1. Introduction

The interesting characteristics of fiber optic sensors, such as compact size, low-cost, and immunity to electromagnetic interference, have attracted extensive interest among the research and industry fields. Among the different fiber optic sensors available, the ones based on long period gratings (LPGs) have been one of the most studied. Since their finding in early 1990s [1,2], they have been used in numerous applications in fiber optic systems. Among them are the capability to act as band rejection filters [2]; as gain flattening filters in erbium-doped fiber amplifiers [1]; mode converters [3]; suppression of stimulated Raman scattering in a double-clad fiber amplifier [4]; couplers [5]; polarizers [6]; and also in a wide range of sensing applications, namely for monitoring strain [7–9]; curvature [7]; torsion [7,10]; temperature [8,9]; refractive index [8]; biological [11,12], etc.

Depending on the application, LPGs sometimes need to be tuned in both loss and wavelength. These tuning properties are the principles behind any type of fiber sensor, where the measurement of the power or wavelength is transduced on the variable being measured. Yet, power measurement schemes are preferable compared to wavelength detection techniques, due to the cost of the equipment’s involved and also due to its simplicity. The wavelength filter location together with the dynamic control of its attenuation find also interesting opportunities in communication applications.

Due to the interesting characteristics presented by LPGs, its fabrication has been widely explored along the years, and different fabrication technologies have been developed. Among them are: the irradiation through CO₂ [9,13], infrared femtosecond laser [14], and ultra-violet [2,15]; electric arc discharge [5]; periodic tapering through chemical etching to produce a corrugated structure [7,16]; and mechanically induced by applying pressure on an optical fiber with a periodic grooved plate [1,15,17]. So far, laser irradiation techniques have been the most preferred method adopted by the scientific community. The reason is inherently related to the good quality of the gratings produced. However, the core to cladding coupling strengths cannot be tuned after fabrication, i.e., loss tunability and, on top of this, laser inscription approaches require capital-intensive equipment.

Periodic tapering through chemical attack is one methodology able to provide loss tunability [7,16]. Yet, it requires a dedicated system to evaporate metal in periodic ring patterns along the length of the fiber. Furthermore, the process needs skilled operators and the use of hazards chemicals.

Pressure induced LPGs were the first type of gratings to be reported in literature [1]. They were produced by pressing a periodic grooved structure onto an optical fiber. The periodic strain distribution causes periodic changes in the fiber refractive index due the photoelastic effect, resulting in the coupling between the fundamental core mode and the forward-propagating cladding modes. The periodic grooved structure has been developed in a variety of ways and recently, the use of simple technologies such as 3D printing revealed to be one simple choice to create these structures [17]. Overall, 3D printing technology has shown to be a great candidate in in a variety of fields [18,19]. The reason is related to its intrinsic advantages such as, simplicity, flexibility, print on demand, fit-for-purpose and fast design as well as production. In this technology, objects are fabricated layer by layer, allowing to build complex geometries that would be time consuming to mill or too expensive to create a mold for it. Common 3D printing methods include the widely used fused deposition modelling (FDM), selective laser sintering (SLS), ink jetting and “vat polymerization” technologies, which include: the stereolithography (SLA), the digital light processing (DLP) and the two photon polymerization (TPP) [19]. In all those methods, the printing material (filament, ink, powder or liquid resin, respectively), changes from a mobile state to a solid state during fabrication. Among all the 3D printing techniques described, those based on light polymerization are the ones that offer the best resolutions, achieving 25 µm for the DLP, 1 µm for the SLA and 200 nm for the TPP, making them very competitive compared for instance with the FDM that has ∼200 µm resolution. While the TPP and the SLA technology offers better resolution, 3D printers using the DLP method are faster (a whole layer is cured at a time instead of a laser scanning) and they are much cheaper, with prices on the market starting from 100 ${\$}$ for standard DLP printers [20], which is twenty, and thousand times lower than their counterparts. The small scale resolutions achieved with these printers revealed interesting opportunities in the fields of optics and photonics, and a variety of devices has already been demonstrated, namely optical fibers [21,22], multimode splitters [23], photonic bridges between fibers and photonic circuits [24], free space lenses [25], optical fiber lenses [26], optical fiber interferometers [27], and also to assist [28], induce [15,17,29,30], and permanently write [15], gratings in optical fibers. Considering the case of induced and permanently written gratings, we have recently shown that the use of 3D printed grooved plates have a dual use, either for UV inscription as well as for pressure induced LPG. While the former requires the use of a dedicated UV inscription system together with a photosensitive fiber, the latter is simple and only requires to press the grooved plate against the mask. However, the physics behind the method restrings its use only for pressure applications, and recently for temperature measurement [30]. For several applications, it would be much more attractive if mechanical forces other than pressure are used. To date, the interesting characteristics of optical fibers led to the development of torsion and shear-strain sensors, that are important mechanical parameters used to monitor the health condition of large scale engineering structures, such as buildings, dams, bridges, robots, etc. [31]. From the several reported fiber optic sensors found in literature, they rely on the use of complex fabrication procedures, special fibers and setups in order to measure these quantities [7,10,31–36]. On top of this, despite the efforts developed by different authors, the majority of the works rely on the use of wavelength detection schemes which lack in attractiveness when compared to the intensity based ones.

