Ultrashort Long-Period Fiber Grating Sensors Inscribed on a Single Mode Fiber Using CO 2 Laser Radiation

Sensing performances of ultrashort (as low as 2.4mm) long-period fiber gratings fabricated with CO2 laser radiation using commercial singlemodefibers are presented.These lengths are, to our knowledge, the shortest of those found in the literature for this kind of sensors, approaching those typical in fiber Bragg gratings. Sensitivity to temperature and refractive index are demonstrated, with performances within the range expected for a single LPFG written on a single mode fiber without any enhancing technique. Analysis on results is made based on both theoretical and experimental data.


Introduction
Laser processing of optical fibers to produce fiber-based sensors has gained importance as a research theme, in particular regarding optical fiber grating sensors.These sensors are classified into two types: short-period gratings (also called reflection or fiber Bragg gratings, FBGs), in which coupling occurs between modes traveling in opposite directions, and transmission gratings (or long-period fiber gratings, LPFGs), where the coupling occurs between modes traveling in the same direction.Compared to other optical devices, LPFGs have a number of unique advantages: low insertion losses, high temperature sensitivity, and relatively simple fabrication.A further advantage of LPFG devices is their higher sensitivity to the environmental refractive index change without the need for access to the evanescent field, as in the case of the FBGs [1].
LPFGs have been developed and improved for decades, which resulted in numerous fabrication techniques and in a set of different sensor types, from simple LPFGs to interferometric systems, plasmonic resonance based sensing, and special fibers like photonic crystals [2][3][4][5].There are many fabrication techniques inducing a permanent change on the refractive index: laser-based inscription systems such as UV [6], femtosecond pulses [7], and CO 2 laser nearinfrared radiation [8], or physically deforming the fiber using other methods such as electric arc discharges [9][10][11], ion implantation [12], or microbends [13].
One important feature of LPFG systems is their potential to be endowed with different degrees of complexity, from single gratings to the application of different sensitivity enhancing techniques, such as mirrored ends [3], tapered LPFGs [14], or chemical etching [15].Other techniques are based on SPR (Surface Plasmonic Resonance) configurations [5], different film coatings [16,17], or nanospheres [18].
In this paper, we present LPFGs written in single mode fibers (Corning SMF-28) using CO 2 laser radiation (10.6 m wavelength) with the remarkable characteristic of having a very short length (less than 10 mm, in the range of 2.4 mm to 8.4 mm).In comparison with the common 25-40 mm length LPFGs, these gratings are, to our knowledge, the shortest obtained so far using single mode fibers and CO 2 laser radiation, very close to the typical lengths of FBGs (typically a few mm).This makes them especially appealing for applications in which compactness is essential [37], or when the application requires probing small volumes.Using single mode fibers allows reducing the cost, when compared with using PCF, and using CO 2 laser radiation allows better repeatability (compared with electric arc) and cheaper cost when compared with other laser technologies (like femtosecondbased technologies) and makes using photosensitive fibers unnecessary (required when using UV radiation).We also analyze the performance of the manufactured gratings as sensors of temperature and refractive index.
In the following section, we review the working principles of LPFGs, the physical bases of LPFGs as temperature and refractive index sensors, and a brief review of these two types of sensors in terms of their main characteristics.The experimental setup and methodologies will be explained in Section 3 and results will be presented and analyzed in Section 4.

