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Abstract
We report on efficient inscription of fiber Bragg gratings (FBGs) in a new type of single mode fiber with nanostructured core and with an effective parabolic graded index profile, using the standard phase mask method and a 248 nm pulsed laser. A nanostructured core allows to obtain high concentration of GeO2 in subwavelength glass rods and simultaneously to maintain low average germanium dopant level of silica similarly to standard single mode fibers. We showed that in a nanostructured core fiber, a factor of 3 better efficiency in gratings inscription was achieved, although the fiber has 20% lower average concentration of GeO2 with respect to SMF-28. In the nanostructured fiber we obtained a significant improvement in temperature sensitivity, while the strain sensitivity of FBG in nGRIN optical fiber is the same as in case of standard single-mode fiber (SMF-28). We have measured the strain sensitivity of 0.72 × 10−6 1/με (1.11 pm/με@1.53μm), and the temperature sensitivity is about 30% higher than for FBG in SMF-28 and equals to 10.2 × 10−6 1/K (15.6 pm/K@1.53μm).
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Devices employing fiber Bragg gratings are one of the most successful and versatile in fiber sensing applications. Most commonly step index single-mode fibers (such as Corning SMF-28) are used for sensing, since they can be used for both transmission and sensing if gratings are written. This is due to their compatibility with optical fiber infrastructure, as well as fiber based components and devices. The permanent refractive index change of such gratings is associated with the concentration of GeO2 defects in the fiber core and thus with the resulting UV absorption at 240 nm [1,2]. The monotonic increase of refractive index change, due to UV irradiation, is also desirable because it provides full control over the process of grating growth. In comparison with 800 nm fs lasers, the used UV wavelength is significantly shorter than the phase mask period (typically 1070 nm for Bragg wavelength at 1550 nm), which ensures effective maximization of ± 1 diffraction orders and minimization of 0-th and other even orders. This, in turn, results in obtaining high contrast of interference pattern behind the phase mask, which directly translates into the high quality of in-written fiber Bragg gratings.
Photosensitivity of SMF-28 fibers and temperature sensing performance of in-written fiber Bragg gratings are limited due to low concentration of GeO2 in fiber core (c.a. 3.5%mol). Hydrogen loading is used to increase UV absorption in the fiber core during the grating inscription [3]. However, this does not improve temperature sensitivity of FBG written in low GeO2 doped SMF-28 [1,2]. Thus the achievable resolution of the temperature measurement using FBGs and commercially available FBG interrogators is not better than 0.1 °C.
It is widespread in FBG technology to control photosensitivity and thus susceptibility to UV radiation (during the grating inscription) with the GeO2 doping concentration in the silica fiber core. Similarly it enhances thermo-optic coefficient of the fiber core, which directly translates into an improvement of temperature sensitivity of the in-written FBGs [4]. On the other hand, increasing of germanium concentration in the fiber core also brings up the core’s refractive index. This in turn results in an increase of numerical aperture of the optical fiber and hence causes mode-field mismatch between photosensitive fiber and a SMF. It also redshifts the multimode cut-off wavelength of the fiber. Thus, in order to provide a single-mode operation of highly germanium doped optical fibers within the spectral range similar to that of SMF, two methods are commonly used to reduce the cut-off wavelength. The first is to reduce the core diameter [5], which makes the photosensitive fiber incompatible with SMF and SMF based components in terms of fiber core and mode field diameters. The second one is introduction of B2O3 co-doping in the fiber core. Although boron reduces the refractive index of the fiber core, it also significantly increases fiber attenuation by up to two orders of magnitude compared to SMF [6]. Moreover, in the case of SMF-compatible Ge/B co-doped photosensitive fibers, the increase of B2O3 concentration results in significant reduction of thermo-optic coefficient, which finally decreases the temperature sensitivity of the FBGs [7]. Another drawback of such fibers is that boron doping worsens the thermal stability of FBG based sensors.
