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Abstract
In-plane lenses are desired for light manipulation within on-chip platforms. Such an in-plane lens can be achieved through optofluidic lens technologies that provide tunability of optical parameters through alterations to the shape or size of the lens. However, passive optofluidic lenses are often more desirable than active optofluidic lenses. In this work, we design a passive mechanically-tuned optofluidic lens. Tunability is brought about by placing a microdroplet between two substrate plates and varying the plate separation. We carry out analyses with an experimental optical setup and theoretical ray tracing. The experimental optical setup makes use of a fluorescent dye filler fluid to assist in the visualization and measurement of the back focal length. Ultimately, the sensitivity of the back focal length to a change in plate separation is shown, with strong agreement between experimental and theoretical analyses. It is envisioned that such a mechanically-tuned optofluidic lens will be used in a myriad of in-plane optical applications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optofluidic systems are technologies that merge developments in photonics, e.g., spherical [1] and aspherical [2] lenses, with microfluidics, e.g., on-chip analytical devices requiring easy integration of focusing elements [3–7]. Traditional optofluidic systems manifest themselves as lab-on-a-chip devices, whereby microfluidic and photonic elements achieve respective actuation [8] and sensing [9] of microlitre and nanolitre volumes of biofluids.
Out of these traditional optofluidic systems has emerged a subset technology, being optofluidic lenses [10,11]. Optofluidic lenses make use of digital (i.e., droplet-based) microfluidic systems [12–14], whereby liquid interfaces of an individual microdroplet can be tuned, forming the microdroplet into a liquid lens with tunable optical parameters (e.g., back focal length [15,16]).
The tunability of optofluidic lenses is a tremendous advantage over fixed focal length (typically glass) lenses. As such, optofluidic lenses have found applications in various technologies requiring real-time diverging, collimating, and telecentric focusing of optical beams [17]. These applications include optical sensing and imaging [18], energy collection and control [19], interferometry [20], spectroscopy [21], and light manipulation for lab-on-a-chip integration [16,17]. For such light manipulation, there is particular interest directed towards in-plane optofluidic lenses [20,22–24], for integration with planar on-chip technologies (e.g., silicon photonic devices [25]).
During operation of in-plane optofluidic lenses, light is manipulated parallel to the plane of the substrate plate. This light manipulation can be brought about using several methods. For example, Lapsley et al. controlled the reflectivity of a fluid-polydimethylsiloxane interface by varying the refractive index of the fluid for optical attenuation [20] and Shi et al. achieved optofluidic tunability by controlling the curvature of an air-liquid interface through altering the liquid flow rate [26]. Other methods include hydrodynamic tuning [27], laser-induced thermal gradients [16], and electrostatic tuning methods, e.g., electrowetting [28] and dielectrophoresis [15,29]. Of these other methods, hydrodynamic tuning and thermal gradients succeed in avoiding high voltage (active electrical) operation. However, they still suffer from other challenges, being the need for complicated microfluidic elements, in the case of hydrodynamic tuning, and the need for a heating circuit, in the case of thermal gradients.
A particularly noteworthy example of in-plane optofluidic lenses, is the dielectrophoresis-actuated optofluidic lens of Chen et al. [30,31]. In this work, the authors formed a microfluidic channel using two parallel substrate plates, providing a closed system filled with silicone oil to create a curved (surrounding media and microdroplet lens) interface. This interface can then be altered with the application of an electric field across two electrodes, altering the back focal length of the in-plane optofluidic lens. The work of Chen et al. is useful for light manipulation in microfluidic networks. However, such electrostatic actuation has disadvantages such as the requirement for an electrode network, complex fabrication (metal deposition), and a limited ability for system scaling as the microdroplet volume is limited by electrode size and applied voltage [32].
