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Optical detection in microflow cytometry requires a tightly focused light beam within a microfluidic channel for effective microparticle analysis. Integrated planar lenses have demonstrated this function, but their design is usually derived from the conventional spherical lens. Compact, efficient, integrated planar kinoform microlenses are proposed for use in microflow cytometry. A detailed design procedure is given and several designs are simulated. A paraxial kinoform lens integrated with a microfluidic channel was then fabricated in a silicate glass material system and characterized for focal position and spotsize, in comparison with light emerging directly from a channel waveguide. Focal spotsizes of 5.6 μm for kinoform lenses have been measured at foci as far as 56 μm into the microfluidic channel.
©2012 Optical Society of America
1. Introduction
Microfluidic chips are finding increasing use in the detection, sorting and analysis of biological cells, due to their small size, ability to handle small sample volumes, potential for mass-production and increased speed because of both reduced dimensions and local use at point-of-care [1]. Optical techniques such as scattering [2], fluorescence [3], and Raman spectroscopy [4] are commonly used for identification and characterization of cells, and optical forces may be used for trapping cells for analysis [4] or for sorting [5]. Integration of electrodes for dielectrophoretic control and analysis of cells are readily integrated with optical techniques [6] and can provide complementary information [7]. Flow cytometry is one of the most important applications of such microsystems and microflow cytometers may also find application to protein analysis based on surface-modified polymer microparticles [8]. The majority of these microsystems use external “bulk” optics [6], or inserted optical fibers [9, 10], for illumination and detection. Recent demonstrations of on-chip integration of optical devices to excite and collect scattering and fluorescence from cells and particles have opened up the prospect of improved sensitivity and selectivity and low-cost integration of an optical toolkit in the lab-on-a-chip to provide multiple optical functions. For example, sophisticated devices such as Arrayed Waveguide Grating multiplexers (AWGs) may be integrated on-chip offering the potential for sample spectroscopy [11] and multi-wavelength microflow cytometry [10]. A key component for manipulation of light in any system is the lens, and lenses integrated closely with microfluidic channels would provide high-resolution scattering angle data [12] and efficient fluorescence collection.
Several integrated lenses have recently been demonstrated for improved focusing or collimation in a microfluidic channel to enable enhanced fluorescence or scattering detection. Lenses located external to the microflow channel are preferred as they do not interfere with microfluidic flow. Most examples have been fabricated in polymers using simple one-step photolithography, molding or stamping, where the optical alignment with microfluidic channels is achieved at fabrication. Camou et al. and Hsiung et al. [13, 14] integrated molded in-plane lenses with microfluidic channels to focus from the end of optical fibers inserted in separate channels for illumination and collection, in PDMS and PMMA respectively. Barat et al. [9] recently demonstrated a microflow cytometer by direct photolithography in SU-8 with an integrated lens and multimode excitation/collection fibers. Seo and Lee integrated molded microchannels and compound in-plane lenses for direct (fiberless) lens-coupling in PDMS fabricated in a single step process [15]. Reconfigurable lenses made from lens-shaped chambers connected by microfluidic channels may be tuned by changing the refractive index of the fluid in them [16] or, alternatively, the pressure of the fluid which modifies the lens shape for elastic polymers [17].
The integration of waveguides to guide light to and from the channel can achieve lower on-chip losses, avoids the insertion of multiple separate optical fibers and allows other operations such as on-chip spectroscopy [11] to be performed. Wang et al. [18] demonstrated a device consisting of SU-8 waveguides and microchannel and a single circular focusing lens protruding into the microfluidic channel wall for scattering and extinction measurements of microparticles. Although the channel wall was perturbed by the lens, the perturbation was minimal for the 0.6 mm wide microchannel. Rosenauer et al. [19] recently demonstrated a miniaturized flow cytometer with 3D hydrodynamic focusing and integrated waveguides and lens in SU-8 resist. For high-volume production, conventional microelectronic production techniques in “hard” materials such as silicon and glass may be an attractive route for integrated optofluidics. Recently we demonstrated a multimode interference device (MMI) for focusing in a microfluidic channel, employing a silica-based microfluidic channel with integrated germania-doped waveguiding plane [20]. More conventional in-plane lenses remain attractive in this technology due to greater design flexibility but diffraction and scattering losses, which are strongly dependent on the lens configuration and waveguide design, must be carefully considered.
