Uniaxial photomechanical motion in large diameter polydimethylsiloxane optical fibers with fluoropolymer claddings

Abstract. This study focuses on the photomechanical behavior of step-index optical fibers with a polydimethylsiloxane (PDMS) core and fluoropolymer claddings. The PDMS hosts dopant graphene nanoplatelets, which are heated when illuminated by visible light. Sample fibers were fabricated by drawing the doped resin into thin fluoropolymer tubing before the resin set. The individual motions of the core and cladding were observed to be coupled, which resulted in a relatively small photomechanical effect. Adding a castor oil lubricant between the core and cladding significantly increased the core’s photomechanical strain. The large strain of the lubricated cores exhibited both irreversible and reversible photomechanical motion. Cycling the pump beam resulted in a fully reversible photomechanical piston that can be modeled by a linear response function to the incident pump beam.


Introduction
Analogous to wires that guide the flow of charge carriers, optical fibers act as guides for light. 1 Just as the conductance, diameter, and work function of electrical wires affects charge carriers, the fiber core diameter and complex refractive index contrast between the core and cladding determines a multimode optical fiber's ability to guide light.3][4] Polymer optical fibers can be easily doped with many organic molecules to add new functionality to optical fibers for use in photonic devices. 5,6ptically transparent, thermoplastic polymers are a common material of choice because they can be fabricated using the same melt-processing techniques as glass-based optical fibers. 7ike polymeric materials commonly used in optical fibers, polydimethylsiloxane (PDMS) is highly transparent in the visible spectrum and can be doped with organic molecules and inorganic particles.[10][11] The photomechanical effect is the observable deformation of an object when illuminated. 12,135][36][37][38][39] Many materials can have multiple photomechanical response mechanisms. 15,405][56][57] Photomechanical devices have also been shown to move over water, 58,59 across terrain, 32,[60][61][62][63] and through the air. 64Photomechanical devices can also be used as components in larger photomechanical systems with both series [65][66][67] and parallel 68,69 configurations.
Doped PDMS has been the focus of many photomechanical studies [70][71][72][73][74][75][76] due to its large coefficient of thermal expansion. 77Because of the recent research interest in both PDMS optical fibers and the photomechanical effect in PDMS composites, we investigated the photomechanical motion of doped PDMS in an optical fiber geometry.Photomechanical optical fibers can be directly pumped from micro-optical sources and serve as optical-mechanical transducers.Some of the optical fibers presented in this study behave like light-driven pistons, which could be used as actuators for linear motion or a component of a light-fueled engine.
In this study, prefabricated fluoropolymer tubes act as a mold and cladding for largediameter optical fibers.Poly(tetrafluoroethylene-co-hexafluoropropylene) (FEP) and polytetrafluoroethylene (PTFE) were chosen as the cladding materials.The low refractive index of FEP makes it an ideal candidate for large-diameter optical fibers. 78The PTFE tubing has a higher refractive index, 79 and the opaqueness causes scattering at the core/cladding interface; however, the relatively low surface energy 80 (useful for "non-stick" applications) was identified as a target for study based on potential device applications.Many photomechanical materials have been illustrated by doping PDMS with various forms of carbon particles such as carbon nanotubes, 81,82 carbon nanoparticles, 83,84 reduced graphene oxide, 85,86 and graphene nanoplates. 87Graphene nanoplates (GNP) were used in this study due to their high thermal conversion efficiency. 88

