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Abstract
The use of 3D-printing for designing a simple wavelength tunable device based on fiber Bragg gratings is demonstrated. Using fused deposition modeling (FDM), the fiber Bragg grating is embedded into a beam of polyethylene terephthalate glycol (PETG). Through bending, resulting in compression or tension of the optical fiber, the Bragg wavelength could be continuously tuned over a range of 60 nm, with maintained reflectivity and 3-dB linewidth.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The introduction of optical fibers has made great impact on modern communications technologies and fiber Bragg gratings (FBGs) represent one of the central inventions that adds functionality to optical fibers. Fiber Bragg gratings are widely used in optical fiber communications and optical fiber-based sensing [1–3]. As the Bragg wavelength changes in response to variations in surrounding conditions, such as temperature or strain, FBGs have been shown to be very useful as optical fiber sensors. Likewise, by modifying external parameters in a controlled manner one can design a tunable, or programmable, wavelength response with useful applications in, e.g., optical sensing [3–5], tunable laser sources [6,7,8] or spectroscopic analysis [9]. For many applications, a wide tunability, while maintaining the bandwidth of the grating wavelength is preferred. Methods commonly used to tune the Bragg wavelength is either by exposing the FBG to stress/strain, or through a change in temperature. In the latter case, the Bragg wavelength shifts approximately linearly with temperature, on the order of ΔλT ∼ 10 - 15 pm/°C for silica based optical fibers [2], and ΔλT ∼ 0.3 - 0.4 nm/°C for polymer optical fibers [10]. Applying tensile or compressive stress on the FBG, with the wavelength-strain response in silica fibers on the order of Δλɛ ∼1.2 pm/µɛ, provides a more convenient means of tuning, as it can be performed both faster and with a larger tuning range [3,5,6,11–13]. Compressive stress is mostly used to tune FBGs as the glass fiber provides greater strength in compression than in tension [6]. In previously reported work on compression tuning, the fiber was glued to the bending beam or molded into a composite beam [10–12].
Additive manufacturing has experienced significant development in recent years, simplifying the process of producing objects of complex shape [14,15]. Fused deposition modeling, which is a commonly used and commercially available 3D printing technology, extrudes thermoplastics layer-by-layer to build 3D objects with easily modified and customized design. An increasing variety of thermoplastics materials being made available, i.e., acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), PETG and nylon, enables 3D printing of objects with tailored thermal and mechanical properties, such as thermal expansion, stiffness, hardness, and electrical conductivity. Due to the small diameter of optical fibers that can easily be embedded during fabrication, 3D printing provides a versatile technique to produce custom designed fiber-based devices, e.g., FBG sensors and actuators [16] or dynamic long period gratings [17]. However, there has been no studies regarding the mechanical tuning behavior and capabilities of embedded FBGs, using FDM 3D printing techniques.
In this work we have used FDM to integrate FBGs into printed beam of PETG. Wavelength tuning is then performed through compression or tension using a simple 3-point bending setup. Embedded FBGs, having a 0.5 nm 3-dB linewidth, could be tuned over 60 nm with maintained spectral reflectivity. The effect of the embedding depth on tuning range, i.e. position of the fiber within the printed beam, was analyzed.
2. Design methodology
The approach for tuning of the FBG is based on a symmetrical three-point beam bending setup, shown schematically in Fig. 1. The coordinate axis of the 3D printed beam is shown in Fig. 1(a), with the beam centered at x = y = z = 0. The optical fiber is placed along the x-axis, at z = 0, at a predetermined distance (y) from the neutral plane, with the FBG positioned at the center of the beam. By reasons of symmetry, the x-z plane through origin corresponds to the neutral plane, which has no net stress, either under compression or tension, and therefore zero strain.
Fig. 1. Schematic layout (a) of the embedded FBG, and (b) the three-point beam bending setup, indicating the neutral plane (dashed line), the length (L), the embedding depth (y) and radius (r) of curvature of the 3D printed bar.
