(248j) Waveguide Based Particle Trapping in Integrated Microfluidic Devices

Introduction

The ability to perform controlled trapping and concentration of nanoscale objects is becoming an important part in the development of high sensitivity, low limit of detection nano-sensor devices. Essential to the development of integrated microfluidic devices incorporating such functionality is the ability to fuse active target handling components with electrical and/or optical sensor elements. Recently, researchers have demonstrated the ability to use optical energy as a means to trap and manipulate¹, and sort² particles in microfluidic environments. These trapping methods allow for a great deal of control in two dimensions, but exhibit a fundamental flaw. It is well known³ that that electromagnetic forces applied to a particle are proportional to the intensity of the incident light. This intensity is equal to optical power divided by the cross sectional area (spot size) of the trapping laser. To achieve the necessary intensity for trapping smaller particles, smaller spot sizes obtained using high numerical aperture lenses are needed. This results in an equivalent decrease in the interaction length. Because of this, it is impossible to apply these forces over more than a few hundred microns (one micron in extreme cases).

Waveguide structures confine light within microscale structures through total internal reflection over extremely long distances. While the majority of the optical energy is confined within the solid core of a waveguide, there exists a near-field non-propagating component called the evanescent field. This field extends from the waveguide surface and exponentially decays into the surrounding medium over a distance of a few hundred nanometers. This rapid decay in optical intensity results in a strong trapping field. Such confinement also enables radiation pressure propulsion of particles along the length of a waveguide. These devices have the potential to develop into sophisticated optical train tracks, allowing for a new paradigm in particle manipulation. To date, particle propulsion on waveguides in a quiescent fluid has been demonstrated for biological cells⁴, gold nanoparticles⁵, and using Y-branch waveguides⁶.

In this work, we present our recent analytical, numerical and experimental work on determining the conditions necessary for trapping stability under microfluidic flow, as illustrated in Figure 1. We establish an empirical relationship for the electromagnetic and hydrodynamic forces acting on a particle as a function of experimentally relevant parameters. In our numerical studies, we use two examples, representative of high (silicon) and low (polymer) index contrast waveguide systems, to translate our model into important design considerations for experimental systems. We also present our experimental results using waveguides fabricated from SU-8 cross-linked polymer integrated with PDMS microfluidics demonstrating the dynamic trapping of flowing particles and subsequent radiation pressure propulsion.

Theory

The Maxwell stress tensor⁷ is ideal for numerical evaluation of the trapping and propulsion forces, as it is solely dependent upon field variables, which can be relatively easily computed from a numerical solution to the wave equation. The electromagnetic force calculated via this method can be cast in orthogonal coordinates, allowing for differentiation between trapping forces (which are perpendicular to the direction of optical propagation) and the propulsion force which is along it. This represents the most general method, applicable to all particle sizes and does not require any assumptions regarding the uniformity of the field over the volume of the particle.

Once confined to the waveguide surface, the release of the particle is most likely to occur transversely due to weaker transverse trapping forces. Our model assumes an orthogonal orientation of waveguide and microchannel, thus fluid drag forces will also aid the particle in overcoming the trapping forces. Assuming a relatively constant drag force on the particle, we show that the particle trapping stability can be written as:

(1)

where S is the stability number, k_B is Boltzmann's constant, T is the temperature, γ_f is the trapping force spatial decay rate, and τ is (F_D/ F_T0), the ratio of the drag force (F_D) to the initial trapping force (F_T0).

Results and Discussion

Numerical Results

Our numerical studies focused on two waveguide systems, one modeled after silicon (n = 3.47) operating at 1550 nm and another representative of polymer systems (n = 1.68) operating at 1064 nm. Both waveguide systems assume single-mode operation. We used the Comsol finite-element software package to obtain solutions for the electromagnetic and flow fields. Using the Maxwell stress tensor, we determined the force acting on a glass spheres ranging in size from 300 nm to 600 nm. We were able to obtain empirical information about the transverse trapping, downward trapping, propagation, and fluid drag forces on particles as a function of particle size, position, flow velocity, and optical power. We also calculate γ_f as a function of particle size and laser power.

As illustrated in Figure 2, we obtained transverse trapping force profiles for both sets for waveguides. The higher index contrast of the silicon waveguide system creates a more confined trapping field, leading to stronger transverse trapping forces compared to a polymer waveguide system. Also, there is a significant dependence of the trapping force dependant on the size of the particle. Also shown is a propulsion velocity profile for the polymer waveguide system, indicating that the propulsion velocity is strongest in the middle, where the mode is confined. In Figure 3, we provide a sample stability diagram for the silicon waveguide system. The main conclusions drawn from our analysis state that larger particles tend to show a larger sensitivity to changes in fluid velocity, although given the correct conditions, they also tend to trap better than smaller particles at similar fluid velocities.

Experimental Results

Our experimental setup is illustrated in Figure 4. The SU-8 waveguide chip and PDMS masters were made using photolithography. The particles used are polystyrene beads of various diameters which are impregnated with green or red fluorescent dyes sensitive to specific wavelengths. Our particle solution is made using a 100 mM 7.0 pH phosphate buffer solution in a 100:1 ratio with our particle suspension.

We were able to achieve trapping of 3 μm polystyrene spheres on our waveguides with bulk particle speeds of 10 μm/s, and at an input laser power of 80 mW. Once trapped, particles exhibited propulsion due to radiation pressure, as seen in Figure 5. The propulsion speed was considerably faster, almost double the bulk particle speed. This resulted in a considerable shift in particle position before and after trapping, even with the relatively short trapping time. The release of particles were due to collision with the channel sidewall (upper particle), and a minor defect in the waveguide (lower particle). As such, electrostatic effects between the waveguide and particle are minimized and the trapping force is the dominant factor. We also observed an increase in fluorescence intensity for particles while on the waveguide. Scattered light from the waveguide is filtered during our experiments; we believe this effect may have been due to two-photon excitation, as our particles are excited at 542 nm, while the laser wavelength is 980 nm.

Figure 5: Time-lapse images of SU-8 waveguide integrated trapping (a) Position of particles pre-trapping (b) Top particle (red) reaches waveguide structure (c) Propulsion of red particle along waveguide structure. Blue particle nears waveguide (d) Red particle no longer trapped on waveguide. Propulsion of blue particle along waveguide (e) Continued propulsion of blue particle (f) Both particles no longer interact with waveguide.

Conclusion

In conclusion, we have outlined our model for particle trapping in an integrated microfluidic system, and have provided a detailed numerical analysis predicting trapping stability using experimentally relevant parameters. We have also demonstrated successful experiments based on our model which illustrates the transition of a particle to a trapped state, along with the potential of using radiation pressure to significantly alter particle paths without altering microfluidic flow behavior.

References

¹ P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436 (7049), 370 (2005).

² MacDonald, G. C. Spalding, and K. Dholakia, Nature 426 (6965), 421 (2003).

³ M. N. Zervas et al., Journal of Lightwave Technology 18 (3), 388 (2000).

⁴ S. Gaugiran, S. Getin, J. M. Fedeli et al., Optics Express 13 (18), 6956 (2005).

⁵ N. Ng, B. J. Luff, M. N. Zervas et al., Optics Communications 208 (1-3), 117 (2002).

⁶ K. Grujic, O. G. Helleso, J. P. Hole et al., Optics Express 13 (1), 1 (2005).

⁷ John David Jackson, Classical electrodynamics, 2d ed. (Wiley, New York, 1975); B.