Experiment
Photomechanical samples were fabricated by mixing GNP (≤ 4 nm thickness) into Sylgard 184 base at a concentration of 0.0083 wt.%.Multiple rounds of shear mixing and bath sonication were performed until a homogeneous mix was achieved.The cross-linker was then introduced with the manufacturer's recommended 1:10 volume ratio and mixed for 5 min.The final mixture was placed in a desiccator under vacuum for 20 min until no visible air bubbles remained.
The pre-cured, viscous liquid was drawn into either FEP or PTFE tubing.Histograms of the FEP and PTFE tubing inner diameters captured from 50 cross-sectional images each are respectively shown in Figs.1(a GNP-PDMS was then placed in an oven and cured at 100 °C for ∼30 min.The cured fibers were placed on a bench in ambient conditions for > 2 h prior to further experimentation.The resultant samples were broadband-absorbing optical fibers with doped PDMS cores which were clad with either an FEP or PTFE fluoropolymer.The typical fiber fabricated with this method had a total length of ∼ 15 cm before being sectioned into smaller units for experimentation.Longer fibers could be drawn using this method; however, the rate at which the PDMS is drawn through the tubing is reduced when per length increment drawn into the tubing. To remove adhesion and reduce friction between the fiber core and cladding, a third type of optical fiber was fabricated.This new type of fiber was fabricated with a lubricant layer between the core and cladding regions, and it was fabricated using the following technique.First, PTFEclad fibers with GNP-PDMS cores were fabricated using the process stated above.A small ∼1 cm length of PTFE tubing was left vacant at one end.Then, a small slit ∼0.5 cm in length was cut through the vacant end of the PTFE tubing using a razor blade.Afterward, the cladding was split into two sections at one end of the fiber.The two cladding pieces at the split end of the fiber were pulled away from each other which tore away the cladding from the entire core resulting in two semi-circular strips of PTFE cladding, which were discarded, and a standalone GNP-PDMS fiber core.Next, FEP tubing was pre-filled with castor using vacuum pressure, and the standalone GNP-PDMS core was submerged in castor oil.After being submerged in castor oil, one end of the core was inserted into the FEP tubing.For the final step, the far end of the FEP tubing was held at vacuum pressure which drew the remaining length of the core into the FEP tubing.Images from various stages of the process are shown in Fig. 2(a).
We fully expected to measure a strain in the free-standing GNP-PDMS fibers upon removing the PTFE core during the processing steps of the lubricated samples.Multiple fibers were measured, and no length change was observed, which indicates a negligible amount of internal stress in the GNP-PDMS core after curing in the PTFE tubing.
For photomechanical experiments, a class IIIb, 445 nm, diode laser was passed through neutral density (ND) filters and a relay-controlled laser shutter.The clad optical fiber was positioned in a hole which was bored through a black-painted aluminum block and then mounted using a thumb screw via a tapped hole facing perpendicular to the length of the fiber.The Fig. 2 (a) After the GNPs are homogenized in the base (i) crosslinker is added and mixed, (ii) the mixture is desiccated, (iii) PTFE tubing is filled under vacuum pressure, (iv) and the fiber is cured resulting in (v) the GNP-PDMS/PTFE fiber.Then, (vi) a fiber end is scored with a razor blade, (vii) the cladding is pulled away from the core, and (viii) the free-standing GNP-PDMS fiber is ready to be submerged in castor oil.(ix) The free-standing fiber is submerged in oil, (x) FEP tubing is attached to the vacuum, and (xi) the freestanding fiber is drawn into the FEP tubing, which cladding was subject to clamped condition by the hole/screw apparatus approximately half of a centimeter from the unilluminated end of the fiber.A microscope was directed vertically downward as illustrated in Fig. 2(b).The red channel was used to take micrographs, and two 550 nm long-pass filters were placed between the fiber and the microscope to reduce channel mixing of the blue laser light.A weak white light source illuminated the sample and holder.The sample and microscope were encased in an acrylic box to reduce dust particles that could scatter light near the fiber end.A 3/8" hole was drilled into the box to allow the laser beam to pass through.
The incident beam illuminated a ∼1 mm diameter spot centered on the fiber core.An Ophir PD300-UV sensor measured the pump power before each experiment after the beam was passed 1 O.D. ND filter.
A preliminary micrograph was recorded, and the shutter was opened for 135 s.The shutter was closed for 180 s to complete the first experimental cycle.Each experiment was cycled three times and the microscope camera collected images periodically at 2 Hz over a 945 s interval.There were 1890 images recorded and analyzed per experiment.A script imported all images after each experiment and measured the change in pixels of the core and cladding edges relative to the fiber mount.Figure 2(c) shows a contrast-enhanced image taken during experimentation and highlights the regions for detecting changes in the left-most edge points.