Microstructured optical fibers, also called photonic crystal fibers (PCF), are another group of optical waveguides developed in some variants for FBGs inscription. Among their undisputable benefits as easiness in shaping of propagation properties, i.e. endlessly single-mode operation [8], shaping of chromatic dispersion for e.g. efficient supercontinuum generation [9] the PCFs are also individually or with built-in fiber gratings very good for sensing purposes [10]. The primary advantage of these fibers compared to classical step-index fibers, is that their propagation properties, and thus spectral and sensing responses of in-written FBGs, can be widely modified by an appropriate design of arrangement, sizes and structural shape of the air-holes in the cladding [10,11]. As it is in the case of step-index fibers, the photosensitivity enhancement of PCFs can be realized by high GeO2 concentration in the core or by hydrogen loading. However, despite their advantages, lattice of air-holes in PCFs also has drawbacks. A serious problem resulting from the existence of air-holes around the fiber core is the strong scattering of UV radiation during the grating inscription [12]. This is a major obstacle in obtaining a series of FBGs with repetitive parameters, as well as complex grating structures with an amplitude and phase modified distribution of periodic refractive index changes in the fiber core, as in the case of phase-shifted, sampled or apodized gratings. PCFs connection with standard optical fibers, fiber components and fiber optic measurement systems is also a nontrivial issue [13]. Fast mechanical connection during the grating fabrication for in situ monitoring of grating growth with the help of immersion fluid is also impossible, due to the capillary effect in PCFs. In turn, incompatibility of microstructured fiber with SMF, as well as air-hole collapse during the splicing adversely affects the insertion loss (due to the high splice attenuation). Moreover, in the case of hydrogenated PCFs, a major technical obstacle in the FBGs fabrication is the rapid hydrogen out-diffusion from the fiber core through the neighboring air-holes [14,15].
Here we propose a novel approach to increase photosensitivity of fibers to UV radiation, while maintaining their good compatibility with standard SMF-28 fibers. We propose to increase locally the concentration of GeO2 in certain subwavelength regions of the fiber core and maintain another subwavelength regions undoped. We begin with a hypothesis, that due to the various growth rate during the gratings inscription that are observed depending on germanium concentration [16], especially in hydrogenated optical fibers [17], the photosensitivity enhancement would increase in such a nanostructured graded index (nGRIN) fiber. On the other hand, propagation properties will be maintained similarly to SMF-28, since mode diameter and average GeO2 is as low as in the case of SMF-28.
We further verify experimentally the feasibility of Bragg grating inscription in this new type of fiber. Our results show, that for the nanostructured optical fiber the inscription efficiency is at least three times better than for SMF-28. We also investigated sensing properties of in-written grating, resulting in 30% better sensitivity to temperature in comparison to Bragg grating inscribed in SMF-28. Such gratings are important for applications in laser systems, where the Bragg peak has to be thermally accurately tuned [18], as well as in temperature sensing with improved resolution.
2. nGRIN optical fiber for Bragg grating inscription
The optical fiber with the nanostructured core composed of 2107 glass rods was fabricated by stack-and-draw method. The glass rods were made of pure fused silica and germanium doped fused silica arranged as shown in Fig. 1. nGRIN optical fiber studied in details in [19] was characterized with use of standard methods and resulting parameters were compared to these of SMF-28, Table 1. Since the photosensitivity of the fiber depends on germanium concentration, we performed particular chemical analysis with use of EDS technique. The results revealed, that the concentration of germanium in weight percentage fraction in the core was around 5.4 ± 0.6 wt.%. We also converted compound concentration on mole fraction to compare it with SMF-28. The maximum concentration of GeO2 in the core of nGRIN optical fiber is higher than in SMF fiber, but due to nanostructurization and the parabolic index distribution, an average Ge concentration in the nGRIN fiber is slightly smaller than in the SMF-28.
Fig. 1 nGRIN optical fiber with nanostructured core: (a) fiber design in form of binary structure, SEM image of cross-section of (b) the fiber core and (e) zoomed core area, (c) subpreform and (d) zoomed subpreform area Areas in black rectangles and image (d) indicate the same rods arrangement in design, subpreform and final fiber [19].
Table 1. Comparison of fundamental parameters of nGRIN optical fiber and SMF-28.
The optical parameters of both fibers (numerical aperture and effective mode diameter) are relatively matched. The cut-off wavelength of nGRIN optical fiber is shorter than 950 nm, which improves single-mode bandwidth. The attenuation is high, but is acceptable for laboratory grade optical fiber.
