1. Introduction

The development of synthetic polymer fibers has greatly increased the usefulness of fibers and textiles in such areas as fire protection and impact resistance. Further enhancements could be made by creating new optical functionality, for instance, better energy/thermal management [1–3 ], data recording and processing [4–6 ], and enhanced signaling. Impediments to developing such functionality include exceptionally tight fabrication tolerances and a very small range of refractive indices. Moreover in order to create such fibers, non-polymeric materials may be required in tandem with polymers and require matching disparate fluid, thermal and chemical properties. Textile retroreflection is accomplished by adding a coating on the textile such as polymer microbeads. However, fiber-based retroreflectivity would be useful since the retroreflective elements will not degrade as easily and increase the comfort of such clothes. Textile polymer fibers, such as polyester, nylon, and polypropylene, are typically produced via melt extrusion. In melt extrusion polymer pellets are compressed, heated and melted along the barrel of an extrusion screw. The polymer melt then passes through a series of distribution plates and a spinneret to achieve the desired cross section design. The resulting fibers are drawn down using a heated draw stand to their final size, which is usually 10-100µm [7]. Though the process can produce large quantities inexpensively, the elevated temperatures needed for drawing allow complex cross sections to deform via surface tension and extrudate swell. Moreover, imperfections on the surface and within the bulk can destroy delicate optical features [8, 9 ]. To our knowledge, no mass-produced fibers yield a useful retroreflection signal. We demonstrate a fiber that could yield a useful retroreflection signal and introduce a new extruded retroreflective fiber. The retroreflective fiber employed here, Fig. 1, works similarly to retroreflective microprisms—around the circumference the twelve 90° inner vertices lead to 2D retroreflection of light with two consecutive bounces if the incidence plane is perpendicular to the fiber’s axis and the surface is reflective [10, 11 ]. We first describe and report the results of the fiber’s fabrication. A simple figure of merit is used to quantify the retroreflectivity. Next, simulations and measurements of the fiber samples are reported. The simulations provide a benchmark with which to compare the measured retroreflectivities. It is found that the measured retroreflection is an order of magnitude lower than what is predicted from simulations of a perfect fiber. Surface tension induced deformation is suspected to be the reason. Finally we present an improved extruded retroreflective fiber design less susceptible to deformation.

 

Fig. 1 (Left) Designed 12-pointed retroreflective fiber core with each inner angle possessing 90° measure (red). (Right) SEM image of extruded retroreflective fiber with G-polymer sheath intact. Both substantial rounding of corners and deviation from 90° inner angle measure are visible.

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2. Fabrication

The retroreflective fibers were prepared in a three-step process: simultaneous extrusion of the sheath and core, removal of the water soluble sheath, and sputter-coating of gold. The extrusion of a bi-component fiber requires that the thermal and fluid properties of the polymers be close to each other. This includes the coefficient of thermal expansion, viscosity, and melting point (see Table 1).The polymers should, however, be immiscible. The fiber’s core, the retroreflective 12-pointed star, is made of polypropylene and the circular sheath is made of G-Polymer, a vinyl alcohol polymer [12]. The fibers were extruded with a tri-component fiber extruder from Hills, Inc [13]. An SEM of the retroreflective fiber in Fig. 1 reveals that the faces are not at 90° to each other and both the outside and inside corners are greatly rounded. Any deviation from 90° destroys complete retroreflection, and rounding of corners decreases the length of the reflecting faces and increases the inner angle relative to the designed cross section. Surface tension is believed to be the main driver for the deformation; at the extrusion temperatures (~230°C), the viscosity is too low to provide resistance to surface tension stresses. Moreover, surface tension stresses are inversely proportional to the radius of curvature. We compare the viscous forces to surface tension via the capillary number, i.e. $\eta \dot{\epsilon }R/\gamma$, where the variables are viscosity, shear rate, radius of curvature and surface tension coefficient respectively [14, 15 ]. It is substantially less than one from the spinneret exit through the first 20 cm of extrusion. Extrudate swell due to the viscoelasticity is not expected to be a major contributor here because of the high draw tension that the fibers experience. After extrusion the sheath is removed with a Soxhlet extractor. After drying and completing the retroreflection measurements, the retroreflective core was sputter coated with 50nm of gold with a DC magnetron.

Table 1. Physical properties of melt polymers.