Results
The attenuation of light through the fiber was measured by coupling low-intensity laser light into the fiber and measuring the transmitted light for fibers of various lengths.All fibers exhibited an exponential decay as a function of length.The results follow the Beer-Lambert law for homogeneous materials.Here, I is the intensity, z is the length through the material, and α is the attenuation coefficient.The multimode, undoped, PDMS/FEP fiber shown in Fig. 3 has an attenuation coefficient of ð0.46 AE 0.10Þ dB∕cm.The difference in the undoped PDMS cores is due to scattering introduced by the PTFE cladding.The attenuation coefficient for the undoped PDMS/PTFE fiber was measured to be ð1.6 AE 0.3Þ dB∕cm.Assuming similar losses from leakage in multimode fibers of similar step indices, the additional loss in the undoped PDMS/PTFE fiber is scattering from the white opaque PTFE tubing.The scattering loss caused by the PTFE cladding for light traveling through undoped PDMS is ∼1.1 dB∕cm.Note that the values are given in decibels, but the fits were performed using an exponential decay with the natural Euler number e as the base and later converted to decibels from Nepers.The GNP-PDMS optical fibers had attenuation coefficients that were significantly larger than the undoped PDMS fibers as shown by the fit lines in Fig. 3.The attenuation coefficients for optical fibers with GNP-PDMS cores were ð5.7 AE 0.2Þ dB∕cm, ð6.8 AE 0.6Þ dB∕cm, and ð6.6 AE 0.2Þ dB∕cm for the respective FEP-clad, PTFE-clad, and lubricated FEP-clad samples.