To simplify the analysis we assume that the three-point bending creates a curvature along the beam, as schematically shown in Fig. 1(b), where r is the radius of the corresponding circle, L is the distance between the two support points, and θ is the central angle. When bending the beam, the strain depends linearly on the displacement from the neutral plane [18]. For a fiber placed at a distance y from the neutral plane, the strain (ɛx) is then given by:
where ɛx < 0 indicates compression mode, and ɛx > 0 tension mode. The wavelength shift (ΔλB) of the FBG is proportional to the strain (ɛx) and is given by [1]: where ρe is the effective photoelastic constant (for silica ρe ∼0.22), and λB is the unstrained Bragg wavelength. Assuming the radius (r) is much greater than the deflection (δ) at the center of the beam, we can approximate the deflection using the versine (sagittal) approximation. The deflection is then given by:3. Experimental setup and preparations
3.1 FBG writing and characterization
A commercial photosensitive fiber (GF3, Thorlabs) with a cladding diameter of 125 µm was used to write FBGs. Type I gratings were recorded in the core of the fiber using a two-beam interferometer and a UV laser operating at 213 nm (Xiton Photonics, IMPRESS 213). To study the impact on various parameters of the 3D printing and the beam design, FBGs with lengths of 3 mm and 10 mm were used. The 3 mm FBGs had an unstrained Bragg wavelength of λB = 1558 nm, a reflectivity of 90%, and a 3-dB bandwidth of 0.5 nm. Corresponding values for the 10 mm long FBGs were λB = 1558 nm, a reflectivity of 60%, and a 3-dB bandwidth of 0.2 nm. Prior to UV exposure the protective coating was mechanically removed, at the location for grating inscription, over a length of either 15 mm or 50 mm. The FBGs were written at the center of the stripped region. To monitor changes in reflectivity and Bragg wavelength, FBGs were monitored in transmission using a white-light source (SuperK Compact, Koheras, spectral range 500–1750 nm), and an optical spectrum analyzer with an optical resolution of 0.06 nm (OSA, HP 86140), as shown in Fig. 2.
3.2 3D printing process
A commercially available FDM 3D printer (FlashForge Dreamer) was used to print the beam. The 3D printed beams in which the FBGs were embedded were designed with a cuboid shape of 100 (L) ${\times} 10 $ (w) ${\times}8$ (h) mm3. The FBG was embedded into the 3D print by pausing the printing process once the build had reached a specific layer, corresponding to a predetermined height (y). Small grooves, 0.4 mm wide, were made on the edges of the beam to help positioning and prevent the fiber from moving during printing. The fiber was then aligned onto the print with the FBG placed at the center using optical fiber clamps mounted on the print table. Once mounted, the printing was resumed. A slight tension ensured that the fiber did not move during the remaining printing process. The infill density of the printed beams was set to 100%. Longitudinal printing pattern, parallel to the fiber axis was used for better adhesion with the fiber and to prevent micro-bending losses due to angled printing tracks across the optical fiber. Layer resolution was set to 150 µm, slightly larger than the 125 µm diameter fiber, to reduce physical contact between the nozzle and bare optical fiber. The extruder temperature was set to Text = 235 °C while the print plate was maintained at 80 °C. The whole printing process, including fiber assembly and embedding the FBG, took approximately 55 mins.
To identify suitable print material for the 3D printed beam three different types of filament were initially evaluated: PETG, ABS, and nylon. Although ABS has higher stiffness compared to PETG and nylon, the 3D printed ABS beam cracked at tuning values below Δλ ∼ 20 nm. Nylon provides high flexibility enabling bending of the 3D printed beam through large angles without breaking. However, repeated wavelength tuning using 3D printed nylon beams resulted in a hysteresis in Bragg wavelength, likely due to relaxation of the material and possible slipping of the fiber. Out of the three materials evaluated, PETG was found to be the most suitable material for the 3D printed beam, having high stiffness while still being relatively flexible. In addition, PETG provided better adhesion to the fiber. In the following section we only include the results using PETG printed beams.
