We report on the development of an opto-fluidic waveguide coupling mechanism for planar solar concentration. This mechanism is self-adaptive and light-responsive to efficiently maintain waveguide coupling and concentration independent of incoming light’s direction. Vapor bubbles are generated inside a planar, liquid waveguide using infrared light on an infrared absorbing glass. Visible light focused onto the bubble is then reflected by total internal reflection (TIR) at the liquid-gas interface and coupled into the waveguide. Vapor bubbles inside the liquid are trapped by a thermal effect and are shown to self-track the location of the infrared focus. Experimentally we show an optical to optical waveguide coupling efficiency of 40% using laser light through a single commercial lens. Optical simulations indicate that coupling efficiency > 90% is possible with custom optics.
© 2012 Optical Society of America
State of the art solar concentrators use a combination of imaging and non-imaging optics to concentrate sunlight . Mechanical actuators track the sun’s position to keep the concentrated light on a small high efficiency solar cell [2, 3]. Solar concentration today is limited to solar farms due to the large size of mechanical actuators and panels. Since the demonstration of the luminescent concentrator in 1978 , a new class of planar self-tracking concentrators has emerged recently. Using a light induced refractive index increase at the focus of a concentrating lens, Baker  recently proposed a planar self-tracking concentrator, extending the work proposed by Karp  based on fixed prism couplers positioned at the focus of the concentrator. Schmaelzle  presents a concentrator using a hydrogel that phase-changes to a diffuse, reflective state above a threshold temperature thus coupling the diffused light in a liquid waveguide. These self-tracking systems are not capable of full diurnal tracking with high efficiency, but instead aim to reduce the complexity of their associated tracking systems by self-tracking over a limited range. Luminescent  and Holographic  solar concentrators both perform a form of self-tracking by coupling sunlight into a waveguide. However these systems have drawbacks such as low concentration ratio (2 – 4x for a holographic concentrator) and low concentration efficiencies (η ≤ 7% for luminescent concentrators, even though new developments might increase this [9, 10]). In 2010 Teledyne Scientific & Imaging started a project on the development of an optofluidic concentrator. They aim to use an array of liquid prisms and electrowetting to refract the incoming light onto a focusing fresnel lens . Another fluidic approach for a one axis passive solar tracking is used commercially whereby a liquid is moved side to side due to differential heating by the sun .
In this paper we propose and demonstrate the key features of a self-tracking waveguide coupling mechanism for planar concentration. The proposed concentrator uses an opto-fluidic approach (similar in function to ) that provides a self-adaptive, light responsive mechanism to couple light into a planar waveguide and guide it towards the edges (see Fig. 1). The concentrator makes use of the energy present in the infrared portion of the solar spectrum to create vapor bubbles in a liquid waveguide as Fig. 1 illustrates. The vapor bubbles act as a micro reflector due to the change in refractive index at the liquid-gas interface from which light is reflected by TIR (Fig. 1(b)). By focusing the light onto an infrared absorber material a heat gradient is generated inside the liquid. Due to the negative temperature coefficient of the surface tension of most liquids and the systems tendency to minimize its overall energy, a flow is generated inside the liquid that traps the vapor bubble at the hotspot . An axicon is aligned with the optical axis of the focusing lens to generate a ring at the bubble for the purpose of restricting the concentrated light to the reflective area on the bubble. A fraction of the light reflected at the liquid/vapor bubble interface is coupled within the waveguide by TIR.
2. Coupling efficiency
The coupling efficiency is here defined as the ratio of output power collected at the edges of the waveguide to the input power at the aperture of the collecting lens for a single lens element. Losses due to Fresnel reflections and absorption are not taken into account. Karp et al. modeled a complete planar system (i.e. multiple lenses simultaneously coupled into a waveguide) and showed that 82% efficiency is possible with concentration up to 300x using the basic geometry  and up to 85% efficiency at 900x if additional concentration is included . Baker et al. proposed a self-tracking mechanism for the planar microoptic concentrator based on an induced change of refractive index in the cladding material of a colloidal suspension . While the simulations estimate an efficiency of 80% at 230x concentration, waveguide coupling using this mechanism has not yet been demonstrated. These values take into account outcoupling from secondary interactions with neighboring coupling elements, Fresnel reflections and absorption in the waveguide. Although we have not optimized and modeled the performance of a complete multi-lens system in this paper, we expect that an optimized system using our proposed self-tracking mechanism will approach these values, and have similar performance trade-offs to those described in the above references.