In this work, we introduce a mechanically-tuned in-plane optofluidic lens that eliminates the need for electrodes, for simpler fabrication, improved scalability, enhanced tunability, and avoidance of high voltage operation [28,33]. (This in-plane operation is defined as in previous work on in-plane optofluidic lenses [22,23,30] and is orthogonal to out-of-plane operation, as in the Appendix of Prasad et al. [15].) The mechanically-tuned optofluidic lens allows the (surrounding media and microdroplet lens) interface to be manipulated by varying the separation between substrate plates. A representation of the introduced mechanically-tuned optofluidic lens is shown in Fig. 1. For a fixed volume, V = ¼ π hd2, of microdroplet fluid, the diameter, d (and therefore radius of curvature, r = d/2), of the optofluidic lens is made larger or shorter with a translation stage to achieve a (top view) long back focal length, as in Fig. 1(a), or a (top view) short back focal length, as in Fig. 1(b). (The back focal length is assumed to be infinite for the side view.) The plate separation, h, can be found to be h = 4Vπ−1d−2. Given the balancing of surface tension within the fluid, the mechanically-tuned optofluidic lens takes on an in-plane bi-convex lens configuration [24] (as opposed to an in-plane plano-convex lens configuration [30]). We carry out experimental and theoretical analyses to study the optical performance of the system.
Fig. 1. The mechanically-tuned optofluidic lens with (a) long and (b) short back focal length for respective large and short diameter operation.
To summarize, the novelty of our work lies in mechanically tuning of the optofluidic lens—without the need for components such as electrodes (for dielectrophoretic tuning), heating circuits (for thermal gradient tuning), and micropumps (for hydrodynamic tuning). Additionally, in-plane operation is highly sought after [20,22,25], and this in-plane operation is achieved through changing the radius of a cylindrical optofluidic lens (as opposed to changing the radius of a spherical optofluidic lens). This novelty is beyond the initial contributions of adaptive lenses based on liquid microdroplets [1,2].
2. Experimental setup and theoretical ray tracing model
In this section, we describe an experimental setup to test the optofluidic lens and perform theoretical analyses. Experimental and theoretical back focal length measurements are compared (in the next section) and found to be in close agreement.
2.1 Experimental optical setup
The aim of our experimental setup is to mechanically-tune the back focal length of an optofluidic lens, as well as to observe the effect of this lens on a collimated beam of light through a fluorescent dye filler fluid in which the mechanically-tuned optofluidic lens is submerged. This fluorescent dye filler fluid allows complete visualization of marginal rays.
To create the mechanically-tuned optofluidic lens, we dispense a microdroplet of fixed volume between two parallel substrate plates, ensuring that the microdroplet is in contact with both substrate plates. To mechanically-tune the back focal length, the radius of curvature of the microdroplet is altered by stretching the microdroplet vertically. The bottom substrate plate is fixed while the top substrate plate is controlled by a mechanized translation stage (mitigating the on-chip high voltage of other optofluidic lens systems [28]). As this top substrate plate is translated vertically, the microdroplet is stretched, and its diameter (and therefore radius of curvature) reduces due to the fixed volume of fluid. (For lab-on-a-chip applications [34,35], small-scale and compact micro-translation stages can be utilized [36] such as Newmark Microslide series with XY and Z Adapter Plates or the Physik Instrumente Compact Micro-Translation Stage.)
The tunable back focal length of the mechanically-tuned optofluidic lens is studied and quantified through interaction with a collimated beam of light. The microdroplet liquid, making up the optofluidic lens, is selected based on two important factors. First, the microdroplet liquid should be immiscible in the dye to allow an (approximately) ninety degree contact angle, which can be confirmed by visually inspecting the exiting beam in the side view plane. Second, the refractive indices of the microdroplet liquid and fluorescent dye filler fluid should be noticeably different, to allow significant refraction and optical focusing. Based on these two important factors, the microdroplet liquid is chosen to be (uncured) Norland Optical Adhesive 68 (NOA 68) (as used in the lens fabrication of Aksit et al. [37]) with refractive index of nlens = 1.54, and the surrounding dye is chosen to be rhodamine B (dissolved in water with concentration of 0.001 mol/L) with refractive index ndye = 1.33. There is minimal dispersion over visible wavelengths [38] and this is desirable for stable back focal lengths at operation over several wavelengths. A wavelength of 650 nm (power of 5 mW) is chosen for the collimated beam of light, as the corresponding photon energy of 1.91 eV is able to activate the fluorescent dye filler fluid, allowing a complete visualization of the focused beam. As the back focal length depends on refractive properties of the microdroplet and dye liquids, the intensity does not affect the back focal length of the lens. As the microdroplet liquid is NOA 68, it can polymerize when exposed to ultraviolet light. However, the filler fluid fluorescent dye of rhodamine B provides sufficient protection against such exposure to ultraviolet light. With the significant absorption of ultraviolet light in rhodamine B [39], the optofluidic lens is well protected from possible curing.