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3. Measurements

To measure retroreflection, we employ the goniometer in Fig. 2 To measure retroreflection, we employ the goniometer in Fig. 2, left. The light source is an Ocean Optics HL-2000 Halogen Light Source connected to an Ocean Optics Reflection/Backscattering Fiber Optic Probe. The incidence angle, the angle between the incoming light beam and retroreflective surface normal, can be adjusted from 2° to approximately 60°. Because the source and detector are housed in the same probe, the observation angle, the angle between the incoming light beam and reflected beam, is always zero. Since the light source is uncollimated the source-to-sample distance is kept nearly constant. Measurements were done on four types of fibers: a round polypropylene fiber, the retroreflective star-shaped polypropylene fiber, and gold-coated versions of the two fibers. The round fibers act as controls. The fibers were glued at the ends across a matte black cardboard frame while avoiding overlapping the fibers (Fig. 2, right). All samples had the same number density. The samples are placed on an elevated platform mounted on a stage. A piece of matte black cardboard is placed underneath the fibers to minimize the amount of light returned to the detector from the background. The back-reflected light from just the stage itself is only 2-3% of the incident flux. With the samples present, this value drops since the back-reflected light is scattered as it passes through the fibers. The ratio of retroreflected light intensity from the samples to the retroreflected light intensity from a reference surface is recorded with an Ocean Optics SD 2000 fiber optic spectrometer. We use that ratio as our figure of merit,

 

Fig. 2 (Left) Goniometer and light source/detector used for retroreflection experiments. The light source is pointed towards the stage. (Right) Uncoated round fiber sample used in measurements.

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At each incidence angle retroreflected light from a white reflector standard was measured and used as the denominator for RRR. The white standard diffuse reflector, Ocean Optics’ WS-1-SL White Reflectance Standard, is over 96% reflective from 250nm to 1500nm and possesses a nearly Lambertian reflection profile [16]. Each sample was measured at an incidence angle of 5°, 10°, 20°, and 30°. The fiber samples were measured with their axes parallel and orthogonal to the incidence plane—differences are expected between the two orientations since the retroreflective features exist only along the axial dimension. To reduce measurement errors, each sample was measured at five different spots for each incidence angle and orientation and then averaged. The distance from the samples to the source was kept constant since RRR is dependent on it via the denominator.

Ray tracing software, Radiant Zemax, is used to simulate the fiber samples for comparison with measurements [17]. The ray optics assumption is a good approximation as the wavelength of light used is less than 1µm and the fiber feature sizes are greater than 10µm. Propagation phases are ignored since the source is incoherent. To accurately reproduce the measured values we recorded the important geometric parameters, including source distance, source size, detector size, source spread, fiber count, fiber orientation and sample dimensions, and incorporated them into the simulations. We take the refractive index of polypropylene to be constant and purely real for wavelengths between 400 and 1000nm. To account for the random positions of the fibers in the sample arrays, we simulated 10 different structures with slightly varying random fiber positions. 500,000 rays were traced which ensured convergence to about 2%. In the limit of large sample numbers, randomly sampling different fiber arrangements should be the same as randomly sampling spots as in the experiments. To simulate the 12-pointed star, the inner angle measure was slightly shifted from 90°.

3. Results and discussion

Previous work on polymer fibers has focused on round fibers and shown low retroreflection values [18, 19 ]. The main impediments to retroreflection are the low index contrast between the fiber and its surroundings and the small retroreflecting cross section. Typical fiber extrusion polymers have indices close to 1.5 at optical wavelengths, thus the reflection coefficient is approximately 0.04 [20, 21 ]. For round fibers, the fraction of the cross section that retroreflects is roughly 0.08. High refractive index polymers could be used, but they are difficult to extrude. We increase the retroreflection by employing both metallic coatings and a more complex fiber to increase the useful cross section. The measured relative retroreflection ratio is plotted in Fig. 3 for four different samples at 5° incidence angle and orthogonal orientation. $RRR=100$ indicates that a sample is as retroreflective as the white diffuse surface. The uncoated fibers have a flat RRR spectrum of about 30 to 40 from 450nm to 950nm. The gold coating greatly increases the retroreflection ratio to a value of about 100 for the control fiber and 120 for the star-shaped retroreflector fiber. Microbeads on a t-shirt (unplotted) are an order of magnitude above these values at around 2000. The microbeads are densely packed while the fibers are sparsely laid on the cardboard frame. About 40% of the incident light intercepts the fibers, thus scaling the fibers’ retroreflection ratio by 1/0.40 pushes the uncoated fibers $RRR$ to just below 100. Given that the index of polypropylene is 1.49 and that a typical ray meets 1-2 interfaces, one would expect a lower value for the relative retroreflection ratio. This higher $RRR$ arises from the internal fiber structure, scattering occurs at the gap between the G-polymer cladding and polypropylene core. The intercepted area rescaling pushes the gold coated fibers up to 250-300.

 

Fig. 3 Measured relative retroreflection ratio (RRR) at 5° incidence and orthogonal orientation.

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The results for the uncoated 12-pointed retroreflective fiber are shown in Fig. 4(a).Little light is retroreflected because of the small index contrast. Most of the returned light is due to diffuse scattering created by the reflecting planes. Note that simulations (circles) correlate well with the measurements and reproduce the trend with increasing incidence angle. The discrepancy below 400nm may be due to near-UV absorption in polypropylene, while discrepancy above 950nm may be attributed to limitations of the spectrometer.

