We present a microfluidic chip in Polymethyl methacrylate (PMMA) for optical trapping of particles in an 80µm wide microchannel using two counterpropagating single-mode beams. The trapping fibers are separated from the sample fluid by 70µm thick polymer walls. We calculate the optical forces that act on particles flowing in the microchannel using wave optics in combination with non-sequential ray-tracing and further mathematical processing. Our results are compared with a theoretical model and the Mie theory. We use a novel fabrication process that consists of a premilling step and ultraprecision diamond tooling for the manufacturing of the molds and double-sided hot embossing for replication, resulting in a robust microfluidic chip for optical trapping. In a proof-of-concept demonstration, we show the trapping capabilities of the hot embossed chip by trapping spherical beads with a diameter of 6µm, 8µm and 10µm and use the power spectrum analysis of the trapped particle displacements to characterize the trap strength.
© 2015 Optical Society of America
Single cell detection and identification is essential to differentiate between cells in a sample under test. In cancer research for example, there is a need for identifying tumour cells and discriminating these from healthy cells. A well-known optical detection method for interrogating cells is Raman spectroscopy. This is a non-destructive label-free method that determines the molecular fingerprint of molecules or cells [1, 2]. However, Raman scattering is a weak process. The low efficiency of Raman scattering can be enhanced using special surface structures, i.e. surface-enhanced Raman spectroscopy (SERS) , but these specialty surfaces are difficult to mass-produce. An alternative method is to stably position the cell under test in the detection area during acquisition of the Raman scattering such that the acquisition time can be increased. Positioning of cells can be done through optical trapping and leads to an enhanced signal-to-noise ratio and thus a more reliable cell identification. The work of Ashkin in 1970 demonstrated the capability of using two counterpropagating laser beams to optically trap a particle . Optical trapping is a non-contact optical manipulation technique that can trap, move and sort cells using optical forces  and has led to a lot of biological and biomedical applications , which will be discussed below.
Most optical detection and manipulation techniques are bulky, expensive, time-consuming and need frequent realignment. Suppose now that a point-of-care analysis of a patient’s blood or urine sample is needed or that one wants to develop low-cost sensors for an in-the-field analysis of drinking water in remote areas. A lab-on-chip (LOC) device could be the gateway toward these application domains. Multiple laboratory analyses are miniaturized and integrated on a LOC device, which reduces the cost and sample consumption of the analyses. A LOC device is portable, user-friendly and leads to various functionalities on-chip such as parallel testing, cell sorting, flow cytometry and point-of-care diagnosis, increasing the degree of automation and the throughput of analyses. These functionalities can be combined with optical trapping [7–9 ]. Optical trapping systems can exist in various physical sizes: on the one hand microscope-sized optical tweezers make use of a high numerical aperture objective to trap particles in the vicinity of its focus and on the other hand optical trapping can also be realized at the microscale. Optical trapping is an example of an additional laboratory process that can be miniaturized and has already been introduced into labs-on-chips in various ways leading to different applications. These can be classified based on their manipulation principle. The positioning can be controlled by a fluid flow , an acoustic field , light directed by fluids  or purely by light. Since our goal is to trap particles with light on a LOC device, we give an overview of several existing configurations within this category.
The integration of optical trapping on chip can for example be achieved using a microprobe based on a combination of four single-mode fibers composing a bundle with beam shaping optics to optically trap particles in a microfluidic system. The beam shaping can be realised either by patterning the core region of the fibers using the focused ion beam technique  or by fabricating micro-prisms on the fiber facets using two-photon lithography . Also the gradient in evanescent fields can be exploited to trap particles. This is done in two dimensions by pushing polystyrene particles, flowing in the proximity of the waveguide surface, against the wall of a microfluidic channel placed on top of the waveguide . Three dimensional trapping of polystyrene beads and yeast cells using evanescent fields is realised by locally enforcing evanescent fields with a deposited array of gold pads on top of the dielectric waveguide . The light from the waveguide is coupled to the surface plasmon resonance of the gold pads that act as plasmonic traps. Photonic crystal cavities can be used as well to enhance the evanescent wave of the cavity mode to trap bacteria . The disadvantage of these devices using evanescent fields is that particles are trapped close to the microprobe or waveguide, which can be impractical for applications where a larger distance is preferred, e. g. for manipulation and analysis of a particle.