3. Inscription and characterization of Bragg gratings
In our first experiment, fiber Bragg gratings were written in the nGRIN fiber and in a SMF-28, using the same writing conditions. For this purpose, the phase mask with the period of 1061 nm and UV pulsed KrF excimer laser operating at 248 nm and with pulse energy of 3mJ and rectangular beam profile (FWHM beam size: 6 mm x 1.5 mm) were used. The UV beam was focused on optical fiber using cylindrical lens with the 19 cm focal length. During the fiber Bragg gratings inscription, their growth was continuously monitored by their spectra measurement in transmission using supercontinuum light source and an optical spectrum analyzer with the 0.02 nm wavelength resolution. In order to enhance photosensitivity, both optical fibers were hydrogen-loaded at 100 bars and at room temperature for two weeks, prior to the inscription process. Transmission spectra of the fabricated FBGs are shown in Fig. 2. In earlier section in Table 1 we showed that the average concentration of GeO2 in the nGRIN fiber core was lower (2.87 ± 0.5% mol) than in the core of a SMF-28 fiber (3.5% mol). Despite this, a significantly higher transmission minimum was obtained for several FBGs inscribed in nGRIN optical fiber, i.e. −25 dB as compared with −8.7 dB for SMF-28. For gratings lengths of 1 cm and assumed fringe pattern visibility v = 1, the estimated amplitude of refractive index changes Δn = 1·10−4 and Δn = 2.2·10−4 was obtained for SMF and nGRIN FBGs, respectively. It follows, that even in relatively low Ge co-doped optical fibers, an appropriate shaping the Ge concentration, and thus photosensitivity profile, leads to a significant improvement of depth of inscribed grating. In this case, local increase of germanium concentration in the center of the fiber core results in stronger grating formation in this volume. For the same reason the propagating fundamental mode is better localized in the center of the core, which ensures strong coupling efficiency of forward and backward (reflected) mode. For both SMF-28 and nGRIN based FBGs thermal post-inscription treatment was applied to remove the hydrogen remains and to stabilize the FBGs parameters. After that the transmission minimum of FBGs written in SMF-28 and nGRIN decreased to −8.2 dB and −21.4 dB, while the Bragg wavelengths change to 1535.75 nm and 1536.0 nm. Thus, larger changes in the spectral parameters of FBGs were observed for the grating written in more photosensitive fiber (nGRIN), which is consistent with the expected results.
Fig. 2 Transmission spectra of FBGs written in a) nGRIN optical fiber, b) SMF-28 with use of the same inscription conditions: pulse energy: 3mJ, pulse repetition 500 Hz, and number of pulses 10000.
In order to compare grating growth in nGRIN and SMF-28 optical fibers, evolutions of transmission spectra during the ~1 cm long gratings inscription were recorded and are presented in Fig. 3. Different number of pulses were selected for both optical fibers to obtain comparable transmission minimum. In both cases, the linear increases of transmission minima (in dB scale) as well as shifts towards longer wavelengths are observed versus number of pulses. It follows that both gratings are type I. Moreover, transmission minimum of SMF-28 based FBG written using 10000 pulses correspond to the grating spectra in nGRIN optical fiber written using only 3000 pulses. This is consistent with results presented in Fig. 2, and c.a. 3 times better efficiency of grating formation in nGRIN optical fiber as compared with SMF-28 was achieved.
In order to examine sensing properties of nGRIN optical fiber based FBGs, the Bragg structures with the central wavelengths around 1064 nm, 1536 nm and 1550 nm were written using phase mask technique. For comparison the FBGs in SMF-28 were inscribed for λB around 1550 nm.
4. Measurement of the Bragg gratings sensitivity to temperature and strain
To verify the performance of the grating, we measured its sensitivity to strain and temperature. For the gratings with Bragg peak around 1060 nm we used supercontinuum light source, for the gratings with λB around 1536 nm and 1550 nm an ASE light source was used. The gratings were written using phase masks with the periods 729.5 nm, 1061 nm, 1066 nm and 1072 nm respectively. The spectra were recorded with an optical spectrum analyzer (OSA) working in a spectral range of 600-1700 nm. The input and output SMF FC patchcords were joined to the tested fiber by FC bare fiber connectors. Investigated fiber was fixed to the two stages with help of two-component epoxy and left for 12 hours. Accordingly with the specification given by the producer (Libella, DISTAL Rapid epoxy), in room temperature the curing time and also time needed for total strength of the weld was only 4 hours. One of the stages with micrometer was used for precise elongation of the fiber under strain sensitivity tests. After that, the central part of the fiber with FBG was placed on Peltier module to investigate temperature sensitivity. The measurement setup is shown in Fig. 4.