3.3 Three-point bending fixture
The setup for the three-point bending tests, shown in Fig. 3, was 3D printed using PLA filament, with 100% infill. The distance between the outer support points was L = 80 mm. Compression and tension tuning was performed by manually adjusting stainless steel bolts, pressing at the center of the beam, without moving the 3D printed beam from the setup, as interpreted in Fig. 3(a). In order to apply a more homogeneous force across the beam, a fixture with a curved inner surface (r = 90 mm), shown in Fig. 3(c), was inserted between the bolt and beam. The fixture was 3D printed using ABS filament and post-treated with acetone vapor to smoothen the contact surfaces. The beam deflection was measured using a digital Vernier caliper.
Fig. 3. (a) The three-point bending set-up. (b) CAD model of the three-point bending fixture. (c) CAD model of the pocket that holds the beam during bending.
3.4 Annealing
Annealing was performed by placing the beam in an oven at room temperature and raising the temperature to 110°C, at a rate of 1°C/min. Once reaching the set temperature, annealing was performed for a duration of 90 minutes and then allowed to cool down to room temperature. The importance of this procedure on the device’s tuning performance will be discussed in section 4.
4. Results and discussion
The Bragg wavelength of the embedded gratings all show a blue-shift of approximately 3 nm, corresponding to a compression of ∼2500 µɛ. Figure 4 shows the reflective spectral recordings of a 3 mm long FBG, measured at room temperature, before and after embedding into the 3D printed beam. The spectral similarity indicates a homogeneous embedding along the length of the FBG. The blue shift after embedding is a result of the elevated temperatures used during the 3D printing process (Text = 235 °C) combined with the large thermal expansion coefficient of PETG (αPETG ∼ 68·10−6 K−1). Once the 3D print cools down to room temperature the fiber will be in compression.
Fig. 4. Reflection spectra of a 3 mm long FBG prior to (black line), and after (red line) embedding in a PETG beam.
Figure 5 shows the reflective spectral characteristics during tuning of a 3 mm long grating embedded into a PETG beam. For this grating the coating was removed over a length of ∼15 mm prior grating inscription with the FBG embedded at a height y = 2.2 mm, relative to the neutral plane. The Bragg wavelength when no force applied (zero deflection) is marked with λ0. A total of Δλ=35 nm tuning was achieved, with 27 nm and 8 nm in tension and compression mode, respectively. Tuning beyond this range was possible but resulted in increasingly distorted spectral shape and decrease in reflection. To further extend the device’s tunability, the beam was annealed as described in section 3. The Bragg wavelength in neutral state shifted from 1554 nm to 1551 nm after annealing. Figure 6 shows the corresponding tuning range after annealing, extending the range to Δλ = 60 nm (Δλ = 35 nm without annealing), with 45 nm and 15 nm in tension and compression mode, respectively. The corresponding changes in FWHM and peak reflectivity during tuning is shown in Fig. 7. During the layer-by-layer printing process, non-uniform residual stress can accumulate in the 3D printed body [19,20], which will be reduced through post-annealing. More importantly, however, post-annealing will increase the strength and stiffness of the PETG, as well as increasing the homogeneity of the print and improving the attachment between the fiber and PETG. The effect would lead to reduced micro-bending along the fiber and grating, which can result in wavelength chirping and bending losses, enabling a larger tuning range without distortion of the FBG spectra.
Fig. 5. Wavelength tuning (Δλ∼35 nm) of 3 mm long FBG with ∼15 mm stripping length in 3D printed PETG beam without post-annealing, with y = 2.2 mm (relative to neutral plane). λ0 corresponds to zero deflection (δ=0).
Fig. 6. Wavelength tuning (Δλ ∼ 60 nm) of 3 mm long FBG with ∼15 mm stripping length in 3D printed PETG beam with post-annealing, with y = 2.2 mm (relative to neutral plane). Here λ0 corresponds to zero deflection (δ=0).
Fig. 7. Changes in (a) FWHM and (b) FBG reflectivity over a tuning range of 60 nm (3 mm grating length, y = 3.6 mm).
