We introduce a novel method of attaining all-optical beam control in an optofluidic device by displacing an optically trapped micro-sphere though a light beam. The micro-sphere causes the beam to be refracted by various degrees as a function of the sphere position, providing tunable attenuation and beam-steering in the device. The device itself consists of the manipulated light beam extending between two buried waveguides which are on either side of a microfluidic channel. This channel contains the micro-spheres which are suspended in water. We simulate this geometry using the Finite Difference Time Domain method and find good agreement between simulation and experiment.
©2005 Optical Society of America
Optofluidics is a new and growing field of research, whose aim is enhanced device functionality through the marriage of microfluidics and micro-photonics . This technology has found application in sensing, compact optical filters and compact tunable lasers and is offering new solutions for bio-technology applications. One of the key drivers of optical fluidics is the optical tunability that can be achieved in ultra-compact structures. Tunability has been achieved by simply introducing fluids into a photonic device , modifying its properties with applied fields  or moving fluids using pressure , thermal , or electrokinetic means . Optofluidic technology allows for a large degree of tunability due to the great variety of fluid chemistry available, from various refractive index matching oils to liquid crystals and gain media. Optofluidics also enable device compactness due to large potential refractive index contrast between the fluid and surrounding air . A natural extension of these developments would be to obtain optical control over microfluidic elements. Various mechanisms have been proposed including thermal actuation at infrared wavelengths  and optical modification of surface energy . Until now, all optofluidic control mechanisms have involved direct electrical interfaces or external pressure actuators. In this paper we introduce optical trapping  also known as optical tweezers as an elegant means of all optical microfluidic control for signal beam manipulation.
Optical trapping (or optical tweezing) of dielectrics was first demonstrated during the 1980’s  and has since seen wide application to the manipulation of cells and other semi-transparent biological entities . The trapping phenomenon relies on the gradient force experienced by dielectric particles in an applied electric field . When the particles are sufficiently small and the electric field gradient sufficiently large the particle is actuated by this force. If the electric field has an appropriate local intensity maximum (such as a tightly focused Gaussian beam) the particle is stably trapped at that location.
In our device, we optically trap a silica micro-sphere using a single trapping beam and position it into a separate signal beam propagating between two buried single mode fibers on either side of a microfluidic channel. We measure transmission as the sphere is displaced across the signal beam. Our measurements show transmission when the sphere is on-axis with the beam, an attenuation of up to 11 dB as the sphere is moved out of the beam and a return to background transmission values as the micro-sphere exits the beam. The micro-sphere is 13 μm in diameter, essentially operating as a spherical lens in this geometry. We model the response of this device using the Finite Difference Time Domain (FDTD) method and see good agreement between experiment and simulation. We performed these experiments in a semi-planar buried fiber geometry.
Recently, similar work was presented by Jensen-McMullin et al.  where polystyrene spheres were trapped in a buried fiber geometry and manipulated in one dimension by a dual-beam trap. In , this trapping geometry was applied to fluorescence detection and sensing. Our work focuses on an application to beam steering in a geometry that provides full three-dimensional control over the trapped micro-sphere. Our proof of concept demonstration represents a first step towards a more general class of optofluidic devices and sensors that could enable new applications in sensing and tunable components. Applications for such components include not only beam modulation by spheres but by other trapped optical components as well, such as more complex lens shapes, mirrors or pieces of photonic crystal material. Optical trapping also allows for changes in trapped particle orientation through manipulation of the trapping beam polarization allowing for in-situ rotation of trapped elements in a beam .
2. Device principle
Figure 1 shows a schematic of the optofluidic experimental geometry. Coming from either side of Fig. 1 is a pair of waveguides; in this case we use SMF-28 optical fiber. The ends of the waveguides are separated by approximately one hundred micrometers, providing a channel for fluid to flow along and a beam that extends from one fiber to the other. In this way, the interaction of the beam emerging from the input SMF (shown red in Fig. 1) can be used for signal control purposes. Our work involves of the inclusion of an optically trapped micro-sphere in the optical path through the microfluidic channel. The microsphere, acting as an optically relocatable spherical lens, manipulates the signal. Ideally the trapping beam would be moved about the device to modulate the signal beam using scanning mirrors, acousto-optic deflectors or fiber optic tweezer devices . However, for the purposes of this demonstration, we effect signal modulation by moving the waveguides with respect to the trapped micro-sphere, thus altering the transmission properties of the device. The trapping beam is shown in yellow in Fig. 1.