In this paper we propose an optimized design procedure for compact integrated kinoform microlenses for microflow cytometers and demonstrate their numerical simulation, fabrication and performance in a silica/germania-based optofluidic technology, to exemplify a key component of the integrated optical toolkit for the lab-on-a-chip.
2. Kinoform theory
The kinoform was developed from the Fresnel lens for focusing coherent radiation with high-efficiency at a single focal point [21, 22]. Like Fresnel lenses, kinoforms offer greatly reduced thickness when compared with a simple refractive lens, making them ideal for miniaturization of integrated devices incorporating planar waveguide lenses. The kinoform can be viewed as a phase hologram or, in the collimating case, as a blazed Fresnel zone plate (FZP). Kinoform operation is dependent on both diffraction and refraction and applies to coherent light so that its zones and thicknesses are precisely defined quantitatively and are dependent on the design wavelength.
An analytical method for the design of planar waveguide kinoform lenses using geometrical optics is given in this section. Fermat's principle is used to define the profile of the kinoform and show the relation to the FZP zones and then the relationship of this design to a simpler paraxial design familiar in the literature [21, 22] is described.
2.1 The kinoform lens profile
Figure 1 shows a geometrical model of a positive kinoform lens profile focusing a plane wave to a point, with the lens region having an effective refractive index, nl , and the surrounding medium having an effective refractive index, ne. The effective wavelengths in these two regions are denoted by λl and λe respectively. The analysis and design of the finite thickness kinoform profile for this positive lens, where nl > ne , has been presented in the literature [21–23]. However, the analysis of a negative kinoform, where nl < ne , which may be useful in integrated optics where the lens can be etched out of a planar waveguide to produce regions of lower effective index, has not been described. The derivation of the positive and negative kinoform profiles using Fermat's principle and their paraxial approximation is given based on an approach similar to that of Moreno et al. [21]. The derivation shows that the profile for the kinoform is made of segments of hyperbolas for positive lenses and ellipses for negative lenses and describes how this profile shape is dependent on the refractive index ratio between the lens and the surrounding medium.
Fig. 1 Illustration of a kinoform in Cartesian coordinates with rays in a zone focusing to a point; nl and ne are the effective indices of the lens and the surrounding medium, respectively.
To derive the kinoform profile using Fermat's principle, the optical path length for diffraction from zone m, represented by BP, and that from refraction within the zones, represented by AP, must be equal so that light in the plane wave incident from the left constructively interferes at point P at a distance d from the lens vertex. This may be written:
With the substitutions n = nl /ne and dr = d + mλe and after some manipulation [24] an equation for a hyperbola is obtainedDividing through by {(nd - dr)/(n2 - 1)}2 and rearranging, the equation can be stated in standard form as a shifted hyperbola in the z-axis with an eccentricity given by the refractive index ratio, n. A similar procedure with the assumption that n2-1 is negative shows that Eq. (1) can also result in a shifted ellipse. Stated more generally
where ζ = sgn(nl - ne), resulting in a hyperbolic function for a positive lens with ζ = 1 and an elliptical function for a negative lens with ζ = −1. The hyperbolic expressions for z0, a, and b for each zone, m, are those given by Moreno et al. [21] while those for an ellipse, not given in the literature, areEquation (3) describes a family of curves, one curve for each zone, which may be for either a positive lens which produces a family of hyperbolas or for a negative lens, which produces a family of ellipses. A kinoform profile is then determined by introducing a line parallel to the x-axis intersecting the curves to define a lens boundary.
McGaugh et al. [23] designed and simulated positive hyperbola kinoforms by introducing a line that crosses the hyperbolas behind the vertex as shown in Fig. 2(a) . The partitioning of the hyperbolas between each zone is then driven by the design of lens thickness. McGaugh et al. chose the plane lens boundary to be the same distance from the vertex as in the case of the standard paraxial kinoform. Here, we choose to partition the hyperbolas by arranging the beginnings of all zone segments to be at the plane of the vertex, as shown in Fig. 2(b), by setting zm(xm) = 0. Rearranging Eq. (3) for a hyperbola and substituting for zm(xm), for each zone, m, and using Eqs. (7) and (8), the square of the position along the x-axis of each zone boundary becomes
Fig. 2 The hyperbola and ellipse curve families and their segmentation into kinoform zones. The schemes used are by McGaugh et al. [23] for hyperbolas (a) and ellipses (c) and the scheme proposed here, with the intersecting line positioned on the vertex for hyperbolas (b) and ellipses (d) giving the familiar zone boundaries in the literature.