In this work we report the fabrication of an LPG fiber sensor with high sensitivity to shear-strain and torsion loads, through the bonding of an optical fiber to a periodic 3D printed grooved plate. The grating formation results from the external mechanical forces applied to the device., that through the photoelastic effect, changes periodically the refractive index of the fiber. This allows to tune the loss of the filter very easily and with high sensitivity. In addition, due to the low drift of the resonance bands observed during the tuning range, a dynamic test will be performed using low-cost intensity based schemes, composed of a laser centered at the resonance band and a photodetector to monitor the dip losses. The use of different grooved plates periods to select the wavelength location of the resonances will be also accomplished. To finalize, it will be shown the capability to fabricate an LPG fiber sensor with specific coupling strength. For that, an amount of shear-strain will be applied to the grooved plate before the fiber to grooved plate bonding process. This LPG fiber sensor still presents the capability to be tuned and tests on this subject will be also performed.

2. Working principle

Long period gratings are optical fiber structures, with periodic refractive index modulations ranging from 100 µm to 1000 µm, capable to couple light from the fundamental guided core mode to the co-propagating cladding modes at selective wavelengths as described by [37]:

When an external load is applied to the structure under mechanical equilibrium, the forces will be equally distributed along the bonded and unbonded regions. Taking into account the photoelastic effect, the fiber refractive index change in each corresponding region (i), may be written as:

 

Fig. 1. Proposed fiber optic sensor composed of a 3D printed polymeric grooved plate with an optical fiber bonded onto it.

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The transmittance of an LPG may be expressed through the ac component of the coupling coefficient $k_{co - cl}^{ac}$, between the core to the cladding. The transmittance has a cosine-squared relationship and is defined following Eq. (3), [37]:

3. Methods

3.1 Grooved plate fabrication

The grooved plates were designed with the help of a computer aided design (CAD) software. For that, a total of 100 rectangular hollow regions with 8 mm in height, spaced by a period Λ and with duty cycle of 50% were considered. The number of periods and duty cycle can be easily changed by the designer. However, the values presented in this work are just used as proof of concept. Yet, it is worth to mention that the high number of periods used in this work (high grating lengths), allow to obtain small linewidths [2], and this could be interesting to improve the precision of the algorithm to find the location of the dip resonance. The periods explored in this work ranged between 500 to 700 µm in steps of 50 µm. The grooved plates were drawn with dimensions of 16 mm in height, 5 mm in width and had lengths given by the grating period times the number of periods (e.g., for a grooved plate of 650 µm period, the total length is about 65 mm). An image of the drawn grooved plate may be seen in Fig. 2(a).

 

Fig. 2. CAD image of the grooved plate (a). Grooved plates right after the 3D printing (b). Picture of a 650 µm grooved plate (c).

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After drawing the grooved plates, the stereolithography files were imported to a low cost (∼150${\$}$) consumer grade DLP 3D printer (Photon from Anycubic [20]). This printer is based on the LCD shadow mask technique, using a 405 nm LED. The LCD has a resolution of 47 µm in both directions. Furthermore, resolutions as high as 1 µm can be achieved in the printing direction. The liquid resin used in this work was a standard clear UV resin from Anycubic (30${\$}$ per liter) [20]. This photosensitive resin provides high-speed solidification (5 to 15 s per layer). Additionally, it provides high success rate of printing and precision. Materials printed through this printer show to be rigid and tough, presenting hardness (D) and tensile strength values of 79 and 23.4 MPa, respectively. The printed objects show also the capability to be elongated up to 14.2%. All these parameters make this resin well suited for the purpose of this work. The grooved plates were printed following the direction indicated by the red arrow shown on Fig. 2(a). The layer thickness was set as 50 µm and the exposure time per layer to 5 s. An additional 60 s of exposure was given for two button layers in order to firmly attach the model onto the building platform. Considering the above parameters, only 30 min are needed to fully print several grooved plates. Furthermore, considering the volume needed to print a single grooved plate, we estimate a total cost of few cents per grooved plate, making the fabrication simple and low cost, which are interesting characteristics for mass production. A picture of the grooved plates right after being 3D printed may be seen in Fig. 2(b). After the fabrication, the excess unpolymerised resin was washed out with isopropyl alcohol in an ultrasound bath, allowing to easily remove the unpolymerized resin clogged in between the patterned holes. The grooved plates are then post-cured in sun for 2 h and then, thermally post-cured at 60°C and 70°C, during 6 h each, allowing to enhance its strength properties. A picture of a grooved plate with 650 µm period is shown in Fig. 2(c).

3.2 Surface bonding of an optical fiber to a 3D printed grooved plate

The fiber sensor approach used in this work is based on the periodic strain transfer from the 3D printed grooved plate to the optical fiber attached onto it, creating a new sensor approach based on the LPG formulation. To achieve this, the fiber was simply bonded to the surface of the grooved plate using the same polymer resin used to print the grooved plate. For that, the resin was carefully brushed onto the surface of the plate, leaving just a thin layer, without dropping it into the hollow regions. The surface tension of the liquid resin onto the periodic pattern ([i.e., associated to the viscosity of the resin (552 mPa/s)] is helpful during this task.

The fiber used in this work was a standard single mode fiber, presenting a cut-off at around 1260 nm, diameters of 8 µm and 125 µm and refractive index of 1.450 and 1.444, for the core and cladding, respectively.

A portion of the optical fiber coating, with length similar to that of the grooved plate, is removed and then, laid down onto the resin covered area of the plate. The fiber portions that run outside the grooved plate are secured with tape to two objects with the same height and placed in the vicinity of the plate. Thus, allowing to keep the fiber in a stable and straight position. The resin is then polymerized using a 365 nm hand-held UV light source (Opticure LED200 from Norland Products Inc.), with a power density of 2.5 W/cm². The schematic of the procedure used to create the grating device may be seen in Fig. 3. To enhance the strength of the device and to remove low strength polymer chains that could easily break during the mechanical characterizations. Finally, the fiber devices were thermally cured in an oven at 60 °C and also at 70 °C, during 12 h each.

