1. Introduction

The optical trapping and manipulation of particles and cells has become a common tool for physicists and biologists since Ashkin’s first demonstration of optical tweezers [1]. Single particle optical traps have proven useful in a range of applications such as examining molecular bonds [2], for measuring the forces exerted by individual proteins [3] and for measuring the force extension relationships for single molecules of DNA [4]. The manipulation of multiple particles is possible using a variety of techniques such as computer generated holograms to produce multiple beams [5], using diffractive optics to create arrays of optical tweezers [6], and also using interferometry techniques [7]. Interferometic optical trapping can be used to assemble lattices of particles with controlled separation both in 2-D [8] and 3-D [9]. Previous work involving interferometric optical trapping has been carried out using free space optics [10, 11]. We previously demonstrated one dimensional interferometric trapping using two diagonal cores of a four core multicore fiber (MCF) that had been lensed using a fusion splicer [12]. In this paper we have demonstrated two dimensional trapping using all four cores of the same fiber, using a diffractive optical element (DOE) [13] to couple with high uniformity into each core of the MCF. The use of a single fiber probe is advantageous with added functionality at the end of the fiber providing greater flexibility compared to using external optics [14]. The use of an electric arc fusion splicer to lens the end of the fiber [15] is also a simple, robust and rapid method of functionalizing the end of the fiber when compared to alternative methods such as chemical etching [16], focused ion beam milling [17] and laser processing [18]. Although our probe shares a similar core geometry to those described in [17] and [18], the different approaches to functionalization results in a markedly different behavior, our fiber traps multiple particles by interferometric optical trapping whereas the previous devices trap single particles in 3-D. Therefore the applications vary between our device and these already reported. Trapping multiple biological particles will allow us to examine the interaction between the cells when held in close proximity and study processes such as quorum sensing, the formation of floc and biofilms and metabolic co-operation studies.

2. Fabrication and sample material preparation

2.1 Lensed fiber fabrication

The MCF used in our experiment is shown in Fig. 1(a). It is a commercial fiber supplied by Fibertronix AB known as a Gemini fiber and has a cut off wavelength of 1 µm. The fiber has four cores of 7 µm diameter, the core centers are arranged in an 80 μm square. The lens was created with a standard electric arc fusion splicer using a similar method as described in our previous work [12] is shown in Fig. 1(b).

 

Fig. 1 (a) End face image of the Gemini 4-core fiber, and (b). Shaped end of the fiber after lensing.

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2.2 Diffractive optical element fabrication

The fan-out operation required to launch the incident light into the four core fiber is performed by means of a scalar domain diffractive optical element [13]. This class of phase-only component, designed using either a closed-form solution to the Fraunhofer diffraction integral (for small number of fan-out orders) or one of the modified Gerchberg-Saxton phase retrieval algorithms (for large numbers of orders) [13], can produce arbitrary distributions of diffraction orders precisely matched to the fiber core geometry. Figures 2(a) and 2(b) show an example of a 2x2 fan-out DOE with zeroth order intensity to facilitate alignment of the DOE to the multicore fiber [19].

 

Fig. 2 (a) Phase profile of 2-level 2x2 fan-out element with lower intensity zeroth order. Black represents 0 relative phase delay and white represents π relative phase delay, and (b) Simulated output from 2x2 fan-out DOE with completely suppressed zeroth order.

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2.3 Bacterial cell cultures

Escherichia coli K-12 CC118/λpir (pSM1880) cells were grown as one or two day batch cultures in liquid Luria-Bertani medium (tryptone, 10 g l⁻¹; yeast extract 5 g l⁻¹; NaCl 4 g l⁻¹) at 37 °C. Cells were either used directly or diluted 1:1 (v:v) with sterile 0.85% (w/v) NaCl after mounting in purpose made glass cover slip chambers. The E. coli K-12 CC118/λpir strain was chosen due to the fact that it contains the high copy number plasmid pSM1880 carrying the green fluorescent protein (gfp) gene under a constitutively expressing P_A1-04/03 promoter enabling the option for fluorescence based imaging.

2.4 Microspheres

2 µm polystyrene microspheres (Polysciences: Polybead® Microspheres) with a refractive index of 1.59 at 589nm were used in the experiments. A concentration a tenth of the bulk sample was used, diluting with distilled water, equating to a suspension density 5.68 x 10⁸ microspheres/ml.