Transmittance
Fiber length (cm) From the results of the attenuation measurements for the undoped PDMS clad with transparent FEP and the undoped PDMS clad with white opaque PTFE, it is clear that scattering at the PDMS-PTFE interface in GNP-PDMS/PTFE fibers causes the increase in attenuation.The additional loss in the GNP-PDMS/Oil/FEP fibers, caused by the introduction of the higher-index castor oil layer, was smaller than observed in the GNP-PDMS/PTFE fibers, but the attenuation was still ∼0.9 dB∕cm greater than that observed in the GNP-PDMS/FEP fibers.Tracing all attenuation curves back to the air/fiber interface (fiber length → 0), all fiber types (undoped PDMS and GNP-PDMS cores) are observed to have similar interfacial coupling losses, ∼10%.
The first photomechanical experiment measured the photomechanical response of a GNP-PDMS/FEP fiber.After images were taken, the location of the measured core+cladding motion [center/green boxed region shown in Fig. 2(b)] and the location of the measured cladding motion in the surrounding regions were recorded as functions of time.After each three-cycle experiment, the pump beam power was changed to check the response as a function of pump power.The sample was 1.5 cm in length, meaning more than 30% of the pump beam's power was transmitted through the sample without being absorbed.
The rate by which the optical fiber heats and cools depends on the thermal properties of the materials used for the core and cladding as well as their dimensions.If the entire core+cladding system was uniformly heated, then Newton's law of cooling for a single system would apply; however, there are two distinct, cylindrically symmetric regions in the optical fiber.Let us assume that most of the heat generated in the core flows through the core/cladding interface.The inner boundary of the cladding then increases in temperature while heat diffuses through the cladding's volume.The cladding's outer surface increases in temperature, which cools via convective boundary conditions at the cladding/air interface.
We can make a few more simplifying approximations for the FEP-clad fibers.Let us consider: 1. the ambient temperature T amb does not change during the experiment, 2. effects from heat flow along the fiber are negligible in comparison to heat flow through the core/cladding boundary, 3. the overwhelming majority of heat generated in the core conducts to the cladding, and 4. the cladding diffuses heat through it much faster than the rate by which it cools.
Under these circumstances we can write a set of coupled, first-order, differential equations in time for the core temperature T core and cladding temperature T clad , which are of the form E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 7 ; 3 3 1 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 7 ; 2 8 5 with the initial conditions, E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 1 1 7 ; 2 5 7 where a 1 and a 2 denote the coefficients of heat transfer between the respective core/cladding and cladding/air interfaces, P is the laser power, and b is the photothermal coefficient.The time-dependent solution for the core temperature from Eqs. ( 2) and ( 3) is biexponential when PðtÞ is a positive constant after the power is stepped on at t ¼ 0. If the amplitude of one of the terms is much greater than the other, then we can simply approximate a heat kernel as a single exponential in time after averaging over the system's volume.Likewise, the cladding can also be reduced to a single exponential with similar arguments.These approximations of either the core or cladding result in the fiber's average temperature asymptotically approaching a maximum via an exponential growth function shortly after the shutter is opened.Similarly, when the pump beam is blocked, all temperatures decay exponentially to the ambient temperature.The growth and decay exponential behaviors have the same rate constant per material.The strain response to a change in temperature is assumed to be much quicker than the thermal response to a step function from photothermal heating by a CW laser source.Thus, a linear response function can be used to model the change in length of the core and cladding as a function of time.
Large viscoelastic effects are commonly observed in pristine elastomeric materials.The greatest transients typically leave the system after the first cycle, and therefore, the linear response function is assumed to best model the photomechanical motion starting from the second cycle in new samples.The length change of the core and cladding are both modeled by the linear response function E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 1 1 4 ; 6 7 6 where RðtÞ is the response function and ΔL ¼ L − L 0 with L being the length at some time t and L 0 being the length when the fiber's temperature is equal to the ambient temperature.The linear response function for the length change is of the form E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 4 ; 6 0 5 where A and a are constants.Figure 4(a) shows the motion of the fiber core's edge as a function of time for two different pump powers.The response function curve from Eqs. ( 5) and ( 6) fit the length change data starting the moment the shutter was opened on the second cycle.There were two fit parameters, a and AP 0 a , where P 0 is the pump beam's power during a given experiment.All fits seem to match the time-dependent data reasonably well, which justifies the earlier approximation that resulted in the form of the response function given by Eq. ( 6).
Figures 4(b) and 4(c) plot the fitted parameters as functions of the pump power.The decay parameter a appears to be reasonably independent of the pump power, as expected.The core's decay constant is an order of magnitude greater than the cladding's decay constant.The trend for AP 0 a is linear for the cladding material.The amplitude for the core appears to be nonlinear in an unexpected way, but the uncertainties are much greater due to the relatively small motion of the edge and the noise from edge detection.A single exponential response fit the observed data quite well for the 1.5 cm GNP-PDMS/ FEP fiber, which is indicative of a simplified Newton cooling model, dT dt ¼ −aðΔTÞ þ bP 0 , where ΔT ¼ T − T amb .It is clear that the steady-state solution occurs when dT dt ¼ 0 which means that the asymptotic temperature is where m is the mass and C is the specific heat for the core and cladding.The fraction of beam power absorbed is γ which is 0.66 for the 1.5 cm GNP-PDMS/FEP fiber from the data provided in Fig. 3. Based on