The paradigm of all-optical control presents a number of advantages over other modulation methods. The major advantage this method of optical control has over current optical modulators (MEMs, optoelectronics, liquid crystals) is that there is no requirement to have an electronic control layer inside the photonic circuit. This means the photonic layer remains all-optical without the need for electronic integration, simplifying fabrication and design. Furthermore, this device is not just an optical modulator. An optically trapped sphere will not be able to modulate a beam as rapidly as, say, an optoelectronic modulator (modulation speed will be discussed below), but a trapped sphere does allow full, three-dimensional optical control of not only spheres, but any trappable dielectric element.
3. Semi-planer buried fiber geometry
We designed and fabricated a semi-planar substrate for conducting these experiments. The “semi-planar” nomenclature refers to the fact that no planar waveguides are fabricated in the traditional sense. Instead, SMF is buried under a layer of photo-polymer and a microfluidic channel is cut across the whole device.
Figure 2 shows a process schematic for the fabrication of the semi-planar device. Figure 2(a) shows initially a length of SMF being held taut 300 μm over a silica glass substrate. Figure 2(b) then shows a UV-curable photo-polymer (in this case NOA-61 from Norland Optical Adhesives) being poured over the entire substrate and fiber. It is important to note that there is no spin-coating or leveling of the liquid polymer layer, other than the viscous spreading that occurs naturally under gravity. Once the polymer has spread over the entire substrate, it is exposed to UV light following manufacturer’s specifications. After this is complete, the SMF is buried some 400 μm below the apex of the cured polymer. Figure 2(c) shows the process used to generate the microfluidic channel between the buried waveguides. A dicing saw with a 30 μm width diamond blade is used to cut a groove all the way along the device, perpendicular to the buried SMF. The diamond blade is polished on one side, so two passes of the blade are made. The resulting channel width is between 60 ~ 100 μm and the channel depth is ~500 μm deep. The depth of the cut is monitored, so that the cut at least bisects the SMF core but never extends into glass substrate. If the entire polymer layer were cut in two, then the opportunity would arise for each half of the polymer layer to move independently on the glass substrate. This is especially problematic if the polymer layers peel away from the substrate at the point of the cut. This is why we endeavor to keep the polymer layer adhered to the substrate in one piece.
There are, however, some disadvantages to using this fabrication method. Firstly, only simple structures are possible. The diamond saw blade, whilst narrow, has a large longitudinal extent, meaning that in order to cut to the depths required in these substrates cut lengths of the order of centimeters are required. This condition on channel length does not lend the technique to creating intricate microfluidic structures. Even so, the long narrow channels are suitable for the work presented here. The second main drawback of these devices is the depth of the microfluidic channel. This means that the trapped micro-spheres must be levitated some hundreds of micrometers to intersect the probe beam. This high levitation also means that there is some intersection of the trapping beam with the walls of the microfluidic channel, providing distortion of the trapping beam. Whist these effects do not prevent trapping in these geometries, higher powered trapping beams than those reported in the literature  must be used to maintain a stable trap.
3. Numerical analysis
We use two numerical methods in the analysis of this experiment. These are the FDTD method, which is a spatial and temporal discretization of the Maxwell’s equations and the Beam Propagation Method (BPM), which solves the wide angle wave equation in guiding structures.
We primarily use the FDTD method to characterize this geometry, as there is strong perpendicular scattering off the micro-sphere that is not captured in the wide-angle BPM. The BPM is used to calculate the modal profiles in the SMF, especially at wavelengths of multimode propagation, where modal beating changes the probe beam profile and thus the spectral response of the micro-sphere. Once the beam profile has been calculated it is propagated using the FDTD method as outlined above. The simulation geometry is a two dimensional approximation of the experiment seen in plan view in Fig. 4.
4. Experimental setup
The description of the experimental setup for this work falls into two categories: bulk optics and micro-scale optics. The bulk optics section describes the free space optics we use to deliver the trapping beam to the substrate. The micro-scale optics section describes the small scale experimental setup used inside the microfluidic channel.
4.1 Bulk optics
Figure 3 shows a schematic of the bulk optics we use to deliver the trapping beam. The trapping beam is generated by a mode-locked, Nd:YVO4 laser emitting pulses at wavelength 1064 nm and duration 7.5 ps with TEM00 mode profile. Trapping experiments have also been performed with this laser operating in CW mode with little difference observed in the trapping properties, so this laser may be thought of as a CW source for the purpose of these experiments. The power of the laser is regulated to 0.8 W average intensity using a pair of polarizers.