Working Principles of LPFG Sensors.
As mentioned before, LPFGs are periodic structures engraved in the optical fiber along its longitudinal axes with the purpose of inducing a slight change in the refractive index of the fiber core.
They can be considered a particular case of FBGs, where the induced birefringence couples the light from the core (core mode) into the cladding, depending on the manufacturing technique and characteristics of the grating, such as period and length.The behavior of the different modes in a waveguide is described analytically by the coupled-mode theory [38].Within the scope of this theory, the electric fields of the propagating modes are described by considering the grating as a dielectric perturbation that affects the effective refractive index of the propagation medium and the field amplitudes of the modes.The mathematical development requires calculating the effective refractive index of the medium for the core and cladding modes and the coupling constant, resulting in general coupled-mode equations [38].The solution of these equations provides the transmission spectra of the grating, which relates the resonance wavelength, the grating's period, and the order of the coupled modes, expressed in the form LP  (acronym for "linearly polarized").For symmetrical modes,  = 0, with  = 1 (LP 01 ) for the fundamental mode.The asymmetric modes are referenced by LP  , with  = 1, 2, 3, . ... The equation that summarizes the basic working principle of LPFGs is the phase matching condition [2] that relates the resonance wavelength  res at which the core and a specific cladding mode are coupled, the difference between the effective refractive indexes of the core and the th cladding mode,  eff,core and   eff,clad , respectively, and the grating's period Λ.
LPFGs are characterized, among their fabrication parameters (period, length), by the coupling coefficient, , which describes the optimal coupling, according to This expression shows that coupling depends directly on the grating's length,  grating , and the product  grating is known as "coupling strength" [37].If  grating < /2, the light is not completely coupled into a cladding mode, while if  grating > /2, the light is first fully coupled into a cladding mode and then back-coupled again into a core mode, a phenomenon known as overcoupling [19].The value of the coupling coefficient depends on the mechanical tension applied to the fiber and on the laser power, as both parameters affect the refractive index modulation in both core and cladding.In this kind of sensors, created under high tension, the coupling constant is usually high, in the order of 10 cm −1 [9].Although  grating does not change the value of  res , the degree of coupling is affected, and the balance between  and  grating is usually established experimentally, while the LPFG is being created.
The sensitivity of a LPFG to an external parameter (induced or not) depends basically on the type of physical changes being induced in the grating.Temperature and refractive index are the examples that were considered in our work.
Grating sensitivity to temperature depends on two effects: one due to the change on the refractive indexes due to temperature variation and the other based on the thermomechanical sensitivity of the grating period [2].
By differentiation of the phase matching condition with respect to temperature, the sensitivity can be expressed mathematically by [2] In this equation, the first term of the second-hand side represents the thermooptic effect (material contribution), where  eff = ( eff - clad ).In addition, Λ⋅ res /Λ represents the contribution of the waveguide effect and (1/) ⋅ / is the thermal expansion coefficient.
The ability to use a LPFG to sense changes in the refractive index of the environment arises from the dependence of the effective refractive index for different th cladding modes upon the difference between the refractive index of the cladding and the refractive index of the surrounding medium; as shown in (1), the resonance depends on the effective refractive index of the aforesaid cladding modes [2].The variation of the transmitted wavelength with the refractive index is therefore given by [39] The term   eff,clad / medium is different for different cladding modes; therefore, the sensitivity of the sensor depends on the specific mode being coupled to.
LPFGs created by CO 2 laser radiation have some particularities regarding the three main physical mechanisms that modulate refractive index and mode coupling: residual stress relaxation, changes in the glass structure, and physical deformation.Residual stress relaxation is produced when LPFGs are written on fibers submitted to high tensile forces and results from different thermal expansion and viscoelastic properties between the core and the cladding.Changes in the glass structure are due to volume increase and glass densification, and the resulting physical deformations induce a variation of the effective refractive index along the fiber axis [40].Since LPFGs are usually created by irradiating one side of the fiber, an asymmetrical refractive index profile is produced.This leads to an asymmetrical mode coupling, which can be considered a distinctive feature of CO 2 laser induced LPFGs [20].
For temperature sensing, the typical values of sensitivities found in the literature range from around 0.05 to 0.3 nm/ ∘ C. The values are higher when more complex sensing structures were created, like, for example, a dual LPFG system [27].Also, as mentioned by Nam et al. [9], sensitivity increases at high temperature: they measured a sensitivity of 0.054 nm/ ∘ C from room temperature to 200 ∘ C, while from 200 ∘ C to 1000 ∘ C, the value was approximately 0.135 nm/ ∘ C [9].
Regarding refraction index sensing, most authors report LPFGs' response to the refractive index in terms of resolution, publishing values one or two orders of magnitude higher than those measured by Abbe refractometers.The resolution values are around 10 −4 to 10 −6 RIU.As with temperature, such high values are obtained with more complex sensing systems instead of a single LPFG, such as the sandwiched system of three LPFGs in [27] or the Mach-Zehnder interferometer in [30].A Photonic Crystal Fiber (PCF) was used by Rindorf and Bang [29].