 

Fig. 3. Schematic of the process used to fabricate the LPG. (a) Brushing the surface of the grooved plate with resin. (b) Fiber attachment to the grooved plate. (c) Hardening process through UV radiation.

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3.3 Shear-strain and torsion characterizations

The characterizations were performed by monitoring the transmission spectra as function of the external forces. For that, one optical fiber terminal is connected to a supercontinuum broadband optical source (Fianium Whitelase model SC-400-2), while the other is connected to an optical spectrum analyzer (Advantest Q8384). During the experiments, all the fibers were kept fixed in order to prevent any possible light fluctuation due to possible polarization dependence created by the fiber device.

For the shear-strain (γ) characterization, a small portion of the grooved plate is immobilized and in the diametrically opposed end a motorized micrometer linear stage (MFA-CC from Newport Corporation) is used to apply the load to the grooved plate. An example of the setup used for the shear-strain tests may be seen in Appendix A1.

The micrometer displacements (d) were made in steps of 10 µm up to 230 µm, which considering the height of the grooved plate (16 mm), corresponds to shear-strain steps of 0.63 mε up to 14.38 mε. An example of the forces in which the fiber filter has been subjected is shown in Fig. 4(a).

 

Fig. 4. Fiber filter when subjected to shear-strain (a) and torsion (b).

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Regarding the torsion tests, a motorized rotation stage (URB100CC from Newport Corporation) was used to apply torsion (θ) to the fiber filter as exemplified in Fig. 4(b). Thus, a small portion at the end of the grooved plate (∼3 mm) is clamped to stay in a static position and in the other terminal, another small portion of the grooved plate is secured at the head of the rotation stage. The schematic setup used for the torsion characterizations may be seen in Appendix A1. The tests were made by applying torsion to the grooved plate in steps of 0.3 deg up to 8.4 deg.

Polymers are known from their viscoelastic properties, meaning that after subjecting them to a step of load, they need a certain amount of time to reach a stable configuration. This occurs due the molecular rearrangement of the polymer chains, which dissipate part of the accumulated energy as plastic deformation. From early studies, we observed that a total of 60 s is enough to reach a steady state, as will be observed in Fig. 9. Thus the spectra obtained in this work were collected 60 s after applying the load, allowing the material to recover to a steady state.

3.4 Dynamic characterizations

Due to the simplicity and low cost opportunities of intensity based detection schemes, we decide to characterize the fiber sensor using this approach. Thus, the wavelength based detection system used in the previous section was replaced by a narrowband laser at the input of the optical fiber and a photodetector at the output. For the purpose of demonstration, a tunable laser [OSICS-ECL module from Yenista (1500–1620 nm)] was centered at one of the resonant wavelengths of the sensor, and a power meter with an acquisition frequency of 2 Hz, was used to measure the power changes induced by the external forces.

To show the possibility of using this fiber sensor in real time operation, we performed low frequency dynamic shear-strain and torsion tests through an automated shear-strain testing scheme. This test comprises alternative changes in the direction of the load and successively increases the tensile and compressive forces. It is worth to mention that, prior to the dynamic characterizations, the fiber sensor had been pre-loaded with ∼3.2 mε and ∼2.5 deg, for the shear-strain and torsion tests, respectively. This allowed the sensors to work at the linear region of the filter transmission ratio response as function of the external load.

3.5 Period-wavelength dependence of the fiber filter

The capability to select the location of the resonance wavelengths can be simply performed by selecting the period of the 3D printed grooved plate. With this in mind, fiber filters with different resonance wavelengths were fabricated by bonding optical fibers to 3D printed grooved plates of different periods, i.e., 500:50:700 µm. After the fabrication, the devices were subjected to an amount of shear-strain capable to induce strong core to cladding couplings.

3.6 Inducing of permanent coupling strengths: pre-straining process

To permanently induce filter resonances with specific dip transmissions, without the need of an external force after the fabrication process, the periodic refractive index modulation associated to the photoelastic effect needs to be “frozen-in stress”. Thus, the fabrication process described in section 3.2, need an additional processing step. Due to the simplicity of the shear-strain testing scheme [see Fig. 4(a)], we decide to use this system. The amount of shear-strain imposed to the 650 µm grooved plate was 20.3 mε (∼2%). The optical fiber was placed onto the surface of the 3D printed grooved plate and the resin was hardened using the same hand-held UV light source. The annealing process was then followed as previously described.

4. Results and discussion

4.1 Grooved plate properties

The 3D printed grooved plates were observed under a microscope (Leica DM750), to quality assess their properties, namely: surface roughness and grating period. The results are shown in Figs. 5(a)–5(c) for the grooved plates with period of 550 and 700 µm. As can be seen, the periods of the grooved plates are well reproduced, presenting similar values to the ones drawn on the CAD software. The surface appears with good quality, presenting a negligible undulation with period of 50 µm [see Fig. 3(c)] associated to the layer thickness defined in the 3D printing settings. The surface quality of the grooved plate could be easily improved by reducing the layer thickness during the writing time (i.e., it can go up to 1 µm step). However, this would increase the printing time and preliminary results regarding the use of these high definition grooved plates didn’t show any benefits compared to the results achieved in this work.