Since in our research we work with two counterpropagating beams emitted by two single-mode fibers, we discuss in more detail the dual fiber optical trap configurations existing nowadays . This optical trap type is the more practical version of the dual beam geometry introduced by Ashkin and consists of two counterpropagating divergent laser beams. The large confinement region of this kind of optical trap leads to its capability to stably hold and manoeuver large cells and to study optical binding effects acting on particles  with a reduced chance on photodamage due to the lower power density in divergent beams compared to a focussed single beam. When using for example one asymmetric laser beam in a dual fiber optical trap, cells can be stably oriented in three dimensions within the trap by rotating this fiber . The large confinement region is compatible with a microfluidic environment and has led to the microfluidic stretcher that deforms trapped cells in a microcapillary . This device is used for cell characterisation based on the viscoelastic signature of the cell under test, leading for example to a discrimination between normal epithelial cells and cancerous ones . The optical stretcher device exists in a monolithic version, with direct implementation of the microfluidic channels and optical waveguides on a glass substrate through femtosecond laser writing . Alternatively, microfluidic channels have been directly integrated onto semiconductor laser material , using lithography. This ensures a direct entering of the laser beams into the test chamber and an intrinsic alignment of the counterpropagating laser beams. However, GaAs/AlGaAs heterostructures require a complex fabrication process and produce a limited amount of power . The dual fiber optical trap has also been integrated in a microfluidic glass chip with flow focusing and combined with Raman spectroscopy to identify and sort different tumour cell types and normal cells in a microfluidic flow . This chip was fabricated using standard photolithography and a two-step wet etching procedure using hydrofluoric acid.
Many other applications of optical trapping exist such as the acquisition of Raman spectra from local parts of primary human keratinocytes while being trapped and moved around , the measurement of the size and refractive index of microparticles by detecting forward scattered light , which could be compatible with the analysis and sorting of cells on a lab-on-chip and the measurement of the three-dimensional optical force field on a trapped Chinese hamster ovary cell . A dual fiber optical trap with lensed fibers  and inclined lensed fibers  has been introduced to trap single beads or even to trap, separate, stack and group multiple beads [31,32].
In this paper we introduce a novel polymer microfluidic device with integrated particle manipulation in which fiber-optic laser beams are used to optically trap particles in a microchannel. The novelty of the device lies in the mass-manufacturing which allows a low-cost microfluidic chip. The chip is made of Polymethyl methacrylate (PMMA) and is robust, which is obtained due to the design of the chip and the use of double-sided hot embossing. Particles are trapped in an 80µm wide microchannel and the single-mode fibers are separated from the microfluidic channel by thin PMMA walls with a width of 70µm. These walls prevent contamination of the trapping fibers by the sample fluid flowing in the microchannel. The paper is structured as follows. In Section II, we introduce the design and the model that we developed to simulate the optical forces that are acting on the particles flowing through the microchannel. These optical forces are calculated by means of wave optics and non-sequential ray-tracing combined with a mathematical code. The model is then validated theoretically and experimentally. In Section III, we discuss the prototyping process of the PMMA chip consisting of a premilling step and ultra precision diamond tooling for the mold fabrication and subsequent replication through hot embossing. We discuss the sealing method of a PMMA top layer to make the microchannel leakproof, resulting in an assembled chip for optical trapping. In Section IV, we use the final chip in a proof-of-concept demonstration setup to trap polystyrene microbeads with a diameter of 6µm, 8µm and 10µm and discuss the detection method and the resulting forces. We draw conclusions in Section V and discuss the possibilities for future improvements.
2. Simulation scheme for optical trapping
2.1. Introduction of the on-chip optical trapping design
The particles under test in the to be developed PMMA lab-on-chip device flow in a microchan-nel with a width of 80 µm and a height of 320 µm. The channel is separated from the trapping fibers by walls with a thickness of 70um, leading to a total fiber separation of 220 µm. These dimensions were chosen as a compromise between the chip robustness and the optical trapping strength. A schematic drawing of the design is shown in Fig. 1. In the axial direction the trap is formed by balancing the radiation pressure applied by either beam. If the particle is displaced in the positive z direction, then the radiation pressure from the beam travelling in the negative z direction increases, providing a restoring force. This differs from other counterpropagating beam traps, in which the focal point of the beams are superimposed and axial trapping is achieved by the gradient forces . In the transverse directions, the optical trap relies on gradient forces originating from the intensity profile of the single-mode Gaussian beams. To qualitatively evaluate the optical forces that act on particles flowing in the trapping area between the two counterpropagating laser beams, we developed a model that is partly based on wave optics and partly on ray-tracing combined with mathematical processing to describe the behavior of a particle in the optical trap.