the dimensions of the fiber and densities 89,90 of the materials, the mass are calculated to be m core ∼ 30 mg and m clad ∼ 160 mg.Also, the specific heats are known to be C core ∼ 1.5 kJ kg −1 °C−189 and C clad ∼ 1 kJ kg −1 °C−1 , 90 which gives an estimate, b ∼ 3.2 °C∕J.We assume that the length change response to an increase in temperature is much faster than the temperature change response to the incident pump beam.Therefore, the temperature change response to the pump beam is essentially the same as the length change response to the pump beam.Therefore, let us use a ¼ 0.024 s −1 at P 0 ¼ 1.38 W for the cladding material length change as a function of time to approximate the time constant for the temperature change, which results in ΔT max ¼ bP 0 ∕a ∼ 180 °C.Note that this high ΔT max value was never realized in experiments due to the slow response time for the cladding material; rather, it is an extrapolated value at t → ∞.From the cladding strain curves shown in Fig. 4(a), the strain reached ∼90% of the asymptotic value.For a linear approximation to thermal expansion, the maximum increase in experimental temperature was ∼162 °C, which occurred when the sample was illuminated with the maximum power beam of 1.38 W for the maximum amount of time, 135 s.Starting from room temperature, the greatest increase in temperature was below the maximum operating temperature of 200 °C listed for both FEP and PDMS. 77,90he coefficient of linear thermal expansion β is defined by the equation ΔL ¼ βL 0 ðΔTÞ.Because the exponential growth is slow as shown by the example curves in Fig. 4(a), the data must be extrapolated to t → ∞ from the fitting parameters given in Figs.4(b) and 4(c).Using these values and taking the limit where ΔL max ¼ βL 0 ΔT max gives an estimated value of β ∼ 10 −4 °C−1 .This estimated value of the linear coefficient of thermal expansion is closer to the value attributed to FEP. 90 It is much smaller than Sylgard 184's linear coefficient of thermal expansion in free-standing films, ∼3.4 × 10 −4 °C−1 . 50Therefore, adhesion between the core and cladding plays a major role in the amount of photomechanical motion observed in the GNP-PDMS/FEP optical fibers.Indeed, we spent a great deal of effort trying to free the fiber from the FEP cladding by forcing core-sized metallic rods into an end of the fiber; all attempts were unsuccessful.Note that we can immediately see the pinning/adhesion effect by observing the disparity in the parameter a between the core and cladding.Basically, the GNP-PDMS quickly expands until stressed caused by adhesion between the core and cladding keep the GNP-PDMS material from further expanding relative to the core-the entire core + cladding cross-section at the fiber's end expands at a slower rate dominated by the much more massive and voluminous FEP cladding material.
The GNP-PDMS core was also studied using a PTFE cladding.The inner diameter of PTFE tubes was nearly identical to those made from FEP; however, the outer diameter was much smaller as shown in the inset of Fig. 1(b).The thinner walls of the PTFE tube can transfer heat out of the system much faster than the FEP cladding.Additionally, scattering at the PDMS-PTFE interface along the fiber can cause increased absorption near the cladding, which in turn can cause increased heat generation near the edges of the fiber's core.
The length change results for GNP-PDMS/PTFE fibers are shown in Fig. 5.One of the most striking features observed in the PTFE-clad optical fibers was the core's apparent contraction relative to the cladding.As with the previously studied fibers, the left-most edges in the middle of the images were used to detect the combined core and cladding movement whereas the upper and lower regions were used to only detect the cladding motion.After subtracting the cladding movement from the combined core + cladding motion, a contraction of the GNP-PMDS core relative to the cladding was consistently reported across all samples and over all cycles.
The thermal and mechanical properties of the FEP and PTFE claddings affected the photomechanical behavior of the core due to the adhesion which occurred while curing.Curing the samples in PTFE and removing the tubing allowed for free standing GNP-PDMS fibers.Castor oil was chosen as the lubricant because of the large molecular sizes of triglycerides which do not swell PDMS. 91he photomechanical behavior for two GNP-PDMS/Oil/FEP optical fibers of different lengths is shown in Fig. 6.The initial response of a pristine sample is the most glaring artifact in both plots.A very large and irreversible motion occurs after initially opening the laser shutter.An initial motion of over 1 mm was observed for the 4 cm optical fiber.The photomechanical motion shows significant stability and reversibility after the first cycle.This initially large motion was observed in all samples.
Regarding length dependence for the irreversible process, the core of the 1 cm-long fiber exhibited a large, but still smaller motion during the first cycle.The amount of irreversible strain was directly proportional to the power absorbed by the sample.The 1 cm fiber absorbed about 3/5 of the pump beam power while the 4 cm fiber absorbed nearly all of the pump beam.Figure 6 shows that the irreversible strain observed in the 1 cm GNP-PDMS/Oil/FEP fiber after the first cycle was about 7/10 of the irreversible strain exhibited by the 4 cm fiber.The 4 cm is longer, where the response time for the first cycle is slower for that sample.Extrapolating the curves in  Fig. 6 shows a trend in which the final irreversible strain of the 1 cm fiber would be closer to 3/5 of the strain in the 4 cm fiber.
The most interesting aspect of the motion in the GNP-PDMS/Oil/FEP fibers shows up in the following cycles.First, there was no worm-like crawling out of the cladding.Instead, the motion became reversible.Another interesting aspect of the reversible motion was the amplitude.Both the 1.5 and 4 cm samples were subject to the same incident power (P 0 ¼ 1.38 W) with the same beam shape and positioning.The amplitude of the reversible motions are approximately same despite the length change.From response model fits, we see that AP 0 a ¼ ð131 AE 9Þ μm W for the 4 cm-long sample and AP 0 a ¼ ð141 AE 7Þ μm W for the 1 cm-long sample, where the amplitudes overlap within uncertainty.One might expect that the reversible motions such that the 1 cm-long fiber would have an amplitude that was about 3/5 of the 4 cm-long sample; however, the amplitudes observed in these nearly-reversible motions were roughly the same.