This is the familiar zone formula encountered in the literature [22] for a non-paraxial kinoform. The advantage of this approach is that the expression for the zone boundaries is simpler than with McGaugh et al.'s method [23] as all zone boundaries start at the vertex line. The elliptical kinoform lenses lend themselves to be thinner in the central zones than the equivalent McGaugh lenses. The McGaugh procedure to divide the kinoform zone segments and our procedure both also apply to elliptical kinoforms, as shown in Fig. 2(c) and 2(d), respectively.
The designer must decide how many zones should be included in the lens design. There is a maximum aperture that the kinoform can take due to the geometrical definition of hyperbolas and ellipses, which is clearly evident in Eq. (3), for a hyperbola ahyper > 0 and for an ellipse z0;ellip ≥ 0. Hence the maximum number of zones, M, for real hyperbolic and elliptical lenses, respectively, is
General analytical expressions have been derived from geometrical optics for kinoform profiles designed to focus a plane wave to a focus point, and a full design procedure for optimized positive and negative kinoform lenses has resulted. Two principal types have been identified, the “conventional” kinoforms and the McGaugh kinoforms.
2.2 The paraxial kinoform lens profile
The general derivation for the kinoform given in Section 2.1 yields a complex expression. In this section, a simpler expression for a kinoform profile is derived using the paraxial approximation to the non-paraxial kinoform profile derived above. The paraxial approximation is valid if, say, the F number of the lens is kept below 5 so that the maximum angle of acceptance is then only ~6°.
To find the paraxial kinoform profile needed for the collimating operation we rearrange the kinoform profile, Eq. (3), to
Taking the Taylor series of the square root, substituting from Eqs. (4) – (6) or Eqs. (7) – (9) and following Moreno et al. [21], with the approximations (1/b)2 << 1 and b2/a ≈d(n - 1) as λe << d in the paraxial regime, leads to a general equation It can be seen that the paraxial kinoform is described by one parabolic profile shifted at each zone boundary so that it is contained within a total thickness given by zmax determined by the freespace wavelength and where ζ is the signum function resulting in a positive lens with ζ = 1 and a negative lens with ζ = −1, as employed in Eq. (3).The efficiency of diffraction of light by kinoform lenses into the desired focal spot as a function of wavelength and in the presence of design tolerances is of critical importance in their design and is well-described using Fourier optics [25]. The phase change suffered by a plane wave passing through a kinoform lens is given by
Use of the paraxial lens design leads to straightforward analysis of diffraction efficiency and is sufficiently accurate for this application, so using Eq. (14) we obtain
where λ0 is the design wavelength, λ′0 is the actual operating wavelength, nl′ and ne′ are the actual effective refractive indices of the lens region and surrounding medium, respectively, and α is the resulting design mismatch ratio between the actual lens and the designed lens. The transmission function (or aperture function) t is the wave emerging from the lens. Since the function is periodic, the Fourier series gives a transmission function with diffraction orders q,Substituting ξ = x2/2λe d, for simplicity, the coefficients are calculated asThe diffraction efficiency is given byEquation (23) describes the chromatic behavior of the paraxial kinoform lens, from which it is clear that a kinoform can diffract with 100% efficiency into any diffraction order depending on the values of α and q. In this application only the first order is of interest and the objective is to achieve ςq as close to unity as possible so as to not diffract power into higher orders. When calculating the diffraction efficiency of a kinoform, Fresnel diffraction is used to establish the use of Fourier analysis in optical problems [25] and this derivation of the standard Fourier optics inherits the paraxial approximation. Rigorous electromagnetic theory is normally used to calculate diffraction efficiency in a nonparaxial optical system. However, Harvey et al. [26] have developed a non-paraxial scalar Fourier transform theory of diffraction. This allows more accurate estimation of the non-paraxial kinoform's diffraction efficiency. It is expected that in the paraxial regime, the diffraction efficiency calculated rigorously will be close to the paraxial solution given by Eq. (23).3. Kinoform microlens simulation
The analytical design of kinoform lenses to focus the maximum proportion of collimated light into a first order was described in Section 2. Numerical simulations are required to determine the distributions of the focused light from a lens illuminated from a waveguide end, to model spotsize in the microfluidic channel, and to calculate efficiency in the presence of diffractive losses in the lens. To image the end of a channel waveguide into the centre of a microfluidic channel the beam must be collimated and re-focused. To achieve this, two identical kinoform lenses as described in Section 2 may be placed back to back, as illustrated in Fig. 3 .