From Fig. 1, it is straightforward to note that the efficiency depends on the F/# of the focusing lens, the axicon angle and the ratio of the beam size to the bubble size. Simulations of the coupling efficiency as a function of these scale invariant parameters were obtained using a ray-tracing design software (Zemax) assuming collimated input solar light with divergence of ±0.25° and normal incidence on the focusing lens (aberration-free paraxial lens). The graphs in Fig. 2 show a volume of the parameter space for which the coupling efficiency is higher than the indicated efficiency value. In Fig. 2(a) the triangle indicates the parameters used in the experimental setup described in section 3, with its values indicated as black spots on the xy, yz and xz axes.
Figure 2(a) shows a volumetric parameter space yielding a coupling efficiency higher than 50%, while Fig. 2(b) shows the parameter space for efficiencies higher than 90%. For example, the point F/# = 7.5, α = 3.3° and DBeam/DBubble = 1.7 can yield 100% efficiency (shown by small triangle and inset in Fig. 2(b)). The scale of the concentrator system (focal length and lens size) can then be chosen to satisfy other system design constraints such as power levels to create a bubble, panel size and concentration. The results of the simulations show that for 50% efficiency a solution exists for any axicon angle > 1.5° but that either the f-number or the DBeam/DBubble ratio is constraining the solution space. As can be seen in Fig. 2(b) the solution space for > 90% efficiency is significantly smaller. While a large range of lens F/# is possible, only large axicon angles and low values of concentration parameter DBeam/DBubble will yield high efficiency.
The coupling efficiency simulation in Fig. 2 is performed for an on-axis illumination. In order to quantify the effect of off-axis illumination on the coupling efficiency, simulations have been conducted using the optimal parameters obtained from Fig. 2(b). Figure 3 compares the coupling efficiency as a function of the light’s incident angle on the lens-axicon, for an ideal, aberration free lens and the aspherized, achromatic lens used in the experiments (f= 15 mm, F/1.18). The results show a high coupling efficiency (> 80%) over an angular range of 28 degrees (±14°) in case of the ideal lens and 24 degrees (±12°) in case of the real lens. The drop in coupling efficiency is due to the increase in both focal ring diameter and thickness and the stronger aberrations present in off-axis illumination. Figure 3 shows the behavior of the coupling efficiency over a 48 degree (±24°) range which is approximately the seasonal angular variation of the sun. The simulation assumes an optimal position of the bubble, which is the center of the ring for small angles but more difficult to predict as the ring elongates beyond the bubble size at large angles. To account for our imprecise knowledge of the trapped bubbles location in simulation, the orange and grey lines describe the coupling efficiency at a 0.1 mm lateral displacement from this position for the two lenses respectively. Since the two lines do not vary significantly over the whole angular range, the simulation appears to hold true even considering variations in the bubble position which would likely occur due to variations in the energy distribution of the ring spot.
3. Experimental demonstration of vapor bubble generation and waveguide coupling
Based on the simulations described above, an off-the-shelf axicon-lens pair was chosen that enables a reasonable coupling efficiency and also satisfies the power constraint for the generation and tracking of a vapor bubble. A commercially available axicon (Edmund Optics NT83-787) with 1° cone angle was selected. With a lens of focal length 15 mm (Edmund Optics NT49-658), the inner ring diameter generated by the axicon is 180 μm, with a ring width of 120 μm. A half-inch lens diameter gives a F/# of 1.18. With these parameters, the expected theoretical coupling efficiency is 49%. The lens-axicon pair is used in the setup shown in Fig. 4. For a cost effective implementation, an array of axicons could be made by using fresnel-axicons (fraxicon) . However, an analysis of such cost related issues has been left for future work. The setup uses two light sources, a laser emitting at 460 nm and an infrared laser diode emitting at 808 nm. The infrared light simulates the IR part of the solar spectrum while the blue laser represents the visible part. To further simulate natural lighting, both lasers are coupled into a 100 μm multimode fiber so that both wavelength sources are co-propagating at the fiber end. They then are collimated with a divergence of ±0.25°, matching the inherent divergence of sunlight, before being directed on the axicon-lens pair. A beam-splitter is positioned in between the axicon and the focusing lens in order to image the bubble generation onto a camera via lens FL and CL.