3. Experimental results

The experimental set up is shown in Fig. 3. An Nd:YLF laser source (Elforlight: model L 500-1047) was used which has a maximum output power of 800 mW at 1047 nm, this wavelength is longer than the fibers specified cut-off wavelength of 1 µm. A custom made DOE as described in Section 2.2 was used to couple light into all four cores of the MCF. The DOE splits the incoming beam of light evenly into four beamlets of the same arrangement and separation as the cores of the MCF at the focus of the coupling lens. The DOE was placed at the back focal plane of an x10, 0.16NA aspheric lens.

 

Fig. 3 Experimental set up.

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The curvature of the end of the fiber refracts the output from the four cores to produce a crossing point in the far field, approximately 250 μm from the end of the fiber in air. At the crossing point high contrast interference fringes are produced in a lattice pattern as shown in Fig. 4(a). The fringe spacing in air is ~2.75 µm. The half wave-plate can be used to improve the visibility of the fringes.

 

Fig. 4 (a) Interference lattice at the crossing point of the output of the 4 cores, and (b) 2 µm microspheres trapped in the high intensity regions of the lattice.

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A solution of microspheres were held between two, 100 µm thick, cover slips and kept in place using a vinyl spacer of 80 µm thickness, between them, as shown in Fig. 3. The fiber was positioned in air outside the cover slips and an imaging system was positioned at the other side. A x100, 0.7NA Mitutoyo, infinity corrected, long working distance lens was used for imaging with at Thorlabs CCD camera (1280 x 1024 pixel resolution). The microspheres were shown to align in the areas of high intensity in the lattice fringe pattern with one particle trapped per fringe. They are held in a two dimensional array, spaced evenly across the lattice pattern as shown in Fig. 4(b). The microspheres are trapped in 2-D along x and y on the plane of the coverslip and are also pushed onto the back coverslip in the z-direction.

The interferences fringes produce intensity gradients across the crossing point creating peaks of high intensity, highest in the central region, where particles can be trapped as can be seen in Figs. 5(a) and 5(b). Figure 5(a) shows the normalized intensity plot of the crossing point of the lensed MCF, here the lattice spacing is 2.75 µm, approximately 250 µm away from the end of the fiber. In comparison, Fig. 5(b) shows simulated results produced using a BeamPROP model as described elsewhere [12]. The lens was estimated to be spherical as we are unable to determine the exact lensing effect on the cores. We found that the lattice spacing is 2.69 µm, at a crossing point 235 µm from the end of the fiber. These results are in good agreement with our experimental results.

 

Fig. 5 (a) Normalized intensity plot of the overlap region of the four core fiber, and (b) BeamPROP simulation of the normalized intensity plot of the overlap region of the four core fiber.

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At full power the maximum output from the fiber was found to be 150 mW. Using a computer code, the intensity plot shown in Fig. 5(a) was split into sections separating each intensity peak. The power in each peak was then estimated by calculating the percentage volume under each of the peaks with comparison to the known total maximum output power. The power of the highest peak was found to be 2.37 mW, though we estimate trapping has been seen at powers as low as 0.38 mW as can be seen in Figs. 4(b) and 6 where particles are held at maxima across the extent of the fringes.

 

Fig. 6 (a) The 2-D lattice pattern at 0° half wave-plate rotation, (b) The previous image viewed through a polarizer,(c) The fringes appear to be more 1-D fringes like with peaks joined along the vertical direction when at 22.5° half wave-plate rotation, (d) The previous image viewed through a polarizer, (e) The pattern appears to be almost the inverse of the high visibility lattice pattern when at 45° half wave-plate rotation, (f) The previous image viewed through a polarizer, (g) A waffle like interference pattern with peaks joined along the horizontal direction when at 67.5° half wave-plate rotation, and (h) The previous image viewed through polarizer.

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By rotating the half wave-plate the appearance of the interference fringes can be varied as shown in Figs. 6(a), 6(c), 6(e) and 6(g). The patterns repeat every 90° turn of the wave-plate, each high visibility lattice pattern is positioned 90° apart with patterns that look like one dimensional fringe patterns or inverse lattice patterns spaced between. Linearly polarized light is launched into the MCF, however as the fiber is not polarization maintaining the fiber itself adds a polarization component to the output image. This can be seen whilst viewing the output image of the 2-D lattice pattern through a polarizer. The visibility of the lattice pattern is improved when only the linear polarization component contributing to this pattern is let through as shown in Fig. 6(b). When the polarizer is rotated the image is not completely distinguished as what would happen if the image was completely linear polarization, resulting in the component from the MCF being visible. For each image taken at 22.5° interval of the half wave-plate an image was also taken through a polarizer, these are shown in Figs. 6(b), 6(d), 6(f) and 6(h) beside the image not taken through the polarizer. Figure 6(d) gives the appearance of a 1-D fringe pattern.