2.2. Motivation of the ray-optics approach
Our model simulates the optical forces that are acting on dielectric particles in the microfluidic channel and their dependence on different design parameters and bead characteristics. The optical trapping of a particle in a light beam results from the optical forces that originate from the interaction of light with matter. This light-matter interaction can be described in different ways, depending on the diameter (d) of the particle with respect to the trapping wavelength (λ). In the Mie regime (d ≫ λ), light is represented as rays normal to the wavefronts and light refracting and reflecting on the surface of a transparent material imparts part of its momentum onto the particle. In the Rayleigh regime (d ≪ λ), the particle can be represented as a dipole and forces are calculated using full-wave methods. For particle sizes on the order of the wavelength (d ≈ λ) the T-matrix method is usually applied where the T-matrix describes the complete scattering properties of the particles . This method is a computationally efficient approach compared to full-wave methods and gives accurate results. However, in cases where exact quantitative values are not of primary importance some approximate approaches such as the ray-optics or geometrical approach can be used. Although the T-matrix method presents an elegant approach for the calculation of optical forces, this method is not directly compatible with the calculation of the light propagation through various microstructures. Within the framework of cell trapping applications, it is particularly relevant to consider particle sizes within the 2–10λ range. These dimensions do not completely justify a ray-optics approach, since in this approach the diameter of the particle should be much larger than the wavelength. Nevertheless, a ray-tracing model has been previously used for the calculation of optical forces on spherical particles with diameters in the range of interest [32,35], which showed a reasonable agreement with the experimental results for dual fiber traps.
We conclude that the ray optics approach is a good approximation for our application, when comparing with literature [32, 35]. This approach requires an appropriate description of the rays propagating through the trapped particle to properly calculate the transfer of momentum. The use of ray-tracing gives additional benefits of combining it with the same ray-tracing software that we use to calculate the light propagation from the fiber facet to the bead. Our model offers several advantages to estimate optical forces being applied on dielectric particles of various sizes relevant to cell applications. It also gives the possibility to implement irregular non-spherical particles and to calculate the resulting torque. Back-reflected rays into and outside the particle are considered using non-sequential ray-tracing. The model enables the prediction of circumstances in which particles are trapped and how they behave in the optical trap, and therefore suits well for designing an integrated optical trap into a microfluidic chip. The ultimate goal of this model is to introduce it for micro-optical systems for biomedical applications to predict the behavior of cells in a dual fiber optical trap, facilitating for example their identification.
2.3. Wave optics and ray-tracing model
Our model combines wave optics with geometrical ray-tracing to respectively cover the light propagation from the fiber to the bead and the light interaction with the bead. Within the Mie regime, we consider the propagation of individual rays, following a Gaussian intensity distribution, through a dielectric particle. Each ray produces an element force and torque, which can be easily obtained from classical (Newtonian) mechanics, by considering the change of momentum of light resulting from the ray reflection and refraction on the bead surface. In biologically-relevant applications, the laser wavelength is chosen in the near-IR region (800–1100 nm) to minimize thermal damage . The influence of absorbed rays is therefore usually neglected in optical force calculations. We use a non-sequential ray-tracing software (Breault, ASAP) to find the incident , reflected and refracted rays and their respective power at every interaction with the bead surface. We export these rays together with their corresponding Fresnel reflection and transmission coefficient (respectively R and T) and calculate the optical forces exerted on a particle in MATLAB® based on Aspnes et al. .
Before being able to trace rays through the bead and calculate the optical forces, the trapping light needs to propagate from the single-mode fiber exit toward a virtual surface at a small distance in front of the bead. We use this virtual plane to make the transition between wave optics and ray-tracing. In order to obtain a reliable intensity distribution of the ray set on that virtual surface we use the Gaussian Beam Propagation method. This method allows a ray-tracing description of a Gaussian beam, both in the far field as well as in the Rayleigh range of the beam. The Gaussian beam is modeled as a base ray, two waist rays and two divergence rays [Fig. 2]. The base ray points towards the direction of the beam propagation, along the beam main axis of symmetry. The waist rays, parallel to the base ray, describe the waist semidiameter of the beam. The divergence rays define the far field divergence angle of the beam.
Since this representation allows to simulate the propagation of a Gaussian laser beam in free space only, we decompose the wavefront in a weighted sum of Gaussian beams. This enables simulating the propagation of this wavefront of a non-paraxial field through a micro-optical system. Each individual beam is then geometrically traced until the predefined virtual surface. The sum of the beams on that surface gives the total field profile in front of the bead. We decompose the intensity profile in weighted rays that are traced through the particle. The optical force can be subsequently calculated based on Aspnes et al. , as mentioned earlier.
2.3.1. Theoretical validation
We apply our model to the dual fiber optical trap configuration with the trapping fibers directly inserted in water. We want to verify the field propagation and the decomposition steps in the model by validating it with an existing analytical solution based on the formula used by Sidick et al. . They calculate the trapping forces analytically in the ray-tracing regime for spherical particles in a dual fiber optical trap. By comparing our model with this, we demonstrate the validity of our ray-tracing results within the ray-optics approach. The transverse trapping efficiency is given byFig. 3(a)]. We work with a wavelength of 785nm, a beam waist of 2.5µm and consider polystyrene (n = 1.5788) spherical beads in water (n = 1.3287) with a radius of 3µm, 5µm and 7.5µm. We observe that when the particle deviates from its equilibrium position in the transverse direction, it is pulled back to this point by the optical forces. Larger beads show a steeper slope and will be pulled back more strongly. We observe a very good agreement between the analytical model and our ray- tracing approach. Due to the centrosymmetric profile of the Gaussian beams and the spherical symmetry of the bead, the trapping behavior is the same in the other transverse direction (y).
