We demonstrate the optical manipulation of cells and dielectric particles on the surface of silicon nitride waveguides. Glass particles with 2μm diameter are propelled at velocities of 15μm/s with a guided power of 20mW. This is approximately 20 times more efficient than previously reported, and permits to use this device on low refractive index objects such as cells. Red blood cells and yeast cells can be trapped on the waveguide and pushed along it by the action of optical forces. This kind of system can easily be combined with various integrated optical structures and opens the way to the development of new microsystems for cell sorting applications.
©2005 Optical Society of America
The experimental demonstration of optical trapping by a laser beam by A. Ashkin in 1970  opened the way to numerous applications in the field of biology  as well as in that of nanofabrication . The optical tweezer is a contactless and non destructive tool adapted to manipulation of particles and biological objects. However, it does not fit very well to sorting applications particularly because particles are moved one by one. Thus several strategies have been used to build optical tools designed for the parallel manipulation of several objects. Some of them are based on the shape modification of the trapping light beam as Bessel beams  or holographic tweezers . Other techniques employ VCSEL  (Vertical Cavity Surface Emitting Laser) arrays that can be produced on a large scale in microelectronics facilities.
This kind of tool makes easier new approaches in the field of cellular sorting or intra-cellular surgery particularly because their dimensions fit well to that of the studied object . For example, biological analysis microsystems can deal with small sample sizes and allow the isolation of rares cells which are hard to extract with traditional techniques. Various physical concepts have been used on Lab-on-a-Chip (electrical, mechanical, magnetic)  but recently some demonstrators combining optics and fluidics have been proved to be specially efficient. For example, Wang et al. designed an optical microcytometer  with high throughput (up to 100 cell/s) and Mac Donalds et al.  used a reconfigurable optical lattice for high efficiency sorting (96% efficiency).
In this paper, we focus on another kind of microsystem for manipulation of biological objects based on waveguides. The optical manipulation of particles by an evanescent field has been demonstrated in 1992 by Kawata and Sugiura  and then used for the propulsion of metallic and dielectric particles on optical waveguides [11,12]. Recently, this kind of device has been used to sort particles on Y-junction branches . However, even if it has been mentioned in the first publication by Kawata and Tani , the technique has never been employed to move biological cells. In this communication, we use silicon nitride waveguides to improve the particle propulsion efficiency and to manipulate, without label, red blood cells and yeast cells.
In the next section, we use simulations to compare the performance of various kinds of waveguides. We then go on to describe the experimental setup and the silicon nitride waveguides. In the fourth section, we present results on propulsion of dielectric particles and cells. We finish with some perspectives.
2. Theoretical comparison of waveguide technologies.
Until now, the particle propulsion on optical waveguides has been mainly performed on waveguides made by potassium or cesium ion exchange  . These works have shown that refractive index contrast between the substrate and the waveguide (Δn) strongly affects the optical forces. In this theoretical section, we are going to compare ion exchange techniques with thin film deposition technologies which allow higher index contrast. We will study three different kinds of structures: potassium ion exchanged waveguides (Δn= 0.01), cesium ion exchanged waveguides (Δn= 0.03) and silicon nitride waveguides (Δn= 0.52).
Several approaches are possible to compute the optical forces on particles located on a waveguide surface. From an analytical point of view, dipolar models are the simplest but they are only valid for Rayleigh particles. For micrometric spheres, the Arbitrary Beam Theory allows the evaluation of particle velocities on an infinite slab waveguide . However, this analytical method does not permit to take into account the lateral confinement of light in a channel waveguide.
We have chosen a numeric approach to the problem, based on the finite element method and the FEMLAB (Comsol) software. This method takes into account the lateral size of the waveguide to calculate the 3D distribution of the electric and magnetic fields. The resulting optical forces can be calculated, thanks to the Maxwell stress tensor , by integration on the external surface S of the particle .
where n⃗ is the outwardly directed unit normal from the surface and f⃗v is the local force density on the particle. For rigid dielectric particles, the radiative forces are distributed according to a volume force density :
where E denotes the amplitude of the local electric field and e is the material permittivity. For homogeneous dielectric particles of refractive index n2 immersed in a medium of index n1 Eq. (2) reduces to a surface force density σ:
The finite element method offers the advantage of using a fine mesh in the regions of interest and a coarse one in other places. This flexibility allows important virtual memory savings compared to other numerical methods as Finite Difference Time Domain (FDTD) . Moreover, the calculation time for the present structures by finite element method are around 10 minutes on a 1GB RAM personal computer. Other solutions, like non temporal finite difference or semi-analytical methods based on plane wave decomposition could also suit the problem .
The waveguide geometrical properties used in the simulation are summarized in Table 1. The vertical dimensions correspond to the optimized thickness for the optical forces when the propagation wave is TE polarized, estimated according to . In all the calculations, the guided power is normalized to 1W, the wavelength is 1064nm, and we study TE polarization. The particles are dielectric spheres (n2 =1.55 at 1064 nm) of 500nm diameter, separated by 2nm from the surface of the waveguide, immersed in water (n1 =1.33). For the sake of computer memory, we could not study larger spheres.
As an example, we show on Fig. 1 the local surface forces acting on the surface of the sphere above a silicon nitride waveguide. For more clarity, we used a coarse mesh on the particle. We observe a strong decrease in the local forces at the top of the sphere. Moreover, the total force on the particle is directed toward the centre of the waveguide and forward in the direction of light propagation. These forces are characteristic of gradient forces and radiation pressure.