The waveguide sample chamber consists of a small fluidic chamber (Fig. 5(a)), made of glass where one side is made of the IR absorbing glass. Fluid is inserted on the side through an entrance and exit channel. The internal pressure in the waveguide chamber is adjusted manually with a syringe, though not measured. The threshold power for generating bubbles in methanol was approximately 98 mW using the set-up in Fig. 4. Methanol was used in all experiments due to its low surface tension (22.70 mN/m) and viscosity values. The optical density (due to absorption) of the IR glass is 4.88 at 808 nm and thus, about 90% of the power is absorbed in the first 200 μm. The IR power is adjustable by changing the injection current in the laser diode.
The IR-absorbing glass (Schott BG 39 ) is positioned at the focal point of the focusing lens. The IR light is absorbed by the glass and creates a vapor bubble while the visible light is used to measure the coupling efficiency enabled by the light induced bubble. A light source placed at the side of the sample provides light in a dark field configuration for imaging purposes in order to measure the bubble radius. The bubble radius is measured by drawing a rectangle around the recorded images of the bubble and taking the arithmetic mean of the two diameters. A picture of the bubble as seen by the camera depicted in Fig. 4 is shown in Fig. 5(b).
Figure 6(a) shows the optical IR power at the focal spot and the bubble diameter created with this power as a function of time in seconds. The graph shows that a constant bubble diameter is generated at a fixed IR power (plateau in the graph). Note that the threshold to generate a bubble (98 mW) is higher than the levels indicated in the graph. This stems from the fact that more energy is needed to create a bubble than to maintain it. We observed that the bubble size for a given IR power can be modulated by changing the pressure inside the chamber. In the experiment of Fig. 6(a), the pressure in the chamber is not regulated in any way. The bubble diameter varies between 160 μm and 300 μm when the IR power varies between 40 and 100 mW.
The amount of infrared solar power above 750 nm at normal incidence on a single half inch lens is 52 mW assuming AM 1.5 G, therefore a maximum of 71 mW is coupled into the waveguide, depending on the initial coupling efficiency of the mechanism. The infrared portion of the solar spectrum over 750 nm provides the required power for the self-tracking, adaptive mechanism. The simplification of external mechanical tracking leads to a reduction in the energy required to power it, and as such corresponds to an increase in the overall system efficiency. In our demonstration the cut-off wavelength for the trapping mechanism was chosen by the availability of the IR glass absorbing material. Given a cut-off wavelength at 1100 nm the ratio between the coupled energy and the energy used to actuate the mechanism is 5.6, compared to 1.4 at 750 nm. Changing this cut-off would change the amount of optical energy available for bubble trapping and would in turn affect the required lens size to power the tracking mechanism. With the current power threshold, a lens aperture of at least 19 mm will be needed to collect the necessary 98 mW for bubble generation.
The solar cell benefits from the increased efficiency possible with concentration, due to the logarithmic increase in the open circuit voltage. The power in the infrared part of the solar spectrum (above 750 nm) is smaller than the necessary power (98 mW) to generate bubbles in methanol, as obtained (using an IR laser diode) from the experiments. The proposed device is targeted to be used with either amorphous silicon (a-Si) or crystalline silicon (c-Si) solar cell. With the bandgap energy of a-Si (1.7 eV), wavelengths higher than 730 nm do not contribute to the generation of electrons, and allows for the infrared part of the spectrum to actuate the self-tracking mechanism. In the case of c-Si however the spectrum up to 1100 nm could be used. In that case, due to the lower power available a collecting lens size of at least 30 mm diameter would be required to generate bubbles. However, as will be discussed in section 4, a lens as small as 2 mm radius could be used to track a pre-generated (permanent) bubble.
The concentration values expected from the proposed concept depends first of all on the ratio between the area receiving the incoming sunlight over the area of the edge of the waveguide. Secondly, since for a complete solar concentrator system, a two-dimensional array of axicons/lenses will be needed, each generated bubble may scatter out some portion of the light guided in the waveguide and decrease the efficiency. Therefore, in order to obtain simultaneously high efficiency and concentration, an optimum between waveguide thickness and the parameter DBeam/DBubble would need to be found. Such an analysis is beyond the scope of this paper and left to future system work. However, expected values can be estimated by the planar concentrator design with lens arrays .