 

Fig. 5. (a) Microscope images of the 3D printed grooved plates with periods of 550 µm and (b) 700 µm. (c) Inset of the region within a grooved period, showing a surface relief with periodicities of ∼50 µm associated to the printing layer thickness. Microscope images taken with different magnifications (d)-(f) for an optical fiber surface bonded to a grooved plate with 650 µm period. Note that the focus was always set at the top most region.

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4.2 Surface bonding of an optical fiber to a 3D printed grooved plate

The attachment of the optical fiber to the grooved plate periodic pattern was easily accomplished through the surface tension created by the resin in the regions composed by the optical fiber and the grooved periods. This can be observed on the microscope images taken for the grooved plate with period of 650 µm shown in Figs. 5(d)–5(f). As can be seen, the hollow areas of the grooved plate were not clogged by the resin, allowing the structure to move freely if subjected to external loads. After bonding the optical fiber to the grooved plate, the output spectrum, shows dip resonances with small coupling strengths (∼1 to 2 dB loss). This was the result of the strain induced by the resin after polymerization, which decreases its volume and compresses the fiber periodically along the length of the grooved plate. Due to the photoelastic effect, a periodic modulation of the refractive index along the length of the fiber is built, allowing to couple light from the fundamental core mode to the forward propagating cladding modes. At the early moments after the device fabrication, the strain built-in along the periodic grooved plate is not yet stabilized due the viscoelastic nature of polymers. As a result, the strength of the core to cladding mode coupling starts to decrease up to the equilibrium in the next hours. The device is not yet fully operational and an annealing process is performed, allowing to break low strength polymeric chains that otherwise would easily break when subjected to external loads. At the end of this fabrication process, the coupling strength is low with dip losses ≤ 1 dB [red spectra shown in Figs. 6(a) and 6(b)].

 

Fig. 6. Transmission spectra obtained for the different core-cladding couplings, as function of shear-strain (γ), shown in (a) and torsion (θ), shown in (b). The arrows indicate the grating growth with increasing load. The period of the grooved plate is 650 µm.

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4.3 Shear-strain and torsion testing results

Based on the assumption that the strain induced in the periodic regions of the grooved plate is transferred to the optical fiber through the bonded regions as is detailed in the theoretical analysis provided in the Appendix A2, the fiber sensors were characterized to external forces such as shear-strain and torsion. The results shown in this section are related to the 650 µm period grooved plate. However, the general conclusions also apply to grooved plates with other periods. The transmission spectra as function of shear-strain and torsion loads are displayed in Figs. 6(a) and 6(b), respectively.

As observed in Figs. 6(a) and 6(b), the fiber filter has a transmission spectra with three dip resonances located at ∼1505 nm, ∼1547 nm and ∼1643 nm. At the very beginning, when neither shear-strain nor torsion are applied to the fiber sensor, these dip resonances show very weak couplings strengths (<1 dB). However, the coupling strength for each resonance mode increases as the external load increases (i.e., shear-strain, torsion). This result was associated to the photoelastic effect, since the increase on the load applied to the fiber sensor increases the periodic refractive index changes. Consequently, stronger couplings between the forward propagating core mode to each of the cladding mode resonances are achieved. A clear analysis of this power transfer is shown in Figs. 7(a) and 7(b), where the transmission ratio of each dip resonance is plotted as function of the shear-strain and torsion, respectively.

 

Fig. 7. Transmission ratio as function of shear-strain (a) and torsion (b), for the three dip resonances that appeared in Fig. 6.

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At the very beginning, when the fiber sensor is unperturbed, the transmission ratio of the dip resonances is around 0.8–0.9. This value is associated to the residual stresses created during the sensor preparation, such as polymer shrinkage due to the photopolymerization process. It is worth to mention that the dip losses found in Figs. 7(a) and 7(b) are slightly different for the shear-strain and torsion tests. Yet, this was the result of the positioning of the fiber sensor in each of the characterization setups.

As the fiber sensor is subjected to an increase load, the transmitted power at each resonance mode becomes weaker (i.e., the dip losses become stronger), presenting a proportional behavior between the transmission ratio and the external load. This linear behavior extends up to 6 mε for the 2^nd and 3^rd dip resonances while 8 mε for the 1^st dip resonance. These values are reached when the transmission ratio is minimum (i.e., ∼0.1, corresponding to ∼10 dB dip loss). The sensitivities regarding the shear-strain characterizations, were 0.10 /mε for the 1^st dip resonance, while 0.12 /mε for the 2^nd and 3^rd dip resonances. We believe that we are in the presence of the first tunable LPG based on a shear-strain load. Furthermore, the tuning range of the device is four times higher than the one reached with Bragg gratings [38], a characteristic we attribute to the host material (polymer), that allows to tune the fiber filter easily without breaking the fiber.

Regarding the torsion tests, the sensitivities obtained for the 1^st, 2^nd and 3^rd dip resonances for the linear region, i.e., ranging from 1-∼4 deg, were 0.19/deg, 0.21/deg and 0.18/deg, respectively. We believe that these sensitivities are the highest reported so far for all fiber sensors [10,35], and two orders of magnitude higher than the one achieved in [7], i.e., 0.0026/deg, for a corrugated LPG created by the strain induced effect as is the case studied in this work. One side effect of this high sensitivity is observed on the low dynamic range of the sensor, which contrasts with the hundreds of degrees’ range presented by the majority of the fiber sensors reported in literature. Yet, the strengths presented by this fiber device are still very interesting and a variety of applications are still valid (see Appendix A4).