Discussion
Multimode, doped, optical fibers were fabricated with PDMS as the core material.Because fluoropolymers have a relatively low refractive index, PTFE and FEP were chosen as the cladding material.A small photomechanical motion was observed in GNP-PDMS/FEP optical fibers, where the central region of the PDMS core's surface on the incident edge expanded.This motion was well-characterized by a simple exponential response function.The core motion had a response time that was an order of magnitude faster than the FEP cladding's response to end-pumping the core.No motion was observed within the precision of the microscope on the opposite end of the fiber for FEP-and PTFE-clad samples when no lubricant was used between the core and cladding.
Interestingly, GNP-PDMS/PTFE optical fibers showed a negative photomechanical motion of the core relative to the PTFE cladding's motion.We did not address the magnitude or the response time.Once the core receded a few pixels, only the cladding was visible to the camera and therefore the extent of the recession into the PTFE material was unattainable.The PTFE tubing was soft, thin-walled, and exhibited greater expansion relative to the FEP tubing, where scattering-induced local heating near the PDMS-PTFE interface and the thickness of the tubing are assumed to be responsible for the observed differences between the photomechanical behavior in GNP-PDMS/PTFE and GNP-PDMS/FEP fibers.
Photomechanical motion of large-diameter optical fibers fabricated from doped PDMS could be problematic for many applications.There are some actuation applications, however, that could benefit from the photomechanical behavior observed in these materials.A large initial photomechanical effect was observed after adding some lubricating oil between the GNP-PDMS core and FEP cladding.Photomechanical motion was observed to be reversible after the initial transient behavior was removed by cycling the pump on/off.The GNP-PDMS/Oil/FEP fiber's end that was opposite of the incident beam did irreversibly recede into the cladding when observing with the naked eye; however, no quantitative transient data was available for analysis due to the direction in which the fiber-end moved and the geometry of the microscope setup.
The large reversible photomechanical motions in the GNP-PDMS/Oil/FEP fibers were surprisingly similar in amplitude between the 1 cm-long and 4 cm-long fiber.There are many possible mechanisms responsible for the nearly identical amplitude as recovered via curve fitting.In fact, the system is quite complicated due to the uncertainty in materials, post-processing, and effects from irreversible transients.Heterogeneities in both the PTFE and FEP tubing can cause narrow and wide locations in the core.There are likely heterogeneities in thermal and mechanical properties in the cured PDMS material at various scales.Coupling these uncertainties with long-time scales and transient behavior can result in large-scale uncertainties in the fiber's photomechanical behavior.
Samples of GNP-PDMS/Oil/PTFE optical fibers were also prepared.In every case, oil oozed out of the ends of the sample upon illumination.The edge of the core and cladding materials were not distinguishable from the oil edges in these samples, and therefore, no image analysis was performed on their photomechanical behavior.
In an attempt to create PTFE-clad optical fibers with large photomechanical responses, GNP-PDMS/Oil/PTFE fibers were fabricated in the same manner as the GNP-PDMS/Oil/ FEP fibers.Every attempt at using these fibers resulted in oil leaking emerging from the fiber end when illuminated by the pump beam.We were unable to distinguish between the fiber edge and the oil surrounding through the microscope images.The white opaque cladding of the PTFE cladding scatters light at the inner boundary unlike the FEP fibers.The effects of this scattering on the propagation of light through the fiber can be seen in Fig. 3 for the PDMS/ PTFE fiber when compared to the PDMS/FEP fiber.Scattering from the PTFE inner wall increases the local light intensity, which in turn increases the heat generation near the thin oil layer.Thus, this increased heat generation caused the consistent oil leakage from the GNP-PDMS/Oil/PTFE fiber ends in these samples.Note that oil also emerged from the end of GNP-PDMS/Oil/FEP samples in some cases, but those were infrequently encountered.
This study used a diode laser to pump doped optical fibers at relatively high CW intensity.In doing so, we sometimes observed chemical reactions at the incident edge of the fiber.Figure 7(a) shows two small "jets" of burning material forming at the edge of the GNP-PDMS core.These would sometimes appear at the highest power used in this study, P 0 ¼ 1.38 W, where hot spots from the focused laser speckle pattern would form.Care was taken to avoid these in edge detection analysis.
There were two instances in which optical fibers catastrophically failed; in these two samples, a lensing effect caused the fibers to become superheated near the incident edge.The incident boundary in both fibers greatly expanded while expelling ignited material in what appeared to be a miniature explosion.The moment just after the material ignited and expulsion began is shown in Fig. 7(b).The FEP material was irreversibly deformed in both cases with the edge bending outward.