The coupling efficiency of the waveguide chamber is measured indirectly by placing a detector in close proximity behind the waveguide sample as the zoom-in insert in Fig. 4 illustrates. The detector measures the light transmitted through the sample (i.e un-coupled). By modeling the transmitted light with the same ray-tracing simulation as used in section 1 and validating it with experiments, one can deduce the system coupling efficiency. The visible light transmitted is measured as a function of bubble diameter (varied experimentally with IR optical power according to Fig. 6(a)).
Figure 6(b) shows the simulation (line) and experimental (points) results in an on-axis configuration. The horizontal axis displays the bubble diameter and the vertical axis is the fraction of power transmitted. Due to the limited power available from the IR light source, the maximum bubble diameter was 370 μm. As can be seen in Fig. 6(b), a bubble diameter of 300 μm yields a minimum light transmission of 17% through the sample, matching the expected simulation value, although with a small error in bubble size. Note that not all of the light that does not reach the detector is actually coupled into the waveguide. A fraction of it, dependent on the bubble diameter, is refracted at the interface BG39 glass/air to such high angles that it misses the detector entirely. The simulation model in Fig. 6(b) features an exact model of the lens used in the experiments. By using a bubble diameter of 300 μm and the lens-axicon parameters, simulation yields a coupling efficiency of 35%. However calculating the coupled light from the minimum power reaching the detector gives a coupling efficiency of 40%, slightly lower than the predicted, theoretical, maximal value of 49%.
4. Bubble tracking
The illustration in Fig. 7 shows a bubble following the location of the spot as it is translated. Patterned chromium-oxide was chosen over the BG39 since it allows a better visualization of the tracking effect due to its structure. We observed experimentally that the optical trap is extremely robust to sudden acceleration of the chamber. Thermal trapping of bubble have been shown to be strong and stable . The surface tension coefficient of Methanol decreases with increasing temperature by a factor of −0.0773 mN/(m · K). By increasing the temperature, ie. absorbing light, a heat gradient is created at the interface which directly results in a surface tension gradient with the lowest surface tension value at the hotspot. Due to this, a flow towards the hotspot is generated. This flow transports a vapor bubble to the center of the hotspot where all the forces acting on it are equalized. Therefore a generated bubble will stay at the focal point of the system and track the slow motion of the focal spot due to the sun’s motion (micrometer/second).
With simple plano-convex or Fresnel lenses the sun’s motion produces an aberrated focal spot when off-axis. By translating the chamber laterally in the experiment, the focal spot retains a constant spot size. The experiment was designed to show the strength of the trap. In contrast to bubble generation, tracking a bubble requires less energy and can be reasonably efficient over angle (see Fig. 3). We showed that the experimental set-up could trap a bubble with as little as 5 mW of power, thus we expect that the aberrated focus spot given by off-axis illumination would still be able to track the bubble. For vapor bubble generation a lens system with well-controlled off-axis aberrations is necessary to avoid reduced irradiance from off-axis aberrations. Two-element plano-convex lens designs can be used to deal with this since they have been shown to have good performance over ±24° [19, 20].
It should be noted here that a reflective particle trapped at the focus of the focusing lens provides similar coupling into a waveguide, however the advantages of using vapor bubbles as opposed to reflective particles is the superior trap strength and the generation of a bubble self-aligned with the focal spot.
We successfully demonstrated the creation of vapor bubbles in a fluidic, methanol filled, waveguide chamber. Infrared power level of 98 mW focused with an axicon-lens arrangement (f=15 mm, DBeam = 8 mm, 1° axicon angle) onto an infrared absorptive glass medium gave rise to a stable bubble diameter of 300 μm. Experimentally, the coupling efficiency to the waveguide reaches 40%. The bubbles track the infrared focal spot at a sufficiently high speed that passive solar tracking is expected to be possible. Although the IR power of 98 mW used for bubble generation requires a rather large lens (19 mm) when used with > 750 nm IR sunlight, a power of only 5 mW is necessary to track the bubble. This suggests that a tracking system with much lower power usage and smaller optics (4 mm lens) could be used if a bubble could be permanently maintained in the liquid chamber.
The opto-fluidic approach, based on a light induced micro-bubble reflector, demonstrates the basic features for the realization of a self-adaptive, passive tracking planar solar concentrator system. Simulations show that the waveguide coupling efficiency can be increased to over 90% by optimizing the optical system, ie. the focusing lens and the axicon.
References and links
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