2.3.2. Comparison with the T-matrix method
We are also interested in how the ray-tracing calculations behave compared to results obtained with the T-matrix method. Therefore, we implement this method based on a mathematical code developed by Simpson et al.  and also apply it to a dual fiber trap configuration in water. In this method, the scattering properties of the spherical particle are completely described by the Mie scattering coefficients, which are the elements of the T-matrix. The incident field is decomposed into a series of basis functions (vector spherical wavefunctions (VSWF) in a spherical geometry) with their corresponding beam shape coefficients. Each VSWF is scattered by the spherical particle in a way that depends on its T-matrix elements. The beam shape coefficients of the incident field can be calculated analytically around the beam waist using the ‘localised approximation method’ . In our case we consider weakly divergent beams with the particle positioned far away from the beam waist. Therefore the beam shape coefficients should be translated and rotated numerically depending on the beam waist separation and the position of the sphere in the trap. We refer to the work in Ref.  for more details about these calculations. The beam shape coefficients of the scattered field for a particular particle position are calculated by a linear transformation, determined by the T-matrix, of the incident beam shape coefficients. Finally, the optical force can be found by integrating the Maxwell stress tensor over a closed surface surrounding the sphere, which in our case of an isolated particle simplifies to a sum of products of the beam shape coefficients of the incident and scattered field.
We simulate the transverse efficiency for the same situation as described above (for fiber separation of 160 µm and beads with a radius of 3µm, 4µm, 5µm and 7.5µm) with the T-matrix method [Fig. 3(a)]. A general observation is that the maximal transverse efficiency calculated with the ray-optics approach is lower in absolute value than the one calculated with the T-matrix method. We also simulated the axial trapping efficiency with the three methods mentioned above for a fiber spacing of 160µm and a bead radius of 3µm [Fig. 3(b)]. Here, we clearly see the difference between the ray-optics approach and the T-matrix method, which takes interference of the trapping beams into account. The axial efficiency, calculated with the T-matrix method, contains a linear component, that also appears in the ray-tracing approximation, and an oscillating component due to interference effects. As the particle size increases, the gradient of the linear part increases, forming a unique trapping point. In general, the effect of the interference fringes will always influence the thermal motion of the trapped particle in the axial direction. The mean slope of the axial trapping efficiency simulated with the T-matrix method indicates that also the axial trapping efficiencies are underestimated by the ray-optics model compared to the T-matrix method.
When comparing our ray-tracing approach with the analytical solution and the T-matrix method, we can conclude that our model has a very good agreement with the theoretical model and that the obtained efficiencies are of the same order as magnitude of the ones calculated by the T-matrix method, although the ray-optics approach systematically underestimates the trapping efficiencies.
2.3.3. Comparing forces for various fiber separation distances
Since our experiments are done in a PMMA (n = 1.48 at 785nm) LOC with a fiber separation of 220µm (channel width = 80µm, wall thickness = 70µm), it is interesting to simulate this situation to predict the trapping behavior in the chip. We calculate the transverse and axial efficiencies with our ray-tracing model for different bead sizes [Figs. 4(a), 4(b)]. To validate this model for different fiber separations, we additionally simulate the trapping efficiencies in a square microcapillary made of Borosilicate glass (n = 1.51 at 785nm) with a fiber separation of 160µm (inner diameter = 80µm, wall thickness = 40µm). For the latter, we have chosen a microcapillary instead of a LOC device because a fiber separation of 160µm might lead for the same channel width of 80µm to too fragile wall thicknesses. The most important difference between these simulations is the fiber separation (160µm vs. 220µm). We observe that the transverse efficiency and thus the transverse trapping forces will be weaker in the chip since the fiber distance is larger in this case. The axial forces will be weaker in the chip for small particles (R = 3µm) but stronger for larger particles (R = 5µm and 7.5µm). Beads with a radius of 7.5µm show an unstable behavior, indicated by the positive slope in Fig. 4(b), in the microcapillary but will be stably trapped in the chip. This can be explained by the underfilling of the 7.5µm radius bead by the trapping beams in the microcapillary optical trap, in contrast to the overfilling of the 5µm radius bead. Suppose the 7.5µm radius bead is displaced towards the right trapping fiber. The bead is then less underfilled by the left trapping fiber, meaning that the intensity of the left beam is more spread out over the bead. This results in an increased light intensity at larger incident angles, giving rise to an increased optical force from the left fiber because of the larger transfer of momentum. The right trapping beam will underfill the bead even more, resulting in a decrease of the optical force since the maximal incident angle of the light on the bead decreases. The combination of these changes in optical force results in the bead being pushed towards the right fiber, so no equilibrium is reached in this case. In contrast, when the 5µm radius bead moves towards the right trapping fiber, the bead will be more overfilled by the left beam and less overfilled by the right beam. This means that more intensity falls onto the bead from the right side. Consequently, the bead will be pushed back to its equilibrium position. In the chip, both the 5µm and 7.5µm radius bead are overfilled by the trapping beams and are stable as a result. After experimental verification, we observed this instability for the 7.5µm radius particles in the microcapillary. Instead of being trapped, the bead was pushed against the wall in the direction of one of the trapping fibers.