 

Fig. 4 Retroreflected power for (a) uncoated and (b) gold-coated 12-pointed star shaped fibers at the various incidence angles for measured orthogonal orientation (blue line), measured parallel orientation (red line), simulated orthogonal orientation (blue circles), and simulated parallel orientation (red circles).

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The retroreflection spectra for the gold-coated 12-pointed star-shaped fibers are plotted in Fig. 4(b). The gold coating is 50nm in thickness which is between 1.2 to 2 skin depths at optical and near IR wavelengths. Ray-tracing simulations of perfect fibers yield an $RRR$ of 1600, but we can obtain good agreement with measurements by slightly changing the inner vertices. The retroreflectivity is nearly the same for all incidence angles, roughly 140. The dip at wavelengths below 600nm is due to the absorptivity of gold. It can be used to determine the degree of retroreflection. First note that the ratio of the measured $RRR$ at 800nm to 400nm is 140/55 ≈2.6. If reflection occurred with two bounces (retroreflection), then the ratio should be roughly the square of gold’s reflectivity at 800 and 400nm, about 5.8. For reflection via a single bounce, the predicted ratio would be roughly 2.4. Thus retroreflection is occurring with usually a single bounce; this is consistent with the assertion that the cross section is distorted. While complete retroreflection cannot happen if the corner features are not exactly 90°, deviation from 90° is tolerable if the detectors are close enough and large enough to catch the misdirected rays. Here the detectors correspond to a viewing angle of 1.64° with respect to the samples.

Of course, perfect star-shaped fibers have limit to how well they retroreflect. Referring to Fig. 1, the inner corners closest to the fiber’s equator will have most of their cross section able to retroreflect, and as one moves further from the equator the faces adjacent to the inner corners become increasingly shaded and unable to retroreflect. One can show that for any number of inner corners the fraction of the cross section able to retroreflect falls between 0.40 and 0.45. An alternative design is the fiber analogue of the microbeads: a fiber with smaller circular fibers embedded on the surface (Fig. 5).). Close to 80% of this fiber’s cross section retroreflects with optimal parameters. Extrusion of this fiber should be easier as the capillary number is much higher since there are no sharp corners with high curvatures. The large inner core fiber could be either metal-coated or highly doped with zinc oxide or titanium dioxide nanoparticles. The smaller outer fibers are clear and semi-embedded in the core fiber. Light enters the smaller fiber, is scattered off the core–ring fiber interface, and redirected back towards the source. Simulations of an array of partially optimized fibers, consisting of a metal-coated inner core fiber with a 50µm radius, outer surface fibers with index of 1.9 and radius of 13µm, modeled with the same set-up as the previous fiber arrays suggest that performance exceeds 20 times a Lambertian surface and approaches that of microbeads on a textile. By tuning the number, index, and diameter of the small outer fibers, it may be possible to further improve performance. In addition, the retroreflection ratio is significantly more robust to fabrication disorder. Simulations show that deformation of the outer surface fibers into elliptical cylinders with a 10% decrease in one axis decreases retroreflection to 10 times a Lambertian surface (Fig. 5). Such deformation could occur during extrusion via surface tension.

 

Fig. 5 The core-ring retroreflective fiber with clear circular surface fibers and blue inner core fiber (a), and 10% deformed surface fibers (b). For fiber (a), the RRR ratio is over 2300, while for fiber (b) it is over 1100.

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Conclusion

It is clear that in the regime of ray optics a simple low index mono-component fiber will not achieve significant retroreflection. To circumvent this problem one can turn to complex shaped fibers as well as metal coated fibers. Significant retroreflection could be achieved with a metal-coated 12-pointed star-shaped fiber; however there is a stringent requirement on the inner corner angle. Currently work is focused on reducing the inner angle deformation and corner rounding. Extrusion at a slightly lower temperature would keep the viscosity high enough to resist the surface tension-induced deformation and allow drawing. In addition, a redesigned extrusion die with inner vertices less than 90° could compensate for the widening. A new fiber design, the core-ring fiber, is also considered. Here, surface tension should play less of a role since the maximum curvature is an order of magnitude smaller. Through optimization of the core-ring fiber geometry and indices it is shown that large improvements in the retroreflection can be achieved, and that high retroreflection persists even if the structure is deformed. Could even higher retroreflection values be attained? One such fiber that, in theory, could work is based on an Eaton lens [22]. Its refractive index is dependent only on radial coordinate and increases monotonically without bound as the center is approached. Within the lens light rays follow an orbit back towards their source. While the intensity is preserved the image orientation is inverted. Fabrication of such a fiber would not be possible now as it requires a diverging refractive index. Future work will examine the effect of weaving the samples and designing new extrusion plates for the core-ring fiber.