As was shown previously in Fig. 1, it is clear that as plate separation, h, is increased, the diameter, d, of the microdroplet reduces, and this reduced radius of curvature causes a shorter back focal length. Our experimental setup therefore enables us to mechanically-tune the back focal length of the optofluidic lens. With placement of an image sensor above the experimental setup, we can capture images of the light beam at different plate separations and study the back focal length tunability.
An isometric view schematic of the experimental optical setup is shown in Fig. 2. The isometric view schematic shows relevant fabrication labels (being the substrate plate (glass), fluorescent dye filler fluid (rhodamine B), and optofluidic lens), experimental labels (being the image sensor and vertical translation of one substrate plate), and dimension labels (being the substrate plate separation, h, and the optofluidic lens diameter, d).
2.2 Theoretical ray tracing model
To develop an analytical optical model of the optofluidic lens system, ray tracing is used. This is a valid approximation as the 650 nm wavelength of the light is significantly smaller, being three orders of magnitude, than the dimensions of the optofluidic lens. It is assumed that only uniform vertical stretching of the mechanically-tuned optofluidic lens takes place. As such, the analysis can be simplified by only considering the two applicable dimensions, i.e., the dimensions that are in-plane with the substrate plate. It should be noted that the assumption of uniform vertical stretching can be made as long as the optofluidic lens maintains its cylindrical shape while remaining in contact with both substrate plates. This cylindrical approximation is also valid given the (approximately) ninety-degree contact angle of the optofluidic lens and the substrate plate. For the experimental work, immiscible fluids were chosen as they were found to yield such a contact angle.
The microdroplet is modelled as a circle, and collimated input rays (with respect to an optical axis through the centre of the mechanically-tuned optofluidic lens) are considered. This is shown in Fig. 3 for paraxial and marginal rays with respect to the optical axis. The theoretical effective focal length of the paraxial ray, fEFL, can be found through
Fig. 3. Visualization of the ray tracing calculations showing the optofluidic lens, marginal ray, paraxial ray, optical axis, focal lengths, and Snell's Law angles. The dimensions are not-to-scale. The subscript acronyms are as follows: TPR is theoretical paraxial ray, TMR is theoretical marginal ray, and EFL is effective focal length.
To calculate the change in back focal length due to a change in plate separation, the new microdroplet diameter is calculated by fixing the volume and by varying the height between substrate plates, and ray tracing is carried out again to find the new back focal length.
It is worth noting that light rays further away from the optical axis (marginal rays) will be refracted at a slightly higher angle than light rays closer to the optical axis (paraxial rays) due to the difference in their incidence angles. This difference is accounted for by defining two different back focal lengths, being the theoretical back focal length of the marginal ray, fTMR, and the theoretical back focal length of the paraxial ray, fTPR. (The difference between these theoretical back focal lengths is the spherical aberration of the optofluidic lens.) In the case of the experimental optical setup, only the marginal back focal length can be determined, and so the experimental back focal length of the marginal ray, fEMR, is measured. The results collected from the experimental optical setup and the theoretical ray tracing model are summarized in the next section.
3. Results
Images are recorded of the collimated beam of light with beam dimension of 900 µm being focused through the optofluidic lens for varying substrate plate separations. From these images, the dimensions of the optofluidic lens and the experimental back focal length of the marginal ray are extracted. This is achieved by defining an optical axis through the centre of the optofluidic lens, and recording the back focal length as the point (corresponding to the minimum output beam waist) minus the point of the liquid interface. The minimum output beam width is considered before the marginal rays intersect (i.e., travel beyond the focal point), which is visible as an outward cone. This cone is present on either side of the focal point. In an image processing tool, the marginal rays (being the top and bottom rays of the 900 µm beam dimension) on either side of the focal point are extended and the intersection with the optical axis is found. The focal point is then considered to be the average of these values. The dimensions of the microdroplet are then used to seed the theoretical ray tracing model and find theoretical back focal lengths of the marginal and paraxial rays.