We can also predict the sensitivity of the trapping capability to tranverse misalignments of the fibers. The transverse and axial stiffness decreases with increasing transverse fiber misalignment and the bead will start oscillating in the trap when a misalignment is present. The stiffness (κ) represents the strength of the trap and is related to the optical force in Eq. (1) according to the following formula:Fig. 5], which was also observed experimentally. Our ray-tracing model also offers other functionalities such as the prediction of the sensitivity of the trapping capability to angular misalignment, the extent of the trapping area and the maximal permitted flow speed in the microchannel.
3. Fabrication of the optical trapping chip
The fabrication process of the optical trapping chip consists of different steps. First, two molds are manufactured through premilling and ultra precision diamond tooling (Moore, Nanotech 350FG). In a next step, these molds are used in a double-sided hot embossing process (Jenoptik, HEX04), as illustrated in Fig. 6, which results in a microstructured PMMA layer containing a 80µm wide microchannel and two grooves for the single-mode fiber alignment. Finally, a PMMA toplayer is bonded to the hot embossed layer to seal the microchannel and microcapillaries are introduced at both ends of the channel to allow particles to flow in the microchannel.
3.1. Manufacturing of the metal molds
The molds are 10cm by 10cm and are made of brass (CuZn39Pb3). We first perform a “rough” milling of the molds that resulted in a microstructure that approaches the targeted dimensions in order to limit the ultra precision diamond tooling to the structures that need precise dimensions and the surfaces that need optical quality. Also holes are provided for fixing and alignment purposes in the next steps. One mold, the fiber mold, contains a structure with a width of 300µm, a height of 320µm and a length of 16mm.
These microstructures are further tailored with ultra precision diamond tooling to the targeted dimensions while ensuring optical quality. First, a notch with a depth of 200µm and a length of 220µm is milled in the center of the premilled fiber structure on the fiber mold. This length will be the fiber spacing in the final chip. The notch is removed from the fiber structure by a diamond milling tool with a diameter of 100µm (±10µm tolerance). Enough material is surrounding the notch to ensure the necessary thermal conductivity during the diamond tooling. Next, a 500µm (±10µm tolerance) diamond milling tool is used to make tapers at both sides of the notch that narrow the 300µm structure to a width of 126µm, which corresponds to the diameter of the single-mode fiber used in our experiments and ensures alignment of the trapping fibers. In addition, two curved notches are foreseen at both sides further from the central notch for prealignment of the fibers to avoid angular misalignment. A detailed view of the described microstructure is shown in Fig. 7(a). The second mold, the microchannel mold, contains a structure with a width of 460µm, a height of 300µm and a length of 21mm after the premilling step. This structure is narrowed in the center using the same 500µm diamond milling tool to a microchannel with a width of 80µm and a length of 1.7mm [Fig. 7(b)]. Along the microchannel, the tool goes 20µm deeper compared to the rest of the mold surface. In the final chip, this will form a ridge that is 20µm higher than the rest of the surrounding PMMA and will avoid clogging of the microchannel in the sealing step, which will be explained later. A detailed view of the microchannel is shown in Fig. 7(b). Alignment crosses are precisely positioned on the corners of the fiber and the microchannel mold with respectively the 100µm and 500µm diamond milling tool, and used for alignment of the molds in the next hot embossing step.
The structures on the molds are measured with a Multisensor Coordinate Measurement Machine (Werth UA400). The width of the fabricated inversed microchannel on the mold is 82µm, the fiber groove 128µm and the notch length (i.e. the future fiber separation) 218µm. These dimensions are close to the targeted dimensions of respectively 80µm, 126µm and 220µm.