When the external load is increased for values higher than those achieved for the linear region (>8 mε and >4 deg, for the shear-strain and torsion loads, respectively), the transmission ratio of the resonances starts to saturate, reaching its minimum (maximum dip loss) at around 10 mε and 6 deg, for the shear-strain and torsion loads, respectively. Then, the transmission ratio starts to increase. This indicates that the power transfer from the core mode to each of the cladding mode resonances reached its maximum. From that point (i.e., maximum coupling efficiency), the cycle is reversed, where the cladding modes will transfer the power to the fundamental core mode. This occurred until the end of the characterizations where the highest loads applied were 14.4 mε and 8.4 deg, for the shear-strain and torsion tests, respectively. This phenomenon is similar to the overexposure case in the fabrication of photoinduced LPGs and is in accordance with the oscillatory transmission function found for LPGs as described by Eq. (3), [37].

One very interesting characteristic shown by the results presented in Fig. 9, is the ability to easily tune the output power with small loads. Another one is the low wavelength shift during the loss tuning. This may be seen in Figs. 8(a) and 8(b), where wavelength shifts lower than 2 nm are obtained during the full power tuning operation range (for shear-strains up to ∼10 mε and torsion loads up to ∼6 deg).

 

Fig. 8. Wavelength shift as function of shear-strain (a) and torsion (b), for the three dip resonances that appeared in Fig. 6.

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Fig. 9. Transmission ratio of a narrowband laser centered at the 2^nd dip wavelength of the fiber sensor, when subjected to dynamic conditions, such as shear-strain (a) and torsion (b). The imposed and calculated shear-strain and torsion loads are also represented. The grooved plate period is 650 µm.

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The wavelength shift response of the fiber sensor for low shear-strain and torsion values (i.e., ∼<3 mε and <2 deg, respectively) shows a non-linear behavior. Yet, for higher loads, it is possible to see that the dip wavelength shift resonances present a proportional behavior with the external load. The associated sensitivities for the for the 1^st, 2^nd and 3^rd dip resonances were 398.1 pm/mε, 387.8 pm/mε and 365.7 pm/mε for the shear-strain characterizations and 240.5 pm/deg, 190.6 pm/deg and 162.2 pm/deg for the torsion tests, respectively. For such linear regions, one could propose the fiber sensor for the simultaneous measurement of shear-strain and torsion, through the construction of a 2 × 2 matrix containing the transmission ratio and the wavelength shift sensitivities..

4.4 Dynamic characterizations

Considering the low wavelength drifts achieved during the full power tuning range of the fiber sensor (i.e., < 2 nm) and taking into account that the 3 dB bandwidth of the gratings is reasonable (5 nm), we may see an interesting application regarding low frequency dynamic low cost intensity based sensors. To show this ability, we measured the output power of a narrowband laser centered at the second dip wavelength resonance, (the one that shows the highest transmission ratio sensitivity), and measured the transmission ratio as function of the imposed shear-strain and torsion loads. The results may be seen in Figs. 9(a) and 9(b). Also in the same figures it is shown the calculated shear-strain and torsion, obtained taking into account the measured transmission ratio and the sensitivities taken from Figs. 7(a) and 7(b), respectively.

As can be observed in Fig. 9, the sensor responds very well to both shear-strain and torsion loads, following the load steps exactly as predicted. Minor errors may be associated to the wavelength shift of the dip resonance, i.e., <0.6 nm, during the characterization tests for the load spans used, i.e., ∼3.2 ± 1.6 mε and ∼2.5 ± 1.6 deg, for the shear-strain and torsion tests, respectively.

One clear difference observed in Figs. 9(a) and 9(b) is associated to the different time scales used to test the fiber sensor to each external parameter. This discrepancy was associated to the time response needed by the fiber sensor to reach a stable behavior in each characterization test. We found that for the shear-strain test it took approximately 60 s to achieve a stable behavior, while only 5 s are needed for the torsion tests. The phenomenon is associated to the elasticity of the 3D printed polymer grooved plate, in each tridimensional direction, being more prone for viscoelastic properties in the shear-strain configuration than in the torsion one. In the overall, for the time spans used in each test, the hysteresis is negligible for small load amounts and the experimental data points seem to perfectly overlap the theoretical ones. Yet, for higher loads, the device requires longer time to relax (due to the memory effect of accumulated stress [39]), and some decay over the allowed time span is observed. In order to estimate the mean errors of the system regarding the imposed and the measured load, we considered the mean of the data points corresponding to the last 20% of the step load. From that, we obtained values of 8.1 µε and 0.03 deg for the shear-strain and torsion tests, respectively.

4.5 Period-wavelength dependence of the fiber filter

After bonding the optical fibers to 3D printed grooved plates of different periods, i.e., 500:50:700 µm, the devices were subjected to an amount of shear-strain capable to induce strong core to cladding couplings. The resultant transmission spectra (with offset), may be seen in Fig. 10(a), while the evolution of the dip resonances as function of the grating period may be seen in Fig. 10(b).

 

Fig. 10. Transmission spectra with offset (a), (tick spacing of 25 dB), obtained for different grooved plates [500:50:700 µm (top to bottom)], induced by applying a certain amount of shear-strain to the fiber filters. Dip wavelengths as function of the grating period (b). The insets show the correspondent HE_1n modes used for the simulation.