Experimental Setups and Methods
The LPFGs fabrication technique consists in a focused CO 2 laser beam (Synrad, 25 W) periodically sweeping the fiber using an automatic system controlled by LabVIEW©, as described in detail in [8,45].The average laser power was 4.5 W (±1 W), the focusing lens was cylindrical, with a working distance of 50 mm, and the exposure time was ∼0.6 s.A set of LPFGs were fabricated with a 600 m period and lengths varying between 2.4 mm and 4.8 mm.A weight of around 80 g (0.78 N) was applied to the engraving fibers, therefore inducing a high strain into the fibers.The period was chosen based on preliminary tests with our methodology [8]: it was one of those showing better repeatability and peak attenuation.
For temperature and refractive index measurements, the gratings were placed in a closed recipient filled with different fluids, as shown in Figure 1.Regarding temperature, the gratings were submerged in either boiling or frozen water, while a thermocouple was used for calibration.The corresponding spectra for each temperature were recorded in real time with an Optical Spectrum Analyzer (OSA) (Agilent 86140B) while the optical fiber was illuminated by a Super Luminescent Diode (SLD) with a central wavelength of 1550 nm and spectral width of ∼160 nm.To test the sensors while measuring the refractive index, dissolution of ethylene glycol at different concentrations was used, having the refractive index of the solution previously measured with an Abbe refractometer (illuminated by a halogen lamp).

Results and Analysis
According to the coupled-mode theory (Section 2.1), and using a Matlab© simulation [46][47][48], under the conditions previously described for the LPFGs, the coupling was found to occur between the LP 01 core mode and the LP 13 azimuthally asymmetric cladding mode ( = 3).This can be illustrated considering Figure 2, which shows the characteristic LPFG's phase matching curve, representing  res versus Λ for a grating with 6 mm length, and considering a 2-layer model and an asymmetrical mode [46][47][48].The plot shows a set of periods (Λ) complying with the phase matching condition (see (1)) for different resonance wavelengths.Each line represents a cladding mode, from the lowest-order mode ( = 1) to the highest-order mode ( = 7) (right to left).Then, for a period of 600 m and a resonance wavelength of around 1.5 m, the mode has an order  = 3.
For predicting the maximum refractive index changes induced in the core and cladding, we used a 3D Finite Element Model developed by the authors [8].Since the experimental conditions are similar to those reported there, the behavior of the refractive index change of the core, Δ core , with the applied force, , in Newton, can be considered linear and given by the empirical equation [8] Δ core = −4.94× 10 −4 ×  + 1.66 × 10 −6 .
The equivalent variation for the cladding was demonstrated to be two orders of magnitude smaller and not significantly changing with  [8].Using the simulator mentioned before [46], it is then possible to study the variation in the attenuation signal at  res for different applied weights or by changing the gratings length.Figure 3(a) exemplifies the change for a 4.8 mm length grating subjected to different weights.The plot shows that, for lower weights, the attenuation is small, which in practice limits the use of the grating as a sensor.Similarly, when using a low weight, in order to produce a useful sensing device, a grating with higher length is required.This effect is exemplified in Figure 3(b), representing the attenuation at  res for different grating lengths, with a fixed weight of 5 g (0.049 N) when compared with the equivalent Figure 3(c) for a fixed weight of 80 g (0.78 N).The range assumed for the latter plot is reduced because although theoretically one can use higher weights when producing longer LPFGs (and obtain attenuations down to −700 dBm for a 50 mm LPFG), in practice this usually leads to fiber breakage, due to the combined effect of glass melting and weight pulling.Even when manufacturing shorter LPFGs with heavier weights, as we did, some tapering effect (and the resulting cladding thickness modulation) appears, as shown in Figure 4 (which shows a microscope photograph of an irradiated fiber under the experimental conditions considered in this work).The imaged zone comprises one 600 m period of a grating irradiated with 4.5 W, for a duration of 0.6 s (each pulse), and subjected to a weight of 80 g (0.78 N).
Thus, although higher pulling forces allow shorter length LPFGs, as predicted by theory, manufacturing can be affected by the resulting pulling force and the tapering effect can lead to breakage.Therefore, complete control of the process during the irradiation is mandatory.Taking this into consideration, with our experimental procedures, we were able to obtain LPFGs with significant attenuations at their resonance wavelength,  res .Figure 5 exemplifies the spectra obtained for two ultrashort LPFGs.Their responses to variations of temperature and environment refractive index are analyzed hereafter.For each of the measurands, we will exemplify with the shorter length that still allows obtaining quality sensors (regarding repeatability and/or attenuation).
4.1.Temperature Sensing.Using the assembly sketched in Figure 1, it was experimentally observed that while the surrounding temperature increases, the resonance peak shifts towards higher wavelengths, while the amplitude (intensity) of the peak decreases, becoming less sharp.Figure 6 shows typical spectra, with the resonance moving towards shorter wavelengths while cooling down.The response of the fiber is linear and sensitivities are within 0.06-0.08nm/ ∘ C in the temperature range of 25 ∘ C to 75 ∘ C, for the LPFG lengths considered in our study.Figure 7 shows an example for a grating with a 600 m period and 4.8 mm length.The error in the linear adjustment obtained by the least squares method does not exceed ±0.01 nm/ ∘ C. The resolution is obtained by dividing the resolution of the OSA (minimum wavelength at FWHM) by the sensitivity derived from the calibration line.In this case, the resolution ranges from 0.75 ∘ C to 1 ∘ C.
In comparison, sensitivities are within the range of values presented in the literature for the temperature ranges considered in our study.Even considering higher ranges, although the values are not among the highest (e.g., [26,27]), these gratings are much smaller than the regular ones, with a small number of "periods," and one of the factors affecting temperature sensitivity (wavelength effect) is directly connected to the number of periods, as discussed in Section 2.1.