Fig. 3 Comparison of differing profiles of negative lenses designed. The colored areas indicate regions of lower refractive index compared to surroundings.
For a weakly guiding waveguide system, compatible with optical fiber input/output connection, it is expected that the kinoform lens structure will need to be etched completely through the guiding layer to give sufficient index contrast between the lens region and surrounding medium to achieve a lens with a practical numerical aperture. In this case, light will not be guided in the etched regions, causing diffractive losses. A negative lens design is therefore preferred as only the relatively small lens region is unguiding, leading to lower losses. This then narrows the selection to elliptical lens designs. There is a clear trade-off between refractive index contrast, n, that would allow for thinner lenses and higher collection efficiency from apertures; and lower refractive index contrast allowing designs to have larger dimensions increasing the photolithographic fabrication tolerances.
To determine comparative performance, the elliptical refractive, elliptical kinoform, paraxial kinoform, and McGaugh kinoform lenses shown in Fig. 3 were chosen for simulation. The lens profiles shown are all analytical solutions to the problem of imaging a focused spot into the middle of a microfluidic channel, but it is the ease of fabrication and the efficiency that determine the final choice of lens design. Figure 3 shows the profiles of kinoform lenses having 26 zones as this is the maximum possible for the elliptical kinoform lens (see Eq. (12)). It is clear that the paraxial kinoform is the thinnest, taking least space and likely to suffer lowest diffractive losses. The figure of merit chosen for the simulations is the power coupling efficiency for launching into waveguide mode at any point of interest along the axis of the device, given by the square of the overlap integral
where φ(x,0) is the launch electric field distribution or channel waveguide fundamental mode profile, φ(x,z) is the electric field distribution at any position z along the z-axis at which the efficiency is to be evaluated, η is a dimensionless figure of merit which describes the efficiency of focusing into an identical waveguide mode. The spotsize may also be estimated at positions close to the focus where the field distribution is approximately Gaussian.The beam propagation method (BPM) was used for simulations employing the commercial package BeamPROP. The 3D problem was transformed to 2D prior to simulation using the effective refractive indices of the slab and lens regions, to reduce computational complexity and hence run time and computer memory. The transformation was performed for a wavelength of 633 nm using a refractive index of 1.474 and a thickness of 1.9 µm for the guiding film and a substrate index of 1.458. This yielded an effective refractive index of 1.469, representative of the material system used experimentally in Section 4.
3.1 Focusing performance in a slab waveguide
First, simulations for all the lens profiles shown in Fig. 3 were performed on a monomode slab waveguide structure excited by a monomode channel waveguide and containing no microfluidic channel, as shown in Fig. 4(a) . f1 is the distance from the face of the input waveguide to the vertex of the lens. Figure 4(b) gives an example 2D simulation of the field strength in the lens and slab waveguide sections in the case of the paraxial kinoform lens. It is clear that in this case the lens focusses well into the first order but that there is some stray light which will result in non-unity efficiency.
Fig. 4 (a) Model lens layout in a slab waveguide and (b) example simulation of an elliptical kinoform lens.
