Measurement of grating visibility of a fiber Bragg grating based on bent-spectral analysis Dinusha S. Gunawardena, Man-Hong Lai, Kok-Sing Lim,* Muhammad M. Ali, and Harith Ahmad Photonics Research Centre, University of Malaya, 50603 Kuala Lumpur, Malaysia *Corresponding author: [email protected] Received 25 November 2014; revised 2 January 2015; accepted 8 January 2015; posted 8 January 2015 (Doc. ID 228499); published 9 February 2015
In this study, a technique for measuring the grating visibility of the fiber Bragg grating (FBG) based on bent-spectral analysis is proposed. From varying ac and dc coupling coefficients at different bending radii, the grating visibility is estimated with the aid of a simple mathematical model. The investigation begins with the estimation of the grating visibility from the transmission spectra of the FBG during the inscription process. After that, the FBGs are subjected to a bending test with reducing radii, and again the transmission spectra are recorded. It is shown that the estimated grating visibility is in agreement with the result determined from the earlier inscription process. © 2015 Optical Society of America OCIS codes: (060.3735) Fiber Bragg gratings; (060.3738) Fiber Bragg gratings, photosensitivity; (060.2400) Fiber properties. http://dx.doi.org/10.1364/AO.54.001146
1. Introduction
Fiber Bragg gratings (FBGs) have a significant role in the field of optical communication and the sensing industries due to their numerous features, e.g., immunity to electromagnetic interference, high insulation, low fabrication cost, high sensitivity, and low weight [1–4]. With the increasing demand for FBGs, several grating inscription techniques have been used [5]. Notably, the phase mask technique is the most commonly used due to its simplicity and high efficiency in writing high-performance FBGs. With the assistance of an excimer laser, the formation of a grating structure can be attained within seconds. Hence, an excimer laser and phase mask is perceived as the best combination for the mass production of FBGs [6]. This technique engages a diffractive optical element to spatially modulate the UV writing beam [7]. Therefore, it is noticed that the effects of UV fluence and bending on the spectral properties of FBGs have largely been explored by various studies, 1559-128X/15/051146-06$15.00/0 © 2015 Optical Society of America 1146
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e.g., macro bend losses for standard single mode fibers [8], wavelength measurement based on bending [9], axially offset FBGs [10], and index growth of germanosilicate fiber upon exposure to continuous UV light [11]. Generally, decreasing bend radius results in decreasing Bragg transmission depth (BTD). In order to reduce the losses created by the bends on optical fibers, a significant series of low bend loss fibers, especially for tight bend diameter applications, such as fiber to the home, are thoroughly studied and developed [12]. As a result of the immense usage of optical fibers in the telecommunication industry today, a comprehensive analysis on the spectral properties of bent FBG is still essential. The index growth of type-I FBGs is interpreted by the variation of the reflection spectrum of the grating during the inscription process [7,13]. The grating strength and reflectivity of an FBG rely on the ac coupling coefficient, which is associated with the grating visibility [14]. Despite the high UV fluence applied in the grating inscription process, the development of grating reflectivity may be appalling due to the poor interference visibility [15]. Thus, it would be beneficial to acquire the details about the interference and
grating visibilities of a particular FBG, as it would provide accurate information about the grating strength of the fiber. The other factor that also gives the motivation to conduct this investigation is to clarify the picture of visibility for the user who purchases different FBGs to be used in various applications, which does not have any information of their visibilities. Therefore, in this work a unique measurement technique for measuring the grating visibility based on bent-spectral analysis is proposed. Mathematical models are presented and used in the analysis. FBGs with different grating visibilities are fabricated and employed in the measurement to justify the validity of this work. The mathematical formulation for the proposed technique is carried out in Section 2. Section 3 elaborates on the experimental procedure for inscription of FBGs and then their respective bending tests. Section 4 provides a detailed analysis of the experimental results. This section is further divided into two subsections to facilitate better understanding of each part of the experiment: visibility analysis before bending and after bending. Finally, the conclusions are drawn out in Section 5. 2. Mathematical Model for Proposed Technique