The trapping beam is delivered to the sample using an inverted microscope setup, that is, the beam is reflected upward at the sample using a dielectric mirror and is focused using a 40X, 0.65 NA microscope objective. This choice of NA provides tight enough focusing for trapping to occur. The focus of the trapping beam occurs inside the microfluidic channel in the device. The device itself is mounted onto a three-axis positioning system. A piezo actuator (10 nm resolution) controls the sample in the plane perpendicular to the buried SMF (the direction in which the sample will be moved to manipulate the beam). The other planar axis is controlled using a hand wound micrometer (1 μm resolution). The z direction (the focus position) is controlled by a stepper motor (40 nm resolution). We essentially keep the micro-sphere trapped in the one position and move the substrate around the sphere.
We illuminate the device from above with white light and visually monitor the experiment using a CCD camera. The SMF in the device is fitted with connectors, which we attach to a broadband halogen white light source for the guided probe beam (λ = 0.8 ~ 1.7 μm). We analyze the resulting output spectra on an optical spectrum analyzer.
4.2 Micro-scale optics
Figure 4 shows a schematic and a photograph of the microfluidic channel as the experiment is about to be performed. For illustrative purposes we have coupled a HeNe laser to the device. Notice the red horizontal striations in the photograph. This is the signal beam scattering off the trapped micro-sphere being held between the SMFs. The signal beam suffers virtually no diffraction propagating across the channel and as such can be treated as having a Gaussian half width of approximately 9 μm
The silica micro-spheres are available commercially as a suspension in water. We dilute this solution by a factor of 500 in Milli-Q water. The micro-spheres (manufactured by Kisker-biotech GbR) have a diameter of 13 μm, though visual comparison to a known scale is always performed. The silica micro-spheres have a refractive index of n = 1.45, whereas the surrounding water has a refractive index of n = 1.33. Having a high index particle in a low index background is a favorable condition for trapping.
A 50 μL drop of the micro-sphere suspension is dispensed onto the device and capillary action fills the microfluidic channel. The channel is sealed with transparent adhesive and allowed to sit so that the micro-spheres could settle to the bottom of the channel. Once in this state the channel is visually examined for suitable micro-spheres. When one is found, the trapping beam is unblanked and the chosen silica micro-sphere becomes levitated into the focus of the trapping beam. The focus is then lifted through the channel to approximately the same level as the SMF cores and the micro-sphere is roughly visually aligned with the center of the fibers. A second, more accurate alignment is performed by observing the scattering of HeNe laser light coupled to the device. As the micro-sphere is moved into the beam, some of the probe beam is scattered out of the plane. This out of plane scattering ceases when the micro-sphere is centered on the probe beam, providing a way to more accurately center the beam. Once the micro-sphere is centered, it is moved off-center in 1 μm increments, recording the transmission spectra at each step.
5. Results and discussion
Figure 5 shows a representative transmission spectrum for a micro-sphere displacement of 5 μm. There is a tall, narrow peak at λ = 1064 nm, due to perpendicular scattering of the trapping beam by the micro-sphere. Also, at the short wavelength end, there are some marked spectral transmission cutoffs. By contrast, at the long wavelength end, the spectrum is slowly varying. We can divide this spectrum into two regions shown by a line in Fig. 5; the short wavelength region where the propagation in SMF is multimode (λ < 1.26 μm) and the long wavelength region where the propagation in the SMF is single mode (λ > 1.26 μm).
In the multimode propagation region, the shape of the probe beam is altered by modal beating along the input SMF, causing distortion of the mode field at the output of the fiber. Due to different wavelengths of light having different modal beat lengths, the shape of the probe beam is strongly dependent on wavelength. This translates to steep spectral features in the multimode region. In the single mode propagation region, however, the mode profile remains symmetric and fundamental, resulting in slowly varying spectral variation in this region. Accordingly, we will only consider the spectral response in the single mode region for the remainder of this paper.
Figure 6 (solid curve) shows the transmission of the device as a function of micro-sphere displacement at a wavelength of 1.5 μm. Fig. 6 (dashed curve) is the numerically calculated transmission of the device as outlined in Section 3. Good agreement is seen between the calculated and experimental transmissions. From these curves we can identify three distinct transmission regimes which are indicated on Fig. 6: “on axis”, “off axis” and “leaving beam”. Figure 7 shows the electric field outputs from the FDTD calculations in these various regimes which are discussed below.