The comparison between experimental and theoretical back focal lengths of the marginal ray is shown in Fig. 4, where the top image in each subfigure shows the results from the experimental optical setup and the bottom image in each subfigure shows the results of the theoretical ray tracing model for the same microdroplet dimensions. From these figures it is clear that as plate separation is increased, microdroplet diameter and hence radius of curvature decreases, which in turn decreases the back focal length. The Fig. 4 results are measured up to an optofluidic lens plate separation of h = 2740 µm, as the optofluidic lens loses contact with the top substrate plate beyond this value. The Fig. 4 results are measured down to an optofluidic lens plate separation of h = 750 µm, as there was leakage of the beam below this value. It should be noted that we work within the millimeter size range due to the ease of experimentation in this size range. However, the results can be scaled down to much smaller sizes [15]. The substrate plate separation will scale down accordingly.
Fig. 4. Experimental and theoretical back focal length of the marginal ray measurements are shown for plate separation, h, being (a) 750 µm, (b) 1080 µm, (c) 1540 µm, and (d) 2740 µm. The collimated beam of light enters the mechanically-tuned optofluidic lens from the left and is focused.
The noise and saturation of the experimental images in Fig. 4 is due to internal reflections and residue within the overall microfluidic structure. However, this does not affect the assessment of the back focal length of the marginal ray. Additionally, the optofluidic lens is found to be very stable during experimentation. Specifically, the back focal length remains constant over long time periods. The authors attribute this to the avoidance of high voltage tuning, which can introduce jitter into the system [32], and due to the use of a filler fluid, which mitigates evaporation of the optofluidic lens [15]. The experiments were carried out within the time range of a few minutes. However, given the negligible evaporation of the closed system and the negligible curing, the optofluidic lens is expected to be stable over longer periods of time (days or weeks).
In Fig. 5, the experimental and theoretical back focal lengths for marginal and paraxial rays are plotted against plate separation. Several important conclusions can be made. First, the theoretical back focal length for the paraxial ray is higher than for the marginal ray. This is expected as this difference is the spherical aberration of the system. It should be noted that spherical aberration can be reduced by either using a smaller beam dimension or by modifying the optofluidic lens design to be elliptical (rather than circular) from the top view (and this is the subject of future research). Second, the experimental and theoretical back focal lengths for the marginal ray are in close agreement, validating the theoretical ray tracing model for any given plate separation. Third, the trend shows that as substrate plate separation is increased by approximately 260%, back focal length is reduced by 70%, indicating great tunability of the mechanically-tuned optofluidic lens. The experiments sufficiently demonstrate proper characterization, as a high R-squared value of 0.997 is found between fEMR and fTMR (i.e., high agreement between experiment and theory).
Fig. 5. Sensitivity of the mechanically-tuned optofluidic lens to a change in plate separation as characterised by back focal length vs. substrate plate separation for theoretical back focal length of the paraxial ray, fTPR (blue diamond symbols), theoretical back focal length of the marginal ray, fTMR (red triangle symbols), and experimental back focal length of the marginal ray, fEMR (green circle symbols). The subscript acronyms are as follows: TPR is theoretical paraxial ray, TMR is theoretical marginal ray, and EMR is experimental marginal ray.
As the back focal length depends on the radius of curvature of the microdroplet, it is expected that the optofluidic system can be scaled down to smaller dimensions if required, without affecting overall tunability. Based on these results, we can conclude that our optofluidic lens provides tremendous benefit for in-plane light manipulation applications.
4. Future work
Lens arrays are an important potential future work for these optofluidic lenses. An array of optofluidic lenses would be possible if care is taken to ensure they are all of uniform size and distance from each other. Additionally, with a hydrophobic liquid used as the droplet liquid, the top and bottom substrate can then be coated with hydrophobic coating in such a way that there is a small uncoated spot where each droplet makes contact with the substrate. This will ensure that the droplets do not move from their position as their height is varied. Another important area of future work is integration of optofluidic lenses with virtual reality, as adaptive focusing is particularly relevant for this application [41,42].
5. Conclusion
We presented a mechanically-tuned optofluidic lens and studied its focusing properties using an experimental optical setup and a theoretical ray tracing model. The results showed close agreement between experimental and theoretical analyses. Ultimately, the presented optofluidic lens was shown to offer significant tunability of back focal length for passive (avoiding high voltage electrical operation) in-plane light manipulation applications.
Funding
Natural Sciences and Engineering Research Council of Canada (NSERC) (04022).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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