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The spectra shown in Fig. 10(a) where obtained for shear-strains capable to induce strong core to cladding couplings. As can be seen, the 500 µm period fiber filter shows four dip resonances. Those are also seen in the following fiber filters (with increasing period), which are shifted to longer wavelengths. By tracking the wavelength of the dip resonances it is possible to observe a monotonous increase at a rate of ∼1.3 to 1.7 nm/µm as is shown in Fig. 10(b), showing the easiness on the wavelength tunability of the fiber filter. Still in Fig. 10(b), it is possible to observe the theoretical phase curves obtained using the optigrating v4.2 software for a standard Ge-doped SMF with diameters of 8.2 µm and 125 µm and refractive index of 1.4491 and 1.4440, for the core and cladding regions, respectively. The gratings were modulated with a refractive index of 2 × 10⁻⁴ considering the coupling of the fundamental HE₁₁ mode to the HE_1n modes, being n = 2, 3, 4 and 5. As is seen in Fig. 10(b), the theoretical curves are in good agreement with the experimental ones. Small discrepancies, could be associated to the resolution of the printer used to fabricate the grooved plates as well as with the precision on the parameters used for the simulation.

As is shown in Fig. 10(a), some fiber filters present coupling strengths that can be as high as 24 dB, as is the case presented for the 2^nd dip resonance of the fiber filter with period of 550 µm. This however, led to achieve lower coupling strengths for the other resonances that appear in the wavelength span used. Yet, stronger coupling ratios for the other resonances are easily achieved through the proper choice of the load amount.

4.6 Inducing permanent coupling strength: pre-straining process

The mode coupling strength achieved by the fiber sensor developed in this work is dependent on the amount of the external load. Yet, for some applications it is worth to have a filter with a permanent coupling strength, without the need to apply an external load. To show this capability, a pre-straining condition of the grooved plate needs to be performed during the fabrication process. For that, a 650 µm period grooved plate was initially subjected to a shear-strain of 20.3 mε (∼2% deformation) before bonding the fiber to the grooved plate. This high value was considered in order to present strong dip couplings even after considering an annealing process. The fiber was laid in a straight position onto the grooved plate covered with a thin layer of the resin, then, the UV curing process was followed. The pre-load is then released and the device is let to stabilize for a few hours in order to remove the polymeric viscoelastic characteristics. Then, an annealing process is performed to strength the mechanical properties of the fiber sensor. The pictures of the final sensor when a broadband light source is injected into it are shown in Figs. 11(a) and 11(b), for the captures made with and without room light. The spectra of the structure and the near-field profiles may be seen in Fig. 11(c).

 

Fig. 11. Pictures of a 650 µm period fiber sensor (fabricated by pre-straining the grooved plate with 20.3 mε before the fiber bonding step), showing a periodic leakage of light at the grooved regions. The pictures were taken by injecting a broadband light source into the fiber sensor and capturing the pictures with (a) and without (b) exterior light. The corresponding grating spectrum is shown in (c), where the insets show the near-field profiles for the of the 1^st and 2^nd dip resonances.

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The pictures shown in Figs. 11(a) and 11(b), show a periodic pattern of light scattering along the length of the fiber attached to the grooved plate. Such characteristic has also been observed in the prior characterization studies, when the loads were high enough to induce strong dip resonances. Thus, the visual observation was an indicator that strong core to cladding mode couplings could be also present in this configuration. The spectrum shown in Fig. 11(c) demonstrates this aspect, showing spectral characteristics resembling the ones shown in Fig. 6 for the grating fabrication without pre-strain. Yet, the dip wavelengths were slightly red-shifted, showing values of center wavelength of ∼1511, ∼1556 and ∼1655 nm, for the 1^st, 2^nd and 3^rd dip resonances, which correspond to ∼6, ∼9 and ∼12 nm shifts, respectively, when compared to the ones obtained when the fiber is bonded to the grooved plate without pre-straining it. The values were much higher than the ones estimated from the shear-strain sensitivities calculated in Fig. 6(a). However, the discrepancies may be related to the change of the grating period when the grooved plate is pre-strained (i.e., the periods of the grooved plate become slightly tilted when the grooved plate is under shear-strain). Overall, the spectrum appears with good spectral profile showing low out-of-band loss and dip losses of ∼10 dB for the 1^st and 3^rd dip resonances, and ∼17 dB for the 2^nd resonance. The near-field profile of the coupled modes for the 1^st and 2^nd resonances were also measured and are shown on the insets of Fig. 11(c). From those, it is possible to see light propagating outside of the core region and also evidences for some symmetry along one axis of the fiber. From the simulation results, the near-field images collected for the 1^st and 2^nd dip resonances should correspond to the HE₁₂ and HE₁₃ modes. We need to take into account that the cleavage process at the far end of the grooved plate is not an easy task and thus, the near field images collected in this work are not perfect.

4.7 Shear-strain characterization of a pre-strained fiber sensor

To verify if the dip losses of the fiber sensor are still tunable after the pre-straining bonding process, we characterize it to shear-strain (i.e., in opposite direction to that used in the fabrication process). The results are shown in Figs. 12(a) and 12(b) for the transmission ratio and for the center wavelength of the transmission dips, respectively.

 

Fig. 12. Transmission ratio (a) and resonance wavelength shift (b), obtained for the different resonance dips when the device is subjected to increasing steps of shear-strain.