The lenses were designed with object plane and image plane at ± 2000 µm from the vertex. This value was chosen so that the F number was ~5, satisfying the condition for paraxial operation, and to be greater than the Rayleigh range for the geometrical optics derivation to be valid. The kinoform lenses all consist of 26 zones as this is the maximum possible for the elliptical kinoform lens as given by Eq. (12). Keeping the lens design constant, the maximum efficiency of focusing in the slab, η, was acquired over a range of f1 from 1700 to 2400 µm. The efficiency was evaluated close to the design focal position at 2000 µm from the lens vertex (at 4000 µm on Fig. 4b), but the exact focal position on the z-axis was varied in order to maximize η. Figure 5 shows the maximum simulated coupling efficiency versus f1 for 2 µm wide channel waveguides. The elliptical refractive lens shows poor performance for the waveguide-waveguide imaging operation compared to the kinoform lenses. The kinoforms perform better in simulations because diffraction (in the x-axis) in the unguided lens region is lower in the kinoforms than in the elliptical refractive lens. This causes less deviation of the phase front from a plane wave in the light reaching the second boundary. Over the range of the simulation, the efficiency curve for the McGaugh lens is flatter than for the other lenses, implying high tolerance to changes in f1. However, in these simulations the paraxial kinoform shows the greatest efficiency because it is the thinnest.
3.2 Focusing into a microfluidic channel
The structure shown in Fig. 6(a) , which includes a microfluidic channel, was then simulated using the BPM model for the three remaining lenses: the elliptical kinoform, paraxial kinoform, and McGaugh kinoform, all having 26 zones. This model includes an additional distance f2, defined as the distance from the lens vertex to the middle of the microfluidic channel. The efficiency is again calculated in terms of the overlap with a waveguide mode field, this time placed in the center of a 20 µm wide microfluidic channel. Figures 6 (b), 6(c), and 6(d) show contour plots of the efficiency versus f1 and f2 with excitation from a 2 µm wide input channel waveguide. Varying f2 simulates the effect of inaccuracies in positioning the microfluidic channel with respect to the lens. The paraxial lens shows a less flat response than the McGaugh lens. However, its efficiency is the highest over a range in f2 of about 300 µm, well within photolithographic alignment tolerances. These simulations confirm that the paraxial kinoform lens is most suitable for fabrication as it shows the highest efficiency in the simulations, and so it was selected for fabrication.
Fig. 6 (a) Simulation layout; efficiency for the (b) paraxial, (c) elliptical, and (d) McGaugh lenses, vs. f1 and f2.
3.3 Tolerance of the paraxial kinoform lens
Simulations of the paraxial kinoform lens were performed to explore fabrication tolerances further. The lengths f1 and f2 were both fixed at 2010 as this was the highest efficiency configuration near 2000 µm shown in Fig. 6(b). Figure 7(a) shows the effect upon the efficiency, for focusing at the center of a 20 µm wide channel, of a deviation in the effective index, neff, of the slab waveguide from the design value of 1.469. It can be seen that an increase in neff can increase the efficiency, which peaks at 64% for an neff of 1.4705. It is estimated that a fabrication error in the slab waveguide core thickness of ± 5% would result in an error in Neff of less than ± 0.0005, and a consequent drop in efficiency of less than 3%.
Fig. 7 (a) Efficiency vs. effective index of the slab region in a paraxial kinoform lens and (b) efficiency vs. microfluidic channel width.
The spotsize in the middle of the channel is an important measure of device performance. The spotsize of the launch field is 1.25 µm and the lens re-focuses this to a spotsize of 2.05 µm at the center of the microfluidic channel, for f1 = f2 = 2010 µm and neff = 1.469. Lens efficiency was studied with changing microfluidic channel width to determine whether a fixed lens design can be used for a range of channel widths. The efficiency was calculated as a function of channel width for several values of the focal distance f1 (with f2 being equal to f1), and with the focal spot in the center of the channel. Figure 7(b) shows that for focal distances of 2000 µm and 2010 µm the lens efficiency differs by a only few percent as the microfluidic channel width is increased from 20 to 200 µm. This potentially allows for scaling of the microfluidic channel width without change in the optical component designs.
The paraxial lens was chosen for fabrication as simulations have shown it to be the most efficient and because the fabrication tolerances are not significantly more stringent than for the other lenses. It was not expected that the paraxial lens would prove to be the most efficient when simulated, and there are two limitations in the analytical design approach which may have led to this. First, the analytical model does not take into account the effect of the diffraction of a plane wave in the lens itself, leading to errors on the second lens boundary through which the light passes. Second, the analytical model is based on the approximation that the lens receives a spherical wavefront at its input lens boundary. Third, the good performance of the paraxial kinoform lens in numerical simulations could be due to it being the thinnest of the lenses and the paraxial approximations being adequate in practice. To improve the design approach, a more detailed analytical model could be developed with better or fewer approximations, including the effects of diffraction. Another option would be to run the BPM with numerical optimization methods, such as spline or genetic algorithms, which could improve the design and simulated performance.