Fig. 4 Measurement system for FBG characterization: central part of the fiber with inscribed FBG grating placed on a Peltier module for temperature changes introduction. The fiber fixed at two points distanced equally in respect to FBG position. Total distance between fixed points was L0. The light sources were: broadband supercontinuum source and ASE laser with a band from 1520 to 1570 nm. The transmission spectra were registered with optical spectrum analyzer (OSA).
The sensitivity properties were measured for FBG inscribed in nGRIN optical fiber at three wavelengths 1062 nm, 1536 nm and 1552 nm as well as for FBG inscribed for SMF-28 fiber at 1536 nm, and 1544 nm. The temperature was changed from 10 to 100 °C with use of a Peltier module and controlled with a thermocouple. The Bragg peak shift related to temperature changes was registered and the temperature sensitivity was estimated. The peak movement due to temperature change and related sensitivity for gratings around 1060 and 1550 nm in nGRIN optical fiber and around 1550 nm in SMF-28 are shown in Fig. 5 to 7, respectively. In Table 2 the sensitivities to temperature are compared for FBG in different fibers and with different Bragg wavelengths λB. Although the hysteresis is observed in measured temperature responses of the FBGs due to the constant delays between the spectral responses measurements resulted from OSA scan time with respect to the immediate temperature measurements (by means of thermocouple) the slope of the resulted characteristics (and thus estimated temperature responses of FBGs) are similar for heating and cooling processes.
Fig. 5 Bragg peak λB = 1061.5 nm registered for FBG2 in nGRIN optical fiber under temperature changes: movement of the peak in transmission spectrum (a) and central wavelength shift estimated for heated and cooled fiber (b).
Fig. 6 Bragg peak at λB = 1551.6 nm registered for FBG0 in nGRIN optical fiber under temperature changes: movement of the peak in transmission spectrum (a) and central wavelength shift estimated for heated and cooled fiber (b).
Fig. 7 Bragg peak λB = 1544.2 nm registered for FBG1 in SMF under temperature changes: movement of the peak in transmission spectrum (a) and central wavelength shift estimated for heated and cooled fiber (b).
Table 2. Sensitivity to temperature measured for FBG in nGRIN optical fiber and in SMF-28.
The Bragg peak shift caused by temperature changes dλB/dT differs between the gratings and can be compared in two ways: between the gratings with the same Bragg wavelengths or between all FBG with normalized sensitivity (1/λB)dλB/dT. The normalized sensitivities to temperature of the FBG in nGRIN optical fiber with different λB are the same and equal to (10.3 ± 0.2) × 10−6 K−1. For the FBG in SMF-28 this value is (8.0 ± 0.3) × 10−6 K−1. The results show that the sensitivity to temperature of the FBG in nGRIN optical fiber is 30% higher than for FBG in SMF-28. It is worth mentioning, that such a result was obtained for nGRIN optical fiber with average Ge concentration lower than in SMF-28. Presented results prove that nanostructurization enables significant improvement of temperature sensitivity in FBG based sensors for two reasons. Firstly, fabrication of nGRIN optical fiber with higher Ge concentration, that increases thermo-optic effect is possible, while maintaining SMF-28 compatibility. Secondly, due to the flexible profiling of core refractive index distribution, highly photosensitive (Ge co-doped) nGRIN optical fibers can be manufactured without B co-doping, thus making it possible to avoid decreased temperature sensitivity and significantly increased fiber attenuation related to introduction of the boron dopant.
The sensitivity to strain was examined in terms of longitudinal stress applied to the FBG. The sections of fiber of length L0 with centrally positioned FBG were elongated up to 1.4 mstrain. The results for the Bragg peak movement related to elongation of the gratings, as well as its strain sensitivity, are presented in Fig. 8 to 10 for FBG in nGRIN optical fiber and in Fig. 11 in SMF-28. The sensitivity to strain coefficients are summarized in Table 3.