The present study describes the effect of the grating and interference visibilities considered as parameters when analyzing the properties of an FBG at different conditions such as bending. The applied UV fluence on an FBG can be used to analyze the grating strength of a fiber [14]. This applied UV fluence is also used to investigate mechanical properties of the Bragg grating such as axial strength [16]. Additional UV fluence is necessitated in the inscription of FBG with equivalent grating strength. A red shift in the Bragg wavelength will be induced when the average refractive index is large and positive. This relationship can be well explained by the ac and dc coupling coefficients in which the growth of the grating strength is influenced by κ, which is called the ac coupling coefficient, and the Bragg wavelength is influenced by σ, which is called the dc coupling coefficient. Their relationship is denoted by [14] κ vg σ∕2;
(1)
where vg is the grating visibility. In an ideal scenario, both interference and grating visibilities are unity, but it is practically challenging due to several factors, e.g., unsuppressed zeroth order and low spatial and spectral coherences. Such limitations can be alleviated by placing the fiber as close as possible to the phase mask to obtain maximum interference visibility. The interference visibility vi of this fringe is estimated using the curve-matching technique, which is discussed further in this study. The factors 1 vi and 1 − vi describe the intensities of the interference fringe spectrum with reference to the average fluence F. The outcome can be represented as
Δnmax Δn1 vi F;
(2)
Δnmin Δn1 − vi F;
(3)
where Δnmax and Δnmin represent the maximum and minimum refractive index change, respectively, and F indicates the cumulated UV fluence. These equations can be related to the average index change Δnave and index modulation Δnmod in the following manner: Δnmax Δnave Δnmod ;
(4)
Δnmin Δnave − Δnmod :
(5)
The parameters Δnave and Δnmod can be obtained experimentally using the equations Δnave λc F∕λD − 1neff ;
(6)
p Δnmod λc Ftanh−1 R∕ηπL;
(7)
where λc F is the center wavelength, which is a function of F, R the reflectivity of the grating, λD the design Bragg wavelength, η the mode overlap parameter, L the grating length, and neff the effective index of the fiber. A relationship between the BTD and the center wavelength is built up. The ultimate result of this approach is estimating the grating visibility of the fiber after the bending process: λcenter 1 εδn∕neff λB ;
(8)
δn λ : λcenter R ∞ 1 neff B
(9)
The equation below can be derived from Eqs. (8) and (9) as 1−η
1 − εδn ; neff
(10)
where δn represents the index modulation amplitude and ε represents the relative coupling coefficient, which is a function based on bending radius and has a value between 0 and 1. Furthermore, η
λcenter R : λcenter R ∞
(11)
The values of left hand side (LHS) of Eq. (10) are calculated using the data of center wavelengths while the right hand side (RHS) of Eq. (10) are calculated using the BTD data. In order to acquire the best fitting graph of these two functions, the visibility value is adjusted until the curves of the functions overlapped with each other and the optimum cross correlation coefficient is achieved. The cross correlation coefficient can be computed with 10 February 2015 / Vol. 54, No. 5 / APPLIED OPTICS
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P x − x¯ y − y¯ ρ q ; P 1 1 y − y¯ 2 x − x¯ 2 K1 K1 1 K1
(12)
where x and y represent the data of LHS and RHS of Eq. (7). x¯ and y¯ denote P the respective mean values, and the summations are taken over a segment of length K 1 [17]. Subsequently, the grating visibilities before the bending process vgi and after the bending process vgb are compared and analyzed. It is observed that the final value of vgi is the same as the value of vgb , which is obtained after bending. The misalignment of LHS and RHS only occurs after the critical bend radius of FUD-2300, which is 0.63 cm. NA, core, and cladding radii are important parameters in this experiment. It is observed that a smaller bending radius results in high optical losses due to the leakage of wave power from the core to the cladding. 3. Experimental Setup for FBG Inscription and Bending