The wave-plate can be used to change the MCF output from 1-D trapping fringes to a 2-D trapping lattice as shown in Figs. 7(a)-7(f) and Media 1. In Media 1 the wave-plate is initially at a position to produce 1-D type fringes the microspheres can be seen to be along the high intensity vertical regions and are close together in the vertical direction, at 15 seconds into the video the wave-plate is rotated to the position where high visibility lattice patterns are produced, the microspheres can then be seen to move into the high intensity regions of the lattice.

 

Fig. 7 (a)-(f), Single frame excerpts from the video recording showing 2 µm microspheres moving from a 1-D fringe pattern (a) and (b), to a 2-D lattice pattern by rotating the half wave-plate to achieve high visibility of the 2-D fringe lattice (c). The corresponding time in the video is included along with the time either before or after the wave-plate is rotated. The microspheres can be seen to move from trapping along the fringes in the 1-D case to trapping in the regions of high intensity in the 2-D case (Media 1).

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The trapping of particles is only achievable in two dimensions not three dimensions due to the gradient force in the optical axis being less than the scattering force. If the degree of curvature was greater and the angles of refraction and intersection of the core output was increased, this would reduce the axial component of the scattering force and reinforce the transverse component of the gradient force resulting in a stiffer trap. This could be achieved if the diameter of the fiber was reduced before the lensing step, i.e. by tapering the fiber first.

As well as microspheres of different sizes we also used our set up to trap E. coli bacteria cells. The E. coli were shown to group together and align in the fringe pattern as shown in Figs. 8(a) and 8(b). E. coli are harder to optically trap as their refractive index of 1.38 [21], is much smaller than that of the microspheres used of 1.59, both refractive indices are for the visible wavelength region. Due to the small size of the cells and the resolution of the camera, the orientation of the rod shaped cells is not distinguishable. To image the E. coli we used a short pass IR filter to block the 1047nm radiation and used a 466 nm LED to illuminate the sample.

 

Fig. 8 (a) Escherichia coli trapped in 2-D using the MCF lensed fiber trapping probe, and (b) single frame excerpt from the video recording showing trapping of E. coli whilst the fiber is in a different position and orientation than the previous image (Media 2).

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Using this lensed MCF we have demonstrated trapping of multiple biological particles. This technique will allow the study of biological cells held in such close proximity such as the formation of biofilms.

4. Conclusions

We have successfully demonstrated two dimensional interferometric optical trapping using a single multicore fiber shaped using an electric arc fusion splicer. Light was coupled evenly into each core of the four core fiber using a custom made diffractive optical element. This provided a simple and effective way to efficiently couple a single beam into the four cores without the need for beam splitters or fan-out devices. Also, we were able to show some degree of control of the fringe appearance by the introduction of a half wave-plate before the DOE achieving high visibility 2-D and 1-D fringe patterns on appropriate settings of the half wave-plate angle. It has been shown that the robust and efficient electric arc fusion technique can be used to generate four-core interactions from a single fiber.

The interference lattice produced at the overlap region can be used for trapping particles in two dimensions. Particles were observed to be trapped in the high intensity regions of the lattice pattern. The overlap was approximately 250 µm from the end of the fiber and the high intensity regions of the lattice were separated by approximately 2.75 µm. This technique can be used to trap multiple particles at evenly spaced sites across the lattice. Using the half wave-plate control, we have shown the rearrangement of microspheres from a 1-D to 2-D array. This, to the best of our knowledge, is the first demonstration of a four-beam interference pattern from a single optical fiber being used for optical micromanipulation.

Using this fiber probe we have shown evidence of the trapping of E. coli in the same way. Trapping multiple biological particles will allow us to examine the interaction between the cells when held in close proximity and also can allow us to manipulate the formation of biological flocs and biofilms, as well as facilitating the study of quorum sensing and metabolic co-operation interactions

This technique has the possibility of being adapted to optical tweezing by increasing the crossing angle of the fiber output. We are currently looking into the tapering of the MCF to enable a lens with a greater curvature to be created. This will produce a stiffer trap closer to the end of the fiber.