Zhang, H.

H. Zhang and K. K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008).
[Crossref] [PubMed]

ACS Nano (1)

J. S. Donner, G. Baffou, D. McCloskey, and R. Quidant, “Plasmon-assisted optofluidics,” ACS Nano 5(7), 5457–5462 (2011).
[Crossref] [PubMed]

Am. J. Phys. (1)

D. D. Jia, J. Hamilton, L. M. Zaman, and A. Goonewardene, “The time, size, viscosity, and temperature dependence of the Brownian motion of polystyrene microspheres,” Am. J. Phys. 75(2), 111–115 (2007).
[Crossref]

Annu. Rev. Biochem. (1)

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77(1), 205–228 (2008).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Y. Y. Sun, L. S. Ong, and X. C. Yuan, “Composite-microlens-array-enabled microfluidic sorting,” Appl. Phys. Lett. 89(14), 141108 (2006).
[Crossref]

Biophys. J. (3)

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997).
[Crossref] [PubMed]

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, “Unzipping DNA with optical tweezers: high sequence sensitivity and force flips,” Biophys. J. 82(3), 1537–1553 (2002).
[Crossref] [PubMed]

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, “Quantitative measurements of force and displacement using an optical trap,” Biophys. J. 70(4), 1813–1822 (1996).
[Crossref] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[Crossref]

IEEE Photon. Technol. Lett. (1)

H. Chen and D. T. K. Tong, “Two-dimensional symmetric multimode interferences in silicon square waveguides,” IEEE Photon. Technol. Lett. 17(4), 801–803 (2005).
[Crossref]

J. Lightwave Technol. (1)

L. B. Soldano and E. C. M. Pennings, “Optical multimode interference devices based on self-imaging - Principles and Applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

J. R. Soc. Interface (1)

H. Zhang and K. K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5(24), 671–690 (2008).
[Crossref] [PubMed]

Lab Chip (3)

E. Eriksson, K. Sott, F. Lundqvist, M. Sveningsson, J. Scrimgeour, D. Hanstorp, M. Goksör, and A. Granéli, “A microfluidic device for reversible environmental changes around single cells using optical tweezers for cell selection and positioning,” Lab Chip 10(5), 617–625 (2010).
[Crossref] [PubMed]

M. Padgett and R. Di Leonardo, “Holographic optical tweezers and their relevance to lab on chip devices,” Lab Chip 11(7), 1196–1205 (2011).
[Crossref] [PubMed]

K. Uhrig, R. Kurre, C. Schmitz, J. E. Curtis, T. Haraszti, A. E. M. Clemen, and J. P. Spatz, “Optical force sensor array in a microfluidic device based on holographic optical tweezers,” Lab Chip 9(5), 661–668 (2009).
[Crossref] [PubMed]

Laser Photon. Rev. (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

Nature (3)

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005).
[Crossref] [PubMed]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003).
[Crossref] [PubMed]

Opt. Commun. (2)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214(1–6), 15–24 (2002).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

A. Rohrbach, “Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory,” Phys. Rev. Lett. 95(16), 168102 (2005).
[Crossref] [PubMed]

Proc. SPIE (1)

C. Butler, S. Fardad, A. Sincore, M. Vangheluwe, M. Baudelet, and M. Richardson, “Multispectral optical tweezers for molecular diagnostics of single biological cells,” Proc. SPIE 8225, 82250C (2012).
[Crossref]

Other (2)

T. Lei and A. W. Poon, “Silicon-on-insulator 100µm-core multimode interferometer waveguides for two-dimensional microparticle trapping and manipulation,” in 2012 IEEE 9th International Conference on Group IV Photonics (IEEE, 2012), pp. 66–68.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

Supplementary Material (1)

» Media 1: MOV (280 KB)     

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Figures (5)