The experiment discussed in this study consists of two stages. Firstly, the FBGs are fabricated using the excimer–phasemask technique. When fabricating the FBG, the size of the UV beam is set to 2 cm with the aid of a beam expander and the grating length is adjusted using an adjustable vertical slit. Pulse energy in the range of 10-20 mJ and a repetition rate of 2 Hz are used in this experiment. During the grating formation process, the transmission spectra are recorded using an Optical Spectrum Analyzer controlled by Labview program via GPIB. By analyzing the data obtained for the grating growth process, the grating and interference visibilities after FBG inscription are determined. Subsequently, the obtained results aid in estimating the value of the grating visibility, which will be used for comparison after the bending process. Secondly, the FBG is recoated with a UV curable acrylate because it has the capability of increasing the flexibility of the fiber so that the fiber can be bent to achieve small bending radii, limiting the breakage of the fiber. The fiber is bent into a knot without the usage of any additional tool, which is a complete circle that consists of a 360° bending angle, as demonstrated in Fig. 1. This technique is used to keep the fiber stable for a long period of time throughout the experiment [18]. Therefore, the experimental setup would not be disturbed in any circumstance when the reading at each decreasing bending radius
Fig. 1. Schematic experimental setup for the proposed FBG bending technique. OSA: optical spectrum analyzer, ASE: amplified spontaneous emission source. 1148
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is recorded. Gradually, the bending radius is decreased till the fiber reaches its saturation level, and the corresponding transmission spectra are recorded. The recorded data are used to calculate the grating visibility of the bent FBG. The FBGs used in this experiment are fabricated in low bending loss photosensitive fibers (Nufern FUD-2300) with the employment of a KrF excimer laser and phase mask method. The UV beam is split into two components that are subsequently recombined to form an interference pattern. The enhanced spatial coherence length of the excimer laser provides an interference field with good contrast behind the mask. The gratings are formed in the fiber by exposing it to the overlapping region of the two beams. In this technique, vi is predicted in such a way that it is almost equal to the starting grating visibility value vg of the fiber, which is close to the ideal grating visibility value. In order to obtain accurate values for vg and vi , small single-pulse energy is used, particularly at the beginning of the FBG inscription process, so that the BTD induced by the first pulse fluence is small and the design wavelength of the FBG can be accurately estimated. 4. Experimental Results and Analysis
In this section the experimental data obtained during the inscription of Bragg gratings is analyzed, and the visibilities before bending are obtained. Similarly the visibilities after bending are also found and compared with the previously obtained results. A. Grating Inscription and Visibility Analysis
FUD-2300 FBGs at different reflectivity values are fabricated in order to analyze the effect on the grating visibilities. Figure 2 indicates the transmission spectra of a FUD-2300 fiber. It is observed that each of the subsequent transmission spectra shifts towards the right, which means that the center wavelength and the BTD of the grating gradually increase with increasing fluence. The FUD-2300 fiber in Fig. 2 indicates a BTD of 23.9 dB. Figure 3 shows the relationship of the center wavelength and the BTD against increasing fluence of a FUD-2300 fiber. Both center wavelength and BTD show similar trends of progression.
Fig. 2. Transmission spectra of a 2 cm long grating written in FUD-2300 fiber.
Fig. 3. Overlaid graph of center wavelength shift and variation of BTD with increasing UV fluence.
The gradual increment of the two parameters, BTD and center wavelength, is due to the increment of the ac and dc coupling of the fiber. With reference to Eq. (8), it can be explained that λcenter can be influenced by bending due to its relationship with the relative coupling coefficient of the fiber. Figure 4(a) displays two functions Δnave and Δnmod , which are represented in terms of fluence. These two functions initiate from the same locality at the commencement of the grating inscription process, and eventually Δnave deviates from Δnmod as the UV fluence increases. Figure 4(b) indicates the functions of Δnmax and Δnmin . The array F of these two functions is subsequently multiplied by the factors 1 vi and 1 − vi [see Fig. 4(c)], where vi is the interference visibility that lies within the range of (0, 1]. The interference visibility is estimated by adjusting the value of vi in such a way that the positions of the two curves in Fig. 4(c) vary and overlap with each other. The best fit value for vi is 0.86.
Fig. 4. (a) Growth of Δnave and Δnmod and (b) Δnmax and Δnmin represented as a function of cumulated fluence F. (c) The points of Δnmax and Δnmin are shifted to the new points Δn1 vi F; and Δn1 − vi F.
Fig. 5. Variation of the grating visibility during FBG inscription process.