Fig. 8 Bragg peak λB = 1061.5 nm registered for FBG2 in nGRIN optical fiber under longitudinal stress changes: movement of the peak in transmission spectrum (a) and central wavelength shift estimated for elongated and released fiber (b).
Fig. 9 Bragg peak λB = 1551.6 nm registered for FBG0 in nGRIN optical fiber under longitudinal stress changes: movement of the peak in transmission spectrum (a) and central wavelength shift estimated for elongated and released fiber (b).
Fig. 10 Bragg peak λB = 1535.6 nm registered for FBG4 in nGRIN optical fiber under longitudinal stress changes: movement of the peak in transmission spectrum (a) and central wavelength shift estimated for elongated and released fiber (b).
Fig. 11 Bragg peak λB = 1536.1 nm registered for FBG3 in SMF-28 fiber under longitudinal stress changes: movement of the peak in transmission spectrum (a) and central wavelength shift estimated for elongated and released fiber (b).
Table 3. Sensitivity to strain measured for FBG in nGRIN optical fiber and in SMF-28.
The normalized sensitivity for the gratings in nGRIN optical fiber is on average (0.72 ± 0.04) × 10−6 1/με. For the FBG in SMF-28 this sensitivity is (0.72 ± 0.02) × 10−6 1/με. Stress sensitivity is then the same for the gratings inscribed in nGRIN optical fiber and in SMF. We have also performed the experimental verification of cross-sensitivity effect, by applying simultaneous temperature and strain changes to nGRIN FBG. Based on obtained results, no relevant cross-sensitivity was observed.
5. Conclusions
In this paper we have verified a possibility of FBGs inscription in silica based nanostructured graded index single mode optical fiber. We showed that FBG can be efficiently inscribed in the fiber core composed of subwavelength silica rods doped with GeO2 with 5.4% weight concentration distributed among pure silica subwavelength rods to create effectively parabolic refractive index profile. Although the nanostructured optical fiber has 20% lower average concentration of GeO2 than the Corning SMF-28, a significantly higher efficiency of the grating inscription was observed. An inscription of FBG is generally nonlinear process that depends, among others, on germanium concentration [16] and hydrogenation [17]. As nanostructurization allows local accumulation of GeO2 in subwavelength nanorods regions, the inscription efficiency can be increased, while an average GeO2 doping level in the core area remains low (2.9% mol).
The performance of inscribed FBGs was also verified by measurement of its sensitivities to strain and temperature. A 30% higher temperature sensitivity was achieved in nGRIN FBG fiber (10.2 × 10−6 1/K) with respect to commonly used Corning SMF-28 based FBG sensors (8.0 × 10−6 1/K). The strain sensitivity in nGRIN FBG fiber (0.72 × 10−6 1/με) was similar to the sensitivity of FBG inscribed in the standard Corning SMF-28 fiber. Obtained results shows that nanostructurization of fiber core is beneficial for achieved sensitivity to temperature values.
On the other hand nanostructurization allows to develop fibers with various properties as large mode area fibers, flat dispersion fibers or high birefringence induced though artificial anisotropy of glass without support of air hole cladding. It opens new opportunities for development of specialty fibers dedicated for FBGs.
Funding
TEAM TECH/2016-1/1 operated within the Foundation for Polish Science Team Programme co-financed by the European Regional Development Found under Smart Growth Operational Programme (SG OP), Priority Axis IV.
References
1. R. Kashyap, Fiber Bragg Gratings (Academic Press, 2009).
2. A. Othonos and K. Kalli, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing, (Artech House, 1999).
3. A. Gillooly, “Growing gratings,” Nat. Photonics 5(8), 468–469 (2011). [CrossRef]
4. O. V. Mazurin, M. V. Streltsina, and T. P. Shvaiko-Shavaikovskaya, Handbook of Glass Data (Elsevier Science, 1985).
5. Fibercore specification note for highly Ge-doped optical fibers: https://www.fibercore.com/product/highly-germanium-doped-fiber.
6. Fibercore specification note for boron doped photosensitive fiber: https://www.fibercore.com/product/boron-doped-photosensitive-fiber.