Fig. 1
Fig. 1 Schematic of the experimental setup. Inset: Schematic of optical trapping and manipulation of particles in a thin fluidic cell using SMART. Fg: the optical gradient force exerted on the particle in the horizontal directions, Fgz: the optical gradient force exerted on the particle in the Z direction, Fs: the optical scattering force exerted on the particle in the Z direction, G: the gravitational force exerted on the particle, Fb: the buoyant force in water, Fc: the convection flow fluidic drag force exerted on the particle in the Z direction. Black solid arrows: the force exerted on the particle. Blue dashed arrows: the absorption-induced fluidic flow. Red solid curves: the light beam intensity distributions in the horizontal and longitudinal directions. Red dashed arrows: beam focal plane.
Fig. 2
Fig. 2 Imaged light beam array patterns of the MMI waveguides. (a) SEM of the fabricated SOI MMI waveguide featuring the end-facet. (b)-(e) NIR images (in gray scale) of the array patterns from the MMI waveguides of various lengths: (b) 11 mm, (c) 5.5 mm, (d) 4.5 mm and (e) 3 mm. (f) Imaged 7 × 7 array light intensity profile (in gray scale shown in false colors) of the MMI waveguide with 3mm length. Inset of (f): schematic of the relative position between the butt-coupled SMF and the MMI waveguide facet. (g)-(j) Imaged light intensity profiles (in gray scale shown in false colors) with the corresponding SMF core offsets from the MMI waveguide facet center.
Fig. 3
Fig. 3 Optical trapping arrays of 2.2 μm and 1 μm polystyrene particles in DI water. (a) Optical photograph of the trapped 2.2 μm particles. (b) Trajectories of the trapped particles taken from a 1-minute video. (c) Histogram of the particle displacements from the trapping center position. (d) Trajectories of three untrapped 2.2 μm particles under Brownian motion. (e) Optical photograph of the trapped 1 μm particles. (f) Trajectories of the trapped particles taken from a 40-second video. (g) Histogram of the particle displacements from the trapping center position. (h) Trajectories of three untrapped 1 μm particles under Brownian motion.
Fig. 4
Fig. 4 Optical manipulation of 2.2 μm polystyrene particles (Media 1, 5× speed). (a) A cluster of 13 trapped particles at 0 s. (b) The cluster is split in the X direction at 14 s. (c) The cluster is further split in the Y direction into four parts at 26 s. (d) The split groups of particles are recombined in the X direction back to two clusters at 45 s. (e) The remaining split groups of particles are recombined in the Y direction back to a single cluster at 58 s. White dashed arrows: the cluster transport directions. First row (from the top): images of the trapped particles; second row: the corresponding imaged MMI output patterns; third row: schematics of the corresponding SMF end-firing positions. Black dashed arrows: the SMF offset directions.
Fig. 5
Fig. 5 FEM-based simulations of the physical mechanisms involved in the multiple-beam optical tweezers. (a) Electric-field amplitude profile of three incident Gaussian beams. (b) Electric-field amplitude profile of the three incident Gaussian beams scattered by three 1 μm particles located at the beam waist centers. (c) Temperature distribution of the fluidic cell of water illuminated by the three Gaussian beams. (d) Flow velocity distribution of the absorption-induced fluidic flow. (e) Electric-field amplitude profile of seven incident Gaussian beams. (f) Electric-field amplitude profile of the seven incident Gaussian beams scattered by seven 2.2 μm particles located at the beam waist centers. (g) Temperature distribution of the fluidic cell of water illuminated by the seven Gaussian beams. (h) Flow velocity distribution of the absorption-induced fluidic flow.

Tables (1)

Tables Icon

Table 1 Variances and trapping stiffness of untrapped (Brownian motion) and trapped 1 μm and 2.2 μm particles in DI water

Equations (3)

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N= 1 L N n λ W 2
k= k B T r 2 P
F = T n d S = 1 2 ε 0 E 2 ( n 2 2 - n 1 2 )d S

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