4. Kinoform microlens and microfluidic channel fabrication
Paraxial kinoforms integrated with microfluidic channels were realized on silica chips using standard planar fabrication processes. A 1.9 µm thick film of SiO2:GeO2 (75:25 wt %) was RF sputtered onto a fused silica substrate. The SiO2:GeO2 film had a refractive index of 1.474 and the substrate 1.458, measured by prism coupling and ellipsometry at a wavelength of 633 nm. Conventional photolithography was used to pattern the channel waveguides and paraxial kinoforms [27–29], and argon ion milling was used to etch the patterns to a depth of 1.9 µm into the film.
Figure 8 is an optical microscope image showing a typical paraxial kinoform lens etched into the waveguide layer before the cladding was deposited. The central zones on the lens are well defined but the outer zones, were not transferred perfectly because of resolution limits of photolithography. An evident effect is a gap along the center of the lens which increases in width from the central zones to the outer zones. The cross-sections of the experimentally realized channel waveguides are not rectangular but quasi-trapezoidal, due to the ion-beam milling process. The top and bottom widths of all the input channel waveguides were 2.6 µm and 5.3 µm, respectively. A 4 µm thick cladding of silica was RF sputtered on top of the etched waveguides and lenses. Conventional photolithography and Ar ion milling was then used to etch a microfluidic channel of depth 9 µm and width 100 µm, centered at the designed focal position of the lenses. Finally, to seal the microfluidic channel, a glass coverslip was affixed to the top of the device using adhesive. For the purposes of comparison, channel waveguides without lenses, crossing the same microfluidic channel, were also included in the design.
The thickness of the paraxial kinoform lens should be constant, as derived in Eq. (14), but it is clear from Fig. 8 that the experimental lens thickness is tapered, decreasing from the central zones to the outer zones. This tapering appears on the e-beam mask and is due to the finite resolution of the e-beam mask-writing process, meaning that the pattern does not replicate the paraxial kinoform lens design exactly. Since most of the light diverging from the channel waveguide into the slab region is contained in the centre of the beam, the well defined central zones are expected to focus the light to a small enough spotsize to demonstrate the correct functioning of the lens.
5. Lens characterisation
Before etching the microfluidic channels into the devices, images of waveguided light scattering from the kinoform lenses were taken to observe their focusing function. Light from a 633nm laser was coupled into an input channel waveguide using a monomode fiber and a polarization controller, and scattered light was observed from the lens region using a CCD camera with a × 10 objective lens. Figure 9 shows a representative example of a raw image made from stitching part images taken of the scattering from the top of a paraxial kinoform lens. Figure 9(a) shows, from the left, TE polarized light entering the slab waveguide region from a channel waveguide and the beam diverging up to the lens 2 mm away. Once at the lens, the light interacts with the lens and focuses to the first order focal point 2 mm beyond it. A second focus can be observed 1 mm beyond the lens and this is believed to be light focused into the second order. Figure 9(b) shows the same lens but with TM polarized light entering from the left. Again, the first order focal point 2 mm from the lens and a second focal point 1 mm from the lens are observed. When measuring the spotsizes at the first order focal point from these images, the spotsizes of TE and TM polarizations differed by 0.1% within the error of the measurement meaning polarization dependence could be considered negligible. The images resemble the simulation image shown in Fig. 4(b), except that non-idealities in the experimental device causes light to be scattered away from the first order focus, which will cause a loss in device transmission.
Fig. 9 Scattering images of a paraxial kinoform lens stitched together for the (a) TE polarization and (b) TM polarization.
The kinoform lenses have been shown to focus in the slab waveguides from which they are constructed. The purpose of this work is to focus light into a microfluidic channel which is etched through the slab waveguide region. Focusing of the beam in the microfluidic channel was then characterized by inserting a fluorescing solution into the channel. Fluorescence in the microfluidic channel was achieved by using Cy 5.5 fluorophore which absorbs the excitation light from the HeNe at 633 nm and emits at approximately 700 nm.