3.2. Hot embossing of the structured PMMA chiplayer
In a next fabrication step, the diamond tooled molds are used in a double-sided hot embossing process to create a structured PMMA layer. The molds are aligned such that the inversed microchannel of one mold fits in between the inversed fiber grooves of the other mold. The alignment is achieved by using a built-in microscope that can be inserted between both molds once they are mounted in the chamber of the hot embossing machine. This microscope looks down to the bottom mold, which allows to determine the position of the alignment crosses on the bottom mold and the imprint of the alignment crosses of the top mold in the replica after a first hot embossing step. The position of the bottom mold is then corrected using micro-actuators to compensate for the measured misalignment. This procedure is repeated until the optimal position, where the alignment crosses on the bottom mold coincide with the imprint of the alignment crosses of the top mold in the replica, is reached. With this method, an alignment accuracy smaller than 2µm is reached.
The inverse structures on the molds (i.e., ridges instead of a channel and groove) are then pressed in both sides of a 500µm thick PMMA plate to hot emboss the microchannel and fiber grooves. The double-sided hot embossing process is shown in Fig. 6. In the resulting PMMA chip [Figs. 8(a) and (b)], walls with a thickness of 70µm will remain between the hot embossed microchannel and fiber grooves. Within the PMMA layer, a minimal overlap in depth is needed between the microchannel and the fiber grooves to enable trapping of particles and lift them approximately 30µm above the channel bottom to avoid any influence of the bottom surface. The achieved overlap depends on the hot embossing parameters and has been measured destructively by milling several chips along the fiber grooves. A milled chip is shown in Fig. 8(a). Table 1 gives an overview of the achieved overlap, measured with a non-contact optical surface profiler (Contour GT-I, Bruker), as a function of the applied force and the original sample size. We clearly see that the overlap within the hot embossed PMMA depends on both the force and the original sample size. In the three different situations the mentioned force is applied during 6 minutes at a temperature of 150°C which is constant for 160s and then drops continuously toward the end of the process. The final chip was realized with a force of 8kN and an original 500µm thick PMMA sample of 21mm by 15mm. A small misalignment of approximately 5µm of the microchannel compared to the fiber grooves was observed resulting in two slightly different wall thicknesses at both sides of the channel.
The effect of the overlap can be intuitively understood by means of Fig. 9. If no overlap or a little overlap (< 63µm, i.e. half the diameter of the single-mode fiber) between the microchannel and the fiber grooves is present, no interaction will occur between the trapping beams exiting the fibers and the particles flowing in the microchannel. Both situations are shown in Fig. 9, which depict destructively milled chips fabricated in the early stages of the fabrication process optimization. Beads will flow in the microchannel without feeling any influence of the trapping beams, as these beams are shining in the PMMA underneath the microchannel. If the overlap is in the range between 63µm and 75µm, the trapping beams could be scattered by the bottom surface of the microchannel. Starting from an overlap of approximately 75µm, the trapping beams reach and can trap the beads in the microchannel without being influenced. When the targeted overlap is achieved (116µm [Fig. 8(a)]), the interaction of the trapping beams with the beads flowing in the microchannel is ensured. The optical axis of the trapping beams (i.e. the height at which the particles will be trapped) is situated at approximately 50µm of the bottom surface of the microchannel. In the destructively milled chips with an average overlap of 86µm, we measured a variation of ±5µm on the overlap distance over 6 measurements (see Table 1). A variation of ±5µm in the final chip means that the optical trap will be situated around 45µm to 55µm from the microchannel bottom which is still far enough from the bottom surface to ignore the additional drag arising from the wall effect. Due to gravity, the particles sink with a certain velocity (depending on the parameters of the bead and the surrounding medium) and the probability of trapping a bead at a height of 50µm in the microchannel will be smaller than at 20µm. Nevertheless, we were able the trap particles in a short time at this height in our experiments.
With the non-contact optical surface profiler we measured an average root mean square (RMS) roughness of the fiber facet and the fiber groove side (indicated in Fig. 10(a)) of respectively 21nm (σRMS = 1nm) and 30nm (σRMS = 5nm), measured within 6 and 12 evaluation areas of 45µm × 60µm respectively. The roughness of the fiber facet and fiber groove side depends on the diamond tools used during the diamond tooling, which were respectively the 100µm and 500µm tool. Since the measured surface roughnesses correspond to λ/30 on average, the beam propagation of the trapping light will not be affected and the optical trapping capabilities will not be influenced.
Prior to the final hot embossing of the optical trapping chip, several tests were performed on the mold alignment and also on other hot embossing parameters, such as the size of the original PMMA layer, the applied force, the temperature and the duration of the applied force. During these hot embossing tests, in some chips tilt in the channel edges was present [Fig. 10(b)], with a maximal observed tilt of 2 to 3°. To predict the effect of eventual tilt in the edges of the microchannel on the optical trapping of particles, we introduce a tilt of 3° in the channel edges in our wave optics and ray-tracing model of the dual fiber optical trap. We observe three changes in the transverse trapping efficiency (Qx). The maximal efficiency drops with 1.25% compared to the situation without tilt in the edges, the equilibrium position is shifted from 0 to −0.03µm and the slope around the equilibrium position drops with 0.8%. The slope of the axial trapping efficiency (Qz) stays approximately constant and the equilibrium position in the axial direction is shifted from 0 to −0.3µm. From these simulations, we can conclude that a possible small tilt of 2° to 3°, observed during the hot embossing tests will not affect the trapping capability significantly.