In order to check our calculations, we confirmed their convergence as a function of the mesh size. Moreover, we compared the results with the analytical expressions based on Rayleigh theory (cf, Fig. 2). The calculation were made for silicon nitride waveguides and we found a good agreement between the two models when the radius of the particles tends to zero, as expected.
We compared the computed forces on different kinds of waveguides. Results normalized by the guided power are reported in Table 2. We can notice that forces strongly increase when the refractive index gap between the guide and the substrate rises. For a given power injected in the waveguide we see that the use of silicon nitride thin films increases the optical forces by a factor of 100 compared to potassium exchanged waveguides. We have estimated the particle velocity which would result from the calculated radiative forces using Stokes law and a modified expression for the viscosity which accounts for the fact that the particle is close to a surface .
These results show that even if the evanescent wave decay is faster on high refractive index waveguides, optical forces on Mie particles remain higher on these structures. Particles with 500nm diameter are larger than the evanescent field extension (d_potassium=235nm, d_cesium=233nm and d_nitride=173nm), therefore the velocity ratio for bigger particles (like cells) should be similar to the results presented in Table 2.
3. Experimental procedures
Waveguides are made of a silicon substrate covered by a 2μm silica film (n=1.45 at 1064 nm) and a silicon nitride strip (n=1.97 at 1064nm). The strips are deposited by LPCVD (Low Pressure Chemical Vapor Deposition) which gives them good optical properties and etched by RIE (Reactive Ion Etching). Silicon nitride film thickness is around 200nm. Different waveguides with strip width ranging from 1μm to 10μm have been studied, which corresponds to multimode waveguides.
The experimental setup is shown in Fig. 3. Linearly polarized light from a continuous Nd:YAG laser source operating at 1.064 μm was coupled into the waveguide through a microscope objective (NA=0.9). Since we do not have tapered structures, insertion losses are important (~10dB) and propagation losses are around 2dB/cm. The effective guided power was monitored using an optical power meter at the end of the waveguide after a microscope objective and a diaphragm.
We used glass particles (n=1.55 at 1064nm) of 2μm diameter and a standard deviation around 35% (as specified by Duke scientific but we can see on Fig. 4 that the real dispersion is much higher). Red blood cells and yeast cells of approximately 5μm diameter were also used. A cell defined by double-sided adhesive tape spacer and a cover slip was glued on the surface sample in order to form a chamber for the particles in de-ionized water (cf. Fig. 3). Motion of the particles was observed using a Navitar zoom system (with a 50X and NA=0.55 microscope objective) and a CCD camera mounted above the waveguide.
4.1 Manipulation of dielectric particles.
The use of silicon nitride waveguides allowed to demonstrate both the trapping and the propulsion of 2μm glass particles and 1μm latex particles (cf. Fig. 4). We noticed that on this kind of structure, there is a strong interaction between the beads and the guided light. In particular, we can clearly visualize the light extracted form the waveguide and scattered upward. Furthermore, we observed the formation of chains of particles as reported in .
Even if the guided power is weak, the propulsion is very efficient. Typically, for glass particles, the mean velocities are around 15μm/s for a guided power near 20mW. This power value has been measured at the end of the waveguide and corrected by taking into account the large light diffraction at the end of the structure. This device efficiency permits, with the same speed, to reduce by approximately 20 times the guided power compared with cesium ion exchanged waveguides. One drawback stems from the high insertion losses but they could be strongly reduced by using tapers at the entrance of the waveguide. Nevertheless, due to the relatively important propagation losses, particle propulsion is limited to distances in the range of one centimetre.
4.2 Propulsion of cells
The propulsion efficiency of dielectric particles on silicon nitride waveguides open the way to cell manipulation. Cells have different optical and physical properties than glass particles: they are bigger (5μm diameter) and have lower refractive index (n≈1.4). We worked with two kinds of cells: red blood cells and yeast cells (Saccharomyces cerevisiae).
Red blood cells were just mixed with EDTA (EthyleneDiamineTetraAcetic) to prevent coagulation and put in a mannitol buffer. On a 10μm width waveguide, we observed the propulsion of the red blood cells with velocities about 1μm/s for nearly 60mW inside the waveguide (Fig. 5). We can notice that, as cell refractive index are smaller than glass one, we need more power to move them. Furthermore, it seems that light does not destroy the cells.
For yeast cells, the propulsion velocities are approximately 1μm/s for a guided power around 40mW (Fig. 6). Like dielectric particles, cells tend to form small chains and even smaller bacteria seems to be attracted toward the yeast cells. Laterally, the attraction of the cells located near the waveguide highlights the presence of an intense gradient force whose range is only a few micrometers or less.
In this paper, we demonstrated, both theoretically and experimentally, that silicon nitride waveguides can move dielectric glass particles of various sizes and biological cells. To the best of our knowledge, it is the first demonstration of biological object manipulation by an evanescent wave.
Thanks to the high confinement rate of light intensity in the silicon nitride films, the power required for dielectric particles propulsion is reduced by a factor around 20 compared to cesium ion exchanged waveguides. This optimized power efficiency allows an extension of this method to the manipulation of low index objects as cells. Yeast cells have been pushed along the waveguide with velocities around 1μm/s and attracted toward the guide by gradient forces.
This kind of device can be easily combined with various integrated optics structures and opens the way to the development of new microsystems for cells sorting applications.
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