The grating visibility of the FBG gradually drops as shown in Fig. 5 with increasing UV fluence. The grating visibility is assumed to be as close as possible to the ideal grating visibility. Therefore, it initiates at 0.86 and decays till 0.37 at the end of the inscription process. The index modulation is directly associated with the grating strength. During the grating inscription process, the Bragg wavelength red-shifts due to the increment of Δnave, and the BTD also increases due to the increment in Δnmod . Since the refractive index change increases at the beginning of the grating inscription process and gradually slows down, the rate of increase of Δn also decreases with increasing UV fluence. The result of the gradual decrement of the grating visibility is closely associated with Δn [19]. B. Determination of Grating Visibility via Bending
After the inscription process, the bending investigation is carried out to analyze the spectral response of the FBG. Figure 6 presents the transmission spectra of FBG at different bending radii in the range of 0.55–1.5 cm. The center wavelength and the BTD of the spectra gradually decrease, which is the exact opposite behavior of Fig. 2. Even though the shift in the center wavelength is approximately 0.1 nm in FUD-2300 FBG, there is a significant change in the BTD. The reason behind this decrement is the increased bending loss that takes place with decreasing bending radius. It is observed in several studies that higher bend losses in different fibers result in larger changes in BTD [20,21]. Figure 7 shows the results
Fig. 6. Transmission spectra of FBG inscribed in FUD-2300 at decreasing bending radii. 10 February 2015 / Vol. 54, No. 5 / APPLIED OPTICS
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Fig. 7. Values of LHS and RHS calculated using data of center wavelength shift and BTD against the variation of bending radius based on Eq. (10).
obtained based on Eq. (10). The two graphs are matched by varying the grating visibility of the fiber. The graphs in Fig. 7 are obtained when vgb 0.37, which is almost the same as the final value of the grating visibility vgi obtained during the FBG inscription process, as shown in Fig. 5. This result indicates that the grating visibility of an FBG can be determined from the variation in the transmission spectrum with decreasing bending radius. This concept is further tested for FUD-2300 fibers at different ranges of grating visibilities by repeating the same procedure described above. Figures 8(a)–8(c)
show the overlaid graphs for the data calculated from LHS and RHS of Eq. (10). The best fitting graphs are obtained by setting the values of vgb as 0.19, 0.29, and 0.4. The fibers are bent starting from a bending radius of 1.55 cm until it reached 0.55 cm. It is observed that the disagreement between LHS and RHS only occurs when the bending radius reaches 0.63, which is the critical bending radius of FUD-2300 fiber. The accuracy of the overlapping of these two functions is assessed based on the calculation of the cross correlation coefficient. The best grating visibility value is attained when the optimum cross correlation coefficient is achieved. Table 1 summarizes the grating visibilities determined from the transmission spectra obtained during FBG inscription vgi; the measured result based on bent-spectral analysis vgb, and the corresponding optimum cross-correlation coefficients. Apparently, the measurement based on bentspectral analysis is in good agreement with that of acquired data from the earlier inscription process. Four different grating visibilities (acquired from inscription process) ranging between 0.18 and 0.39 are investigated and a small error of ∼0.01 is observed in the measurement with cross correlation coefficients greater than 0.9. The experiment was repeated for grating visibility values above 0.5 as well. The difficulty at this stage is that vgb does not take the same value as vgi . In order to achieve a high value for vgi , the grating inscription with lower cumulative fluence should be carried out. Nevertheless, it may result in a lower Δn and BTD. This increases the difficulty in achieving accurate results due to low values in Δnave and Δnmod . The variations in the spectral characteristics with decreasing bending radius are relatively smaller if compared with the experimental uncertainty. This results in larger error in the measurement. Therefore, this study concentrates on a specific range of the grating visibility (0.1–0.4), and the results obtained justify the goal mentioned at the beginning of this paper. The increased probability of fiber breakage due to smaller bending radii during the bending process is the major challenge in the measurement. Besides, accurate measurements rely on several other factors, such as the uniformity of the fiber bent radius when the fiber is bent into a knot of 360° bending angle and stress incurred along the fiber or twisting of the fiber. It is beneficial to acquire the grating visibility that reflects the performance of the grating inscription system. Moreover, these measurement results provide information that can be incorporated in the performance optimization of the grating inscription Table 1. Grating Visibility Values Obtained after FBG Inscription and Bending Including the Respective Cross Correlation Coefficients