7. P. M. Cavaleiro, F. M. Araujo, L. A. Ferreira, J. L. Santos, and F. Farahi, “Simultaneous Measurement of Strain and Temperature Using Bragg Gratings Written in Germanosilicate and Boron-Codoped Germanosilicate Fibers,” IEEE Photonics Technol. Lett. 11(12), 1635–1637 (1999). [CrossRef]
8. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22(13), 961–963 (1997). [CrossRef] [PubMed]
9. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
10. S. Sulejmani, C. Sonnenfeld, T. Geernaert, G. Luyckx, D. Van Hemelrijck, P. Mergo, W. Urbanczyk, K. Chah, C. Caucheteur, P. Mégret, H. Thienpont, and F. Berghmans, “Shear stress sensing with Bragg grating-based sensors in microstructured optical fibers,” Opt. Express 21(17), 20404–20416 (2013). [CrossRef] [PubMed]
11. T. Geernaert, M. Becker, P. Mergo, T. Nasilowski, J. Wojcik, W. Urbanczyk, M. Rothhardt, C. Chojetzki, H. Bartelt, H. Terryn, F. Berghmans, and H. Thienpont, “Bragg Grating Inscription in GeO2-Doped Microstructured Optical Fibers,” J. Lightwave Technol. 28(10), 1459–1467 (2010). [CrossRef]
12. G. D. Marshall, D. J. Kan, A. A. Asatryan, L. C. Botten, and M. J. Withford, “Transverse coupling to the core of a photonic crystal fiber: the photo-inscription of gratings,” Opt. Express 15(12), 7876–7887 (2007). [CrossRef] [PubMed]
13. L. Xiao, M. S. Demokan, W. Jin, Y. Wang, and C. Zhao, “Fusion Splicing Photonic Crystal Fibers and Conventional Single-Mode Fibers: Microhole Collapse Effect,” J. Lightwave Technol. 25(11), 3563–3574 (2007). [CrossRef]
14. H. R. Sørensen, J. B. Jensen, J. Bo Jensen, F. Bruyere, and K. P. Hansen, “Practical hydrogen loading of air silica fibres,” in Proc. BGPP, 2005, pp. 247–249.
15. I. R. Ivascu, R. Gumenyuk, S. Kivistö, A. N. Denisov, A. F. Kosolapov, Y. P. Yatsenko, S. L. Semjonov, and O. G. Okhotnikov, “Fiber Bragg gratings written in photosensitive photonic crystal fibers and its sensing applications,” Optoelectron. Adv. Mater. Rapid Commun. 5, 704–708 (2011).
16. J. Albert, B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, and S. Thériault, “Comparison of one-photon and two-photon effects in the photosensitivity of germanium-doped silica optical fibers exposed to intense ArF excimer laser pulses,” Appl. Phys. Lett. 67(24), 3529–3531 (1995). [CrossRef]
17. M. Konstantaki, G. Tamiolakis, A. Argyris, A. Othonos, and A. Ikiades, “Effects of Ge concentration, boron co-doping and hydrogenation on fiber Brgg grating characteristics,” Microw. Opt. Technol. Lett. 44(2), 148–152 (2005). [CrossRef]
18. D. S. Moon, U.-C. Paek, Y. Chung, X. Dong, and P. Shum, “Multi-wavelength linear-cavity tunable fiber laser using a chirped fiber Bragg grating and a few-mode fiber Bragg grating,” Opt. Express 13(15), 5614–5620 (2005). [CrossRef] [PubMed]
19. A. Anuszkiewicz, R. Kasztelanic, A. Filipkowski, G. Stepniewski, T. Stefaniuk, B. Siwicki, D. Pysz, M. Klimczak, and R. Buczynski, “Fused silica optical fibers with graded index nanostructured core,” Sci. Rep. 8(1), 12329 (2018). [CrossRef] [PubMed]
20. Corning SMF-28® technical note: http://www.corning.com/media/worldwide/coc/documents/Fiber/PI1463_07-14_English.pdf.
21. F. Juelich and J. Roths, “Determination of the effective refractive index of various single mode fibres for fibre Bragg grating sensor applications,” in Proc. OPTO, 2009, pp. 119–125.