Refractive Index Sensing.
Using the same setup as for the temperature measurement testing (Figure 1), it was also observed that while increasing the refractive index of the surrounding environment, the resonance peak shifts linearly towards shorter wavelengths.Figure 8 shows a typical spectrum for a grating subjected to variations of the refractive index of the surrounding medium.In this case, the attenuation of the resonance peak becomes sharper and more pronounced while the refractive index increases.The increase of the attenuation could be explained by the absorption of this solvent at the infrared band, as explained in [49].This potentially allows replacing an OSA by a much simpler power meter or by an Optical Time-Domain Reflectometer (OTDR), therefore leading to cheaper interrogation methods.
In Figure 9, we show some examples of the response of the gratings to changes of the refractive index, with an Figure 9: Responses of (a) the resonance wavelength and (b) attenuation of the signal with regard to the refractive index variation, for a grating with 2.4 mm length.
absolute sensitivity of around 30 nm/RIU (about 14 nm/RIU, if we analyze the change in the attenuation of the signal), in the range of 1.333 to 1.431 RIU, which leads to resolutions in the order of magnitude of 10 −3 RIU.The error in the linear adjustment is in the range of approximately ±3 nm/RIU, obtained by the method of least squares.The response of the gratings and their sensitivities are consistent with results reported for these types of sensors, although the comparison with the values mentioned in the literature (Section 2.2) shows that resolution is worse than that provided by a typical Abbe refractometer, which can be of the order of 10 −5 RIU in the range of 1.33 to 1.58 RIU.In fact, the resolution of the OSA used in these experiments, 0.06 nm, is actually limiting the resolution of these gratings.

Conclusions
The possibility of manufacturing ultrashort LPFGs by irradiating single mode fibers with CO 2 laser radiation and high tension (up to 0.78 N) was clearly demonstrated.Grating lengths (for a 600 m period) reached 2.4 and 4.8 mm, far smaller than the 25 to 40 mm usually reported in the literature, but performances are alike.Performance of these LPFGs was assessed for measuring temperature and refractive index demonstrating, (i) for the temperature, sensitivities in the interval 0.06-0.08nm/ ∘ C in the measuring range of 25 to 75 ∘ C and for the overall LPFG lengths being studied; (ii) for the refractive index, sensitivities of around −30 nm/RIU in the measuring range of 1.333 to 1.431 RIU.
These values are fully consistent with the results reported in the literature for much longer LPFGs written in single mode fibers and under similar sensing operation, therefore demonstrating the sensing capabilities of our much shorter sensors.We anticipate that these small LPFGs demonstrate a high potential for applications requiring small sizes and compact sensing, especially in the areas of biosensing with less invasive devices, or civil engineering and structural health, by facilitating the embedding into the hosting material.Postinscription application of enhancing techniques like nanoparticles deposition is expected to give these gratings an even better sensitivity.Future work will follow this line of research and will explore the use of these ultrashort length gratings in the creation of more complex sensors, as concatenated LPFGs.

Figure 1 :
Figure 1: Schematic of the setup used for refractive index and temperature sensing tests.

6 Figure 2 :
Figure 2: Phase matching curves, for a 6 mm length grating;  indicates the order of the mode.

Figure 3 :Figure 4 :
Figure 3: Theoretical attenuation at the resonance peak of a 600 m period LPFG when considering (a) a length of 4.8 mm and different weights and (b) 5 g (0.049 N) and (c) 80 g (0.78 N) weights and different length.

Figure 8 :
Figure 8: Example of the peak attenuation with the change in the refractive index of the medium (water with a variable percentage of ethylene glycol), for a grating with 2.4 mm length.