Hot embossing suffers from shrinkage during the cooling down process, which lies between 1 and 2%. Also, a chip-to-chip variation of approximately ±1% was observed, by measuring the fiber separation distance (i.e. the notch length) in 8 different hot embossed chips, resulting in a variation of approximately ±2µm. We introduce this variation of 4µm in our model to illustrate the effect of the fiber distance variation on the trapping efficiencies (Qx, Qz). The simulation shows that the maximal value of Qx only drops with 0.9%. The slope of the axial efficiency drops with approximately 0.5%. This efficiencies demonstrate that the chip-to-chip variation of the dimensions within the chip due to hot embossing will not have a significant effect on the trapping capability.
The use of double-sided hot embossing allows us to replicate the microfluidic component at low-cost in a variety of thermoplastic polymers. Due to the possibility of hot embossing wafers with sizes up to 300mm, we could realize approximately 200 chips in one cycle of 10 minutes.
3.3. Sealing of the PMMA chip
A top layer with a thickness of 300µm and the same size as the hot embossed layer (20mm by 15mm) is bonded on the latter to seal the microfluidic channel. The bonding is done with a spin coated UV curing adhesive (Loctite 3301), which is a nonfluorescing, slightly flexible, UV/visible adhesive with a low viscosity and excellently suited for bonding thermoplastics. The ridges at both sides of the microchannel slow down the capillary force effect and reduce the risk of channel clogging. In a last step, we glued microcapillaries in both ends of the channel to enable a particles flow. A picture of the final microfluidic chip is shown in Fig. 11.
4. Proof-of-concept demonstration
4.1. Experimental setup description
A pigtailed laser (continuous wave, λ = 785nm, power at SMF output = 280mW) is used to trap particles in the PMMA chip that is clamped on a 3-axis translation stage in the proof-of-concept demonstration setup (Fig. 12). The laser light is split by a 50:50 fiber splitter and each half is coupled into a single-mode trapping fiber (MFD = 5µm, NA = 0.13), which is mounted on a 3-axis translation stage. This trapping light is scattered by the trapped bead in the microchannel and is partly captured by an infinity corrected objective (50X, NA = 0.3). The scattered laser light propagates via a mirror and a dichroic mirror (reflection band 784-786nm) and is finally detected by a position-sensing detector (PSD), that tracks the displacements of the incident light and converts these into voltage signals. The dichroic mirror allows the visible light to reach a CCD camera for visual observation of a trapping event. The position-sensing detector is connected to a T-Cube Controller that outputs the x-channel and y-channel voltage signals, respectively representing the axial and transverse bead displacements in the trap, and the sum signal. Each voltage signal is fed into an anti-alias filter with a cutoff frequency of 10kHz to eliminate unwanted high frequency noise. Each filter is shielded to avoid electronic crosstalk between the channels. The filtered voltage signals are subsequently sampled at 20kHz using a data acquisition card. We introduce polystyrene beads (Polysciences, Inc) with a diameter of approximately 6µm, 8µm and 10µm in the microchannel. In order to know the strength of the harmonic restoring forces and thus the trap strength that can be achieved in the hot embossed chip, we use the power spectrum analysis of the bead displacements . When a bead is trapped between two Gaussian beams it executes a Brownian motion in a harmonic potential well. The resulting forces from these Gaussian beams on the bead are approximately linear in the bead displacements with respect to its equilibrium position. The combination of the random Brownian motion and the restoring forces results in a Gaussian distribution of positions, which are tracked by the position-sensing detector. In a next step, the power spectrum is calculated from these time series of voltages representing the position fluctuations and fitted with a Lorentzian spectrum [Eq. (3)], according to the Einstein-Ornstein-Uhlenbeck theory :Eq. (4)], far from any PMMA surface.