An aqueous solution of 50 µM Cy 5.5 dye was prepared for filling the channels. A coverslip, 160 ± 10 µm thick, was cut to size and fixed onto the chip, to cover the microfluidic channel, with UV-curing adhesive. The dye solution was then placed in one of the reservoirs at the ends of the channels and flowed to the other reservoir through capillary action, filling the channel. The same apparatus as that used to measure scattering was used for the imaging of fluorescence in the channel, except that a × 20 microscope objective lens was used for imaging and a short wavelength cutoff filter was used to block scattered excitation light at 633 nm but pass fluorescent light at wavelengths beyond 675nm.
Figure 10 shows representative fluorescence images taken of the microfluidic channel for a channel waveguide and a paraxial negative elliptical kinoform lens. The left column shows the cropped original fluorescence images as collected by the camera through the filter. The images in the right column are of Gaussian fits in the x-axis for each element in the z-axis. The black dashed line shows the best fit for the Gaussian beam equation parameters, namely, beam waist (spotsize at focus) ω0, the Rayleigh range zR (as a measure of depth of focus) and the distance focused into the microfluidic channel zc. The results for the measurements of several devices are tabulated in Table 1 , with the tolerances representing the standard deviation of the measured values over all the measured devices.
Fig. 10 Fluorescent images of microfluidic channels for (a) a channel waveguide and (c) a negative elliptical kinoform lens with the Gaussian beam best fits (b) and (d), respectively.
Table 1. Gaussian Beam Parameters for Fluorescence Images in the Microfluidic Channel for a Channel Waveguide and Paraxial Kinoform Lens
Table 1 shows that, in contrast to the diverging beam emerging from the waveguide end, the paraxial kinoform lens focuses the light from a channel waveguide close to the center of the microfluidic channel, although the error in measured focal position is high due to measurement error in positioning the true edge of the microfluidic channel and small variations due to fabrication tolerances. The spotsize of the focus from the kinoform lens is more than twice that predicted by simulation. However, the measured spotsize of the beam emerging from the channel waveguide, equivalent to the launch field for the lens, is also more than twice that simulated, due to broadening of the fabricated waveguide in photolithography. These deviations from the design are mostly due to the limitations of the analytical design and fabrication tolerances. Limitations on the analytical design could be corrected or improved by altering the profiles using optimization algorithms with the simulations and fabrication tolerances improved to achieve better performance from the kinoform lenses.
6. Conclusion
Optical detection in microflow cytometry requires a small focused light beam within a microfluidic channel for particle analysis. Integrated planar lenses have demonstrated this function, but their design is usually derived from the conventional spherical lens. More compact, efficient, integrated planar kinoform microlenses have been studies here for use in microflow cytometry. Kinoform lenses can be used on an optofluidic chip to focus a beam into a small focal spot in the middle of a microfluidic channel, by imaging the end of a channel waveguide. An improvement on Fresnel zone plate diffraction efficiency can be achieved by employing a kinoform profile which is essentially a blazing necessary to concentrate the power into one focused order. This kinoform lens has a theoretical efficiency of 100%, but is limited by the analytical model used to design it and, of course, fabrication tolerances and imperfections.
The elliptical refractive lens, the elliptical McGaugh kinoform lens, the elliptical kinoform lens, and the paraxial kinoform lens were all designed analytically and then simulated by BPM. Due to limitations in the analytical methods used for lens design the paraxial kinoform lens was found to be the most efficient at imaging the end of a channel waveguide. This paraxial lens was further simulated to model performance for focusing into the middle of a microfluidic channel, and the lens design generated was predicted to focus the end of a waveguide to a spotsize of 2.05 µm in the middle of a 20 µm microfluidic channel with an efficiency of 60%. The same lens design was found to be capable of focusing into the middle of microfluidic channels of width from 20 µm to 200 µm with a very small variation in efficiency.
Experimentally-realized paraxial kinoform lenses in a germania-doped silica waveguide system were found to focus close to the center of a 100 µm wide microfluidic channel, with a spotsize of 5.6 µm, when excited by an input waveguide with 2.5 µm spotsize. Further improvements in fabrication processes are expected to achieve smaller spotsizes, rendering these compact and efficient devices invaluable for on-chip microflow cytometry.
Acknowledgments
We would like to thank Dr. P. Hua for preparation of the Cy 5.5 solution and the UK Engineering and Physical Science Research Council for a studentship (HCH).
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