Conclusion
This research aimed to investigate the photomechanical motion of doped PDMS in an optical fiber geometry, focusing on the interaction between core and cladding materials.The experimental results demonstrated that GNP-PDMS cores in FEP-clad optical fibers exhibited a detectable photomechanical response characterized by an simple exponential response.The core's response time in FEP-clad fibers was significantly greater than the cladding.The study also explored the application of lubricating oil between the core and cladding, which resulted in large irreversible photomechanical strains followed by reversible motion when cycling the pump on/off.Sampleto-sample variations were identified in fibers with complex fabrication steps, which necessitates future processing methods with greater precision.
The investigation into GNP-PDMS cores with thin PTFE cladding revealed an intriguing phenomenon-a negative photomechanical motion of the core relative to the cladding.The study also highlighted potential challenges associated with high-intensity laser pumping, such as irreversible reactions and catastrophic failures at the incident edge of the optical fibers.Overall, this research sheds light on the complex interplay between material properties, geometry, and experimental conditions in determining the photomechanical behavior of optical fibers.Further exploration is warranted to better understand and control the photomechanical motion in step-index optical fibers.

Fig. 1
Photomechanical samples were fabricated by mixing GNP (≤ 4 nm thickness) into Sylgard 184 base at a concentration of 0.0083 wt.%.Multiple rounds of shear mixing and bath sonication were performed until a homogeneous mix was achieved.The cross-linker was then introduced with the manufacturer's recommended 1:10 volume ratio and mixed for 5 min.The final mixture was placed in a desiccator under vacuum for 20 min until no visible air bubbles remained.The pre-cured, viscous liquid was drawn into either FEP or PTFE tubing.Histograms of the FEP and PTFE tubing inner diameters captured from 50 cross-sectional images each are respectively shown in Figs.1(a) and 1(b), where both histograms follow a normal distribution.The mean inner diameter of the FEP tubing was approximately 1.60 mm with a standard deviation of 20 μm.The PTFE tubing inner diameter had a mean of 1.58 mm with a standard deviation of 20 μm.During the drawing process, one end of a tube was submerged into the pre-cured elastomer mixture while the other was held at vacuum pressure.The tubing filled with uncured Fig.2(a) After the GNPs are homogenized in the base (i) crosslinker is added and mixed, (ii) the mixture is desiccated, (iii) PTFE tubing is filled under vacuum pressure, (iv) and the fiber is cured resulting in (v) the GNP-PDMS/PTFE fiber.Then, (vi) a fiber end is scored with a razor blade, (vii) the cladding is pulled away from the core, and (viii) the free-standing GNP-PDMS fiber is ready to be submerged in castor oil.(ix) The free-standing fiber is submerged in oil, (x) FEP tubing is attached to the vacuum, and (xi) the freestanding fiber is drawn into the FEP tubing, which (xii) results in a GNP-PDMS/Oil/FEP fiber.(b) The main experimental setup for characterizing photomechanical optical fibers.(c) The regions for left-edge detection shown over the top of a lubricated GNP-PDMS/FEP optical fiber image during an experiment.

Fig. 3
Fig.3Power transmittance of optical fibers as a function of length.

P = 1 Fig. 4
Fig.4(a) Core and cladding expansion at the incident beam interface for an unlubricated GNP-PDMS/FEP optical fiber as a function of time at two different pump powers.The (b) GNP-PDMS core and (c) FEP cladding edges were fit with a response function with parameters shown in the respective plots.

Fig. 6
Fig.6The edge position of two GNP-PDMS/Oil/FEP optical fibers as functions of time.The inset on the upper plot shows images of the optical fiber before illumination, immediately after the shutter was turned off for the first time, and after the completion of the first cycle.

Fig. 5
Fig.5The motion as a function of time for incident-beam edges of three different GNP-PDMS/ PTFE optical fibers.

Fig. 7
Fig. 7 (a) Reactions caused by diode laser hot spots.(b) Rare occasion ofgrinder complete optical fiber failure at high intensity.