To compare the tuning characteristics of the FBG as a function of embedding height (y), several gratings where embedded at y = 2.2, 1, 0, −1, −2.2 mm (relative to the neutral plane). All FBGs had a length of 3 mm, with 50 mm of the coating removed at the grating location, and were annealed after embedding. The results are summarized in Fig. 8. Here experimental data is shown as symbols, and numerical values acquired using Eq. 4, as solid lines. Table 1 lists a comparison between calculated slope and experimentally measured slope using simple linear regression. The simplified expression (Eq. 4) predicts the linear relation between the shift in Bragg wavelength with the beam center deflection quite well, with increasing y-values resulting in larger slope. For large deflections however, there is a small walk-off between simulated and experimental values. The deviation is likely due to the assumption that the radius (r) is much greater than the deflection (δ) at the center of the beam, as well as the shape of the beam not having an ideal fixed radius curvature. For the same absolute values, i.e., at the same distance above or below the neutral plane, the results are quite similar indicating a homogeneous 3D print across the beam.
Fig. 8. Bragg wavelength vs beam deflection, showing measured values (symbol) and simulated values (lines) for gratings embedded at different depths (y). Measurement errors are ± 0.05 nm for Bragg wavelength and ± 0.05 mm for deflection.
Table 1. Slope coefficients of wavelength vs beam center deflection plot.
When increasing the length of the embedded FBG from 3 mm to 10 mm, the achievable tuning range was reduced significantly, as is shown in Fig. 9(a). Furthermore, the 10 mm long FBG showed significant distortion of the reflection spectra even for tension tuning as low as Δλ ∼ 5 nm, indicating poor quality of the embedding.
Fig. 9. Wavelength tuning of 10 mm long FBG with (a) 15 mm, and (b) 50 mm section of the coating removed.
By increasing the length of the removed coating from 15 mm (Fig. 9(a)), to 50 mm (Fig. 9(b)), the tuning range and spectral properties of the 10 mm long FBG was improved significantly, increasing to Δλ ∼ 20 nm. By only partially removing the fiber coating there is a discontinuity in diameter of the embedded fiber, corresponding to a change in diameter of 250 µm (fiber with coating) to 125 µm (fiber without coating). During the layer-by-layer printing the viscosity of PETG is not low enough to properly wet the fiber near the discontinued area of the glass fiber and polymer coating, resulting in an air-pocket and subsequently poor, or no adhesion between fiber and printed PETG at this location. With only 15 mm of coating removed, these printing defects are positioned in proximity to the 10 mm long gratings, affecting the strain distribution across the FBG. By removing the coating over a length of 50 mm, the effect of these defects is reduced, enabling larger tuning range. However, for greater deflection, slight chirping of the reflection spectra is still present, as shown in Fig. 9(b).
We also evaluated the tuning range of 3 mm long FBGs with 15 mm, and 50 mm coating removed. With the longer length of coating removed, the tuning range was reduced by approximately 20%, suggesting that the adhesion of PETG to the bare fiber is lower compared to the fiber coating causing slipping and micro-bending of the fiber within the printed beam for large values of deflection.
5. Conclusions
In this paper we demonstrate a simple method to fabricate a wavelength tunable filter based on fiber Bragg gratings. Using a commercially available FDM 3D printer fiber gratings were embedded within a polymer beam with wavelength tuning achieved, using a simple three-point bending setup, through compressive or tensile stress. Out of the different polymers evaluated, including ABS and nylon, PETG was found most suitable. The influence of the position of the fiber within the beam with relation to tuning range was evaluated both numerically and experimentally. The wavelength of a 3 mm long fiber Bragg grating near 1550 nm could be tuned over 60 nm without inducing loss in reflectivity or cause broadening of the reflection spectra. Factors influencing the tuning range are discussed, e.g., thermal post-annealing and adhesion between the optical fiber and the PETG. With an increasing availability of printing materials and multi-material deposition, such as carbon-fiber reinforced prints, the tuning range can likely be expanded even further.
The use of 3D printing and the ease of integrating fiber Bragg gratings into the print provides a flexible method to custom design fiber sensors, tunable fiber lasers and actuators for a wide number of applications, or towards prototyping and concept verification.
Funding
Stiftelsen för Strategisk Forskning (RMA15-0135); Knut och Alice Wallenbergs Stiftelse (2016.0104).
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