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In this test, the characterizations were taken up to ∼24 mε, allowing to see how the device behaves for shear-strains up and above that used on the pre-strained condition (i.e., 20 mε). As can be seen, for shear-strains ranging from ∼2 mε up to ∼10 mε, the transmission of the dip resonances increases proportionally with the increasing strain, showing sensitivities of 0.09/mε, 0.10/mε and 0.09/mε, for the 1^st, 2^nd and 3^rd dip resonances, respectively. Then, for shear-strain values above ∼13 mε, up to values of ∼20 mε, the cycle is reversed and the transmission ratio decreases to its minimum, showing sensitivities of 0.14 /mε, for the 1^st dip resonance and 0.16/mε for the 2^nd and 3^rd dip resonances. For values above 20 mε the cycle is repeated again, where the transmission ratio starts to increase again, with agreement with the cosine squared relationship presented in Eq. (3). Note that the transmission ration for shear-strains of 20 mε (the same amount used to pre-strain the grooved plate), would be expected to be close to 1 (minimum dip losses). However, the polymer conformation after hardening the liquid resin, removing the pre-strain and performing the annealing process, leads to have specific core to cladding coupling strength.

The shear-strain characterization was only conducted up to ∼24 mε since we could reach the plastic regime of the device. Yet, the power transfer between the fundamental core mode to the forward propagating cladding modes will follow the same cycle tendency. The dip wavelengths where also monitored during the characterization showing a blue-shift for shear-strains up to 20 mε and a red-shift for values above that, which coincides exactly with the value used to pre-strain the grooved plate. Due the low dip loss reached at 12 mε, together with the increase of resonance bandwidth, the accuracy on the detection of the center wavelength is poor. Because of that, the linear regression model was only applied to the data points below 8 mε, showing sensitivities of −337.8 pm/mε, −402.2 pm/mε and −515.6 pm/mε, for the 1^st, 2^nd and 3^rd dip resonances, respectively, which were similar in absolute value to the ones measured in prior experiments for the fiber sensor fabricated without pre-strain. By characterizing the dip transmission ratio and dip wavelength shift as function of torsion, one could reach a fiber sensor capable to simultaneous measure shear-strain and torsion as previously described for the induced LPG. Yet, due the cosine-squared relationship the simultaneous measurement could only be performed for shear-strains and torsion loads that are within the first linear regions.

The temperature cross sensitivity needs always to be taken into account when developing a fiber optic sensor. The temperature sensitivities of the fiber device were 0.003/°C, 0.002/°C and 0.002/°C, for the 1^st, 2^nd, and 3^rd dip resonances, respectively, as is shown in the Appendix A3. Considering the shear-strains ranging from ∼2 mε up to ∼10 mε, the cross sensitivities can be calculated as 0.03 mε/°C, 0.02 mε/°C and 0.02 mε/°C, respectively. These cross sensitivities are low but cannot be neglected when the sensor is operating in high temperature variations. Thus, discrimination between both parameters needs to be implemented. One possible solution could be through the use of an in-series reference sensor operating in a different wavelength range, such as the one shown in Fig. 10(a) for the 1^st dip resonance, for the 500 µm period grooved plate.

In the overall, we showed the possibility to modulate periodically the fiber refractive index in a permanently way by shear-straining the grooved plate before the fiber to grooved plate bonding process. Furthermore, the fabricated fiber sensor is still able to tune the losses of the transmission bands by subjecting the fiber device to external loads.

5. Conclusion

In this work we have shown the capability to periodically modulate the refractive index of an optical fiber through shear-strain and torsion loads. The fiber sensor is fabricated by surface bonding an optical fiber to a 3D printed periodic grooved plate. The loss tunability of the device was tested by subjecting it to external loads, such as shear-strain and torsion. The results showed the capability to fully tune the coupling strength (∼0 up to ∼20 dB) of the core propagating mode to each of the cladding mode resonances with values as low as ∼10 mε and ∼6 deg, for the shear-strain and torsion tests, respectively. Results regarding the dips transmission ratio as function of the external load showed linear behaviors with high sensitivities, achieving values of 0.10/mε to 0.12/mε and 0.18/mε to 0.21/deg, for the shear-strain and torsion tests, respectively. To the best of our knowledge these are the highest values found in the state of art. Another interesting characteristic was associated to the low wavelength shift (<2 nm) achieved during the full tuning operation range. Such characteristic was used to show the device working in low frequency dynamic applications and with intensity detection schemes which are interesting for low cost applications. The fiber sensor presented good response, following the load exactly as predicted.

The capability to select the wavelength at which the resonance wavelengths occurs has also been demonstrated by the use of different grooved plate periods.

The fabrication of a permanent LPG with specific coupling strength and still capable to be loss tunable was also demonstrated. This was achieved by pre-straining the 3D printed grooved plate with a shear-strain of 20 mε, before the fiber to grooved plate bonding process. The result was a permanent LPG with dip resonances up to 17 dB. Nevertheless, the possibility to tune the loss of the resonance modes is still possible to achieve and this has been performed by subjecting the fiber sensor to shear-strain loads. The results showed sensitivities similar to the ones obtained for the fiber sensor created without pre-straining the grooved plate.

The devices presented in this work are very simple and require low operator skills to construct. They are low cost, compact and have the possibility to be used with simple demodulation schemes such as the ones based on intensity. Those characteristics make this fiber sensor very appealing for the monitoring of loads in engineering structures, by surface bonding the device to the structure under test (see examples of application in Appendix A4). Furthermore, the tuning characteristics of the filter make it very interesting for dynamic fiber components applied to communications. To finalize the filters presented in this work pave the way for an easy, simple and cost effective solution to induce LPG tunable filters for both sensor and communications applications.