5.1 On axis
First, in this transmission regime, the micro-sphere is centered in the probe beam, exhibiting enhanced transmission when compared to the background level. Figure 7a shows the electric field output in this regime: the micro-sphere is focusing the incident probe beam, coupling more of the incident probe light into the output SMF.
5.2 Off axis
In this regime, the micro-sphere is being moved off the axis of the probe beam. In this region of the transmission curve we observe an increasing attenuation which reaches a maximum value of 11 dB at a micro-sphere displacement of 5 μm. Figure 7b shows the FDTD field output for the same micro-sphere position. The most notable feature of the field is the beam steering that is occurring. Most of the input light has been steered approximately 4 μm right of the SMF core, with another low intensity beam directed 4 μm to the left.
5.3 Leaving beam
Finally, in this regime, the micro-sphere is leaving the probe beam and the transmitted power is returning to its background value. Figure 7(c) shows FDTD field output for a micro-sphere displacement of 10 μm. From Fig. 7(c) we can see that the sphere is only slightly perturbing the beam, with most of the probe light being captured by the output fiber.
Figure 8 is an animation showing the steering of the beam as the micro-sphere is moved away from the center of the probe beam. The various transmission regimes are clearly identified by observing where the majority of the probe beam is directed. As the micro-sphere moves off-axis the beam is progressively steered away from the SMF core until, at a displacement of 5 μm, the transmission attenuation reaches a maximum. As the micro-sphere continues to move, the beam is steered back toward the SMF core, the micro-sphere exerting less influence on the beam.
The silica micro-spheres used here have a diameter of 13 μm, about twice the diameter of the probe beam and almost ten times larger than the average probe wavelength. The relative dimensions of micro-sphere to the beam and wavelength places the sphere far outside of the Rayleigh scattering regime and into the realm of geometrical optics [15,16]. A sphere of these relative dimensions can, in fact, be considered a spherical lens, evident from the FDTD field in Figs. 7 and 8. The physics of optical trapping is well known and does not warrant in depth discussion here. From the literature, we may write the tweezer force as F= QPn 1/ c where Q is the trapping efficiency, P is the power of the trapping beam, n 1 is the refractive index of the fluid, and c is the speed of light.
When the sphere is near the center of the trap, the restoring force becomes linear in displacement so we can write Q = Q 0 x where x is the displacement of the sphere from the trap axis. The response time of the trap is given by τ = γ / κ where γ is the viscous drag coefficient γ = 6πηa, η is the fluid viscosity, and a is the radius of the microsphere. These considerations yield a maximum trapping force of 1.3nN and a response time of 1ms.
An important source of noise in the positioning precision of the trapped microsphere is Brownian motion. According to the equipartition theorem, the root mean square deviation of a trapped particle from its equilibrium point is given by where k B T is the thermal energy. In our case this amounts to 6nm. Fluid flow in the system will also apply additional forces to the trapped microsphere, but these are expected to be minimal in normal circumstances. A flow rate as high as 10μm/sec will result in a viscous drag force of 1.2pN resulting in a 10nm microsphere offset. In some cases, these forces might be used to advantage to provide flow rate sensing capability.
There are several potential applications of this optical trapping geometry. By choosing the appropriate sphere dimension, the on-axis focusing can be used for enhanced optical coupling in a very compact geometry. Further, the beam steering demonstrated above can be used to select different waveguides in a more compact planar geometry. With a more complex trapping beam pattern, other optical elements could be placed in the probe beam, such as small pieces of dielectric mirror or other designs of lenses.
We introduce the principle of all-optical manipulation of light beams using optically trapped microfluidic elements. We have demonstrated this all-optical manipulation of a beam using an optically trapped silica micro-sphere which is displaced through a beam. We perform these experiments in a semi-planar, buried fiber geometry. We observed enhanced coupling and beam steering as the trapped micro-sphere is moved through the probe beam. The sphere is dimensioned such that it is behaving as a spherical lens in this geometry. This demonstration is a proof of concept of a general class of all-optical devices using optically trapped optofluidic elements to attain beam control on a micro scale. This scheme has potential applications in optical attenuation, filtering, fluid detection and monitoring.
This work was produced with the assistance of the Australian Research Council (ARC) under the Discovery Grants program.
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