The trap strength is represented by its stiffness (κ), which is related to the corner frequency of the power spectrum [Eq. (5)]:
4.2. Results and discussion
We record ten time series of 40sec of bead displacements for a bead size with a diameter of 6µm, 8µm and 10µm in the square microcapillary and the optical trapping chip at different trapping powers. Next, the power spectrum of each time series is calculated and fitted with a Lorentzian spectrum in a frequency range from 5Hz to 2000Hz. An example of a power spectrum of the transverse displacements (along the x-axis, indicated in Figs. 1 and 8) of a 10µm diameter bead at a total trapping power of 130mW is shown in Fig. 13. The average transverse stiffness (κx) of the trap is calculated from the corner frequencies fc of the power spectra, according to Eq. (5). These are plotted for the three bead sizes together with the 50% confidence interval error bars on Fig. 14. We clearly see a dependency of the trapping stiffness on the trapping power, the bead size and the fiber separation. A higher power leads to a stronger trap and larger beads experience larger optical forces compared to smaller ones. The graph shows a lower trapping stiffness in the chip than in the square capillary which means that the optical trap is weaker in the chip because of the larger fiber separation, as predicted by our model. However, we observe that the measured tranverse trapping stiffnesses are larger than the simulated values by an average factor of 1.8, which could be due to the underestimation of the trapping stiffness in our model. A further elaboration on the model could be for example realized by exporting the field that propagated from the fiber exit to the virtual plane in front of the bead from ASAP and use a full-wave method, such as the finite-difference time-domain (FDTD) method, to simulate the interaction of this field with the bead. However, this kind of simulations takes several hours and falls outside the scope of this paper. Our model is less accurate but it is a good tool to predict the optical trapping behavior in various situations.
Due to an unwanted low frequency drift of the bead we were not able to measure the axial trapping stiffness. Since the axial forces are weak, the expected corner frequency corresponding to these axial stiffnesses is situated below 2Hz and could not be properly fitted in this area. Nevertheless, we were able to demonstrate the trapping capabilities of the hot embossed chip and to characterize the trap strength in the transverse direction for beads with a diameter of 6µm, 8µm and 10µm in a square capillary and in the hot embossed lab-on-chip device.
We presented the design, simulation, fabrication process and proof-of-concept demonstration of a low-cost, robust PMMA chip for optical trapping of particles in an 80 µm wide microchannel. This chip was fabricated using a novel fabrication process that consists of a premilling step and ultraprecision diamond tooling for the manufacturing of the molds and double-sided hot embossing for replication. The chip is robust in the sense that in thin PMMA walls of 70µm no cracks were observed during the fabrication process and the proof-of-concept demonstration. This is due to the limited height of these walls (i.e. the overlap region between the microchannel and the fiber grooves). During the first hot embossing alignment steps we observed that even thinner walls (approximately 50µm) withstood this process, which means that there is still room for improvement and that a stronger optical trap could be realized within the chip. Our target is indeed to lower the fiber separation distance in the optical trapping chip in a future fabrication run. The PMMA chip is a low-cost device, since it is mass-manufacturable using a hot embossing replication process. The chip can be seen as a plug and play device with respect to fiber alignment and sample supply. The overlap of 115µm allows particles to be trapped at a height above the channel bottom where influences of the bottom surface are avoided. We showed the trapping capability of the hot embossed chip by trapping polystyrene beads with a diameter of 6µm, 8µm and 10µm. When manipulating biological samples, our device could also be used at other trapping wavelengths within the near-infrared region, such as 1064nm.
We were able to trap the polystyrene beads in the hot embossed chip and to characterize the trap strength in a square capillary and the hot embossed chip using the power spectrum analysis of the bead position fluctuations. We were able to trap these beads in the hot embossed chip and observed lower trapping stiffnesses than in the square microcapillary due to the larger fiber separation, as predicted by our model. We also saw a dependence of the trapping stiffness on the laser power and the bead size. We measured trapping stiffnesses of the same order of magnitude as the values predicted by our model. We can conclude that our model is a useful tool to describe the behavior of beads in the optical trap and to predict unstable behavior, the effect of misalignments and many more parameters. The dimensions of the microchannel and the fiber grooves were chosen as a compromise between the chip robustness and the trap strength. However, as mentioned above, the trap strength of the hot embossed optical trapping chip could be improved by designing a smaller notch length (i.e. the fiber separation in the chip) resulting in thinner PMMA walls between the microchannel and the fiber grooves. In this work, we demonstrated the possibility of using double-sided hot embossing to realize an on-chip optical trap with two single-mode fibers facing each other at both sides of the microchannel. This fabrication process could also be used to integrate microstructures in both excitation paths, which is an alternative method to enhance the strength of the optical trap by shaping the trapping laser beams. This research paves the way toward mass-manufacturable microfluidic polymer chips for dual fiber optical trapping.
The authors would like to thank Dries Rosseel and Kurt Rochlitz for their technical support in the fabrication of the molds, the hot embossing of the optical trapping chip and the Multisensor Coordinate Measurement Machine measurements on the molds. J. Van Erps acknowledges the financial support of the FWO Vlaanderen under a postdoctoral Research Fellowship. This work was supported in part by FWO ( G008413N), IWT, the MP1205 COST Action, BELSPO IAP Photonics@be, the Methusalem and Hercules foundations, Flanders Make, and the OZR of the Vrije Universiteit Brussel.
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