Appendix A1

Fiber optic sensor characterizations

The shear-strain characterizations were performed by placing the grooved plate, on top of a motorized micrometer linear stage (MFA-CC from Newport Corporation), being this last secured to the optical table. The fiber that is bonded to the grooved plate is facing upwards and is parallel to the motorized stage movement. The setup includes one bolt that is fixed onto the optical table, used to immobilize one corner of the grooved plate. On the opposed end of the grooved plate, another bolt is fixed onto the moving part of the micrometer stage. The micrometer displacements (d) were made in steps of 10 µm up to 230 µm, which considering the height of the grooved plate (16 mm), corresponds to shear-strain steps of 0.63 mε up to 14.38 mε. A schematic representation of the setup used for the characterization may be seen in Fig. 13(a).

 

Fig. 13. Drawings of the mechanical setups used for the shear-strain (a) and (b) torsion characterizations.

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For the torsion characterizations, a small portion of the grooved plate (∼3 mm), is secured onto the motorized rotation stage (URB100CC from Newport Corporation), being this last secured to the optical table. On the other end of the grooved plate, a small portion of it is secured and fixed onto the mechanical table through mechanical posts. The mechanical parts used to secure the grooved plate contain holes that allow the fiber to pass through. The tests were made by applying torsion to the grooved plate in steps of 0.3 deg up to 8.4 deg. A schematic representation of the setup used for the characterization may be seen in Fig. 13(b).

Appendix A2

Theoretical stress distribution along the optical fiber device

When the proposed fiber optic sensor is subjected to shear-strain or torsion loads, the amount of strain in the bonded and unbonded regions changes, leading to change the refractive index of the fiber through the photoelastic effect. To better understand the stress distribution across the optical fiber, we performed a finite element analysis (FEA) of the proposed structure under the loads described in this work. The optical fiber was drawn with 125 µm and was placed on top of the grooved plate. In each grooved period it was drawn a structure mimicking the bonded region of the fiber onto the grooved plate, as is show on the xy view shown in Fig. 14(a).

 

Fig. 14. Cross sectional views of the fiber sensor.

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The thickness of the bonded layer is 150 µm and the base (the region where the polymerizable resin spreads onto the grooved plate), is set to 500 µm. The profile between the point that touches the grooved plate up to the maximum height of the resin layer, follows a spline curve. The fiber structure on the two other orthogonal views may be seen in Figs. 14(b) and 14(c).

The materials used in the FEA were glass for the optical fiber while acrylate was chosen for the grooved plate, due to the similarities with the resin material used in our work.

For the shear-strain analysis, a 3-mm-top section of the grooved plate (xy view) is immobilized in one terminal, while in the opposite terminal, force is applied in a 3 mm button section of the grooved plate. Regarding the torsion analysis, one terminal of the grooved plate was immobilized, while at the other end the, torque was applied considering the axis of rotation passing through the middle region of the grooved plate. The FEA stress results may be seen in Figs. 15(a) and 15(b), for the shear-strain and torsion loads, respectively.

 

Fig. 15. Cross sectional view of the stress distributions around the fiber to grooved plate bonded region, for the (a) shear-strain and (b) torsion loads.

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The stress distributions shown either in Figs. 15(a) and 15(b), reveal a periodic stress distribution as initially predicted. Thus, due to the photoelastic effect, the stress distributions seen on these figures, will periodically modulate the refractive index of the optical fiber, allowing to change the coupling strength of the core to cladding mode resonances.

Appendix A3

Temperature response of pre-strained grooved plate fiber sensor

The temperature cross sensitivity in optical fiber sensors needs always to be taken into account when projecting a new fiber sensor. With this in mind, we decide to characterize the fiber sensor fabricated through the pre-straining process to temperature changes. For that, the fiber device was placed inside a climatic chamber (Angelantoni CH340) and the temperature was varied from 20°C up to 34°C in steps of 2°C. The transmission ratio and the wavelength shift of each dip resonance may be seen in Figs. 16(a) and 16(b), respectively.

 

Fig. 16. (a) Transmission ratio and (b) dip wavelength shift of each of the three dip resonances, as function of temperature. The inset in (a) shows the corresponding spectra with increasing temperature.

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The transmission ratio of the 1^st, 2^nd and 3^rd dip resonances show a sensitivity of 0.003/°C, 0.002/°C and 0.002/°C, respectively. Furthermore, the dip wavelength shift measured for those resonances, does not show linearity. Yet, the wavelength shifts observed for the temperature range studied in this work was about ∼0.7 nm, ∼0.5 nm and ∼2 nm for the 1^st, 2^nd and 3^rd dip resonances.

Appendix A4

Examples of implementation of the proposed fiber sensor

The fiber sensors developed in this work are very simple to fabricate, easy to work and could also be considered simple to install. Their implementation in a structure depends on the type of forces involved. Below (Fig. 17) there are two possible examples of applications, were the fiber device may be simply bonded on their sides, either to monitor the shear-strain involved in a crack. (Examples of implementation, where the fiber device is simply bonded trough the edges of the grooved plate onto the surface under analysis, either to monitor shear-strain in a crack or to measure torsion in a beam.)

 

Fig. 17. Examples of implementation, where the fiber device is simply bonded trough the edges of the grooved plate onto the surface under analysis, either to monitor shear-strain in a crack or to measure torsion in a beam.

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Funding

Fundação para a Ciência e a Tecnologia (AQUATICsens (POCI-01-0145-FEDER-032057), FOPEComSens (PTDC/EEI-TEL/1511/20), UIDB/50008/2020-UIDP/50008/2020).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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