Fig. 8. (a)–(c) Values of LHS and RHS calculated using data of center wavelength shift and BTD against the variation of bending radius based on Eq. (10). 1150
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vgi
vgb
Cross Correlation Coefficient ρ
0.18 0.30 0.37 0.39
0.19 0.29 0.37 0.40
0.91 0.96 0.99 0.94
system. It is particularly useful for the FBG manufacturers in achieving efficient production of quality FBGs and preventing excessive UV irradiation that would weaken the fiber glass strength and lead to glass brittleness. In future works, the investigation will be extended to the grating visibility measurement for nonuniform grating structures such as apodized, phase-shifted, and chirped gratings. 5. Conclusion
In conclusion, the technique for the measurement of FBG visibility has been proposed by estimating the interference as well as grating visibilities of FUD2300 FBGs under applied UV fluence and bending conditions. The spectral properties of the FBGs during these two stages have also been analyzed. The curve matching technique has been used to estimate the interference visibility during the inscription process. Measurements of the grating visibility after inscription and with decreasing bending radius are compared by representing the two functions on an overlaid graph. The experiment is repeated for different visibility ranges to verify the validity of the results. The accuracy of these results has been verified by investigating the cross correlation coefficient of the functions. Hence, because of cost effectiveness and the importance in calculating the interference and grating visibilities, it can be considered that this method is more appealing to be used in practical applications. This work was supported by University of Malaya HIR (UM.C/625/1/HIR/181, a/c no. J-21001-73860), FRGS (FP002-2013B), and PPP (PG004-2014A). References 1. M. Lancry and B. Poumellec, “UV laser processing and multiphoton absorption processes in optical telecommunication fiber materials,” Phys. Rep. 523, 207–229 (2013). 2. J. M. López-Higuera, L. R. Cobo, A. Q. Incera, and A. Cobo, “Fiber optic sensors in structural health monitoring,” J. Lightwave Technol. 29, 587–608 (2011). 3. I. Riant, “Fiber Bragg gratings for optical telecommunications,” C. R. Phys. 4, 41–49 (2003). 4. C. R. Dennison, P. M. Wild, D. R. Wilson, and P. A. Cripton, “A minimally invasive in-fiber Bragg grating sensor for intervertebral disc pressure measurements,” Meas. Sci. Technol. 19, 1–12 (2008). 5. R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Academic, 2009).
6. N. Singh, S. C. Jain, A. K. Aggarwal, and R. P. Bajpai, “Fibre Bragg grating writing using phasemask technology,” J. Sci. Ind. Res. 64, 108–115 (2005). 7. D. Z. Anderson, V. Mizrahi, T. Erdogan, and A. E. White, “Production of in-fibre gratings using a diffractive optical element,” Electron. Lett. 29, 566–568 (1993). 8. Q. Wang, G. Farrell, and T. Freir, “Theoretical and experimental investigations of macro-bend losses for standard single mode fibers,” Opt. Express 13, 4476–4484 (2005). 9. Q. Wang, G. Farrell, T. Freir, G. Rajan, and P. Wang, “Low-cost wavelength measurement based on macro-bending singlemode fiber,” Opt. Lett. 31, 1785–1787 (2006). 10. X. Chen, C. Zhang, D. J. Webb, K. Kalli, and G. D. Peng, “Highly sensitive bend sensor based on Bragg grating in eccentric core polymer fiber,” IEEE Photon. Technol. Lett. 22, 850–852 (2010). 11. G. A. Miller, C. G. Askins, A. C. Geoffry, and E. J. Friebele, “Early index growth in germanosilicate fiber upon exposure to continuous-wave ultraviolet light,” J. Lightwave Technol. 25, 1034–1044 (2007). 12. M. J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” J. Lightwave Technol. 27, 376–382 (2009). 13. H. Patrick and S. L. Gilbert, “Growth of Bragg gratings produced by continuous-wave ultraviolet light in optical fiber,” Opt. Lett. 18, 1484–1486 (1993). 14. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997). 15. J. Huebner, M. Svalgaard, L. Gruener-Nielsen, and M. Kristensen, “Phenomenological model of UV-induced Bragg grating growth in germanosilicate fibers,” Proc. SPIE 2998, 11–21 (1997). 16. B. Poumellec, P. Niay, M. Douay, and J. F. Bayon, “The UVinduced refractive index grating in Ge:SiO2 preforms: additional CW experiments and the macroscopic origin of the change in index,” J. Phys. D 29, 1842–1846 (1996). 17. R. M. Aarts, R. Irwan, and A. J. E. M. Janssen, “Efficient tracking of the cross-correlation coefficient,” IEEE Trans. Audio Speech Lang. Process. 10, 391–402 (2002). 18. K. S. Lim, H. Z. Yang, A. Becir, M. H. Lai, M. M. Ali, X. Qiao, and H. Ahmad, “Spectral analysis of bent fiber Bragg gratings: theory and experiment,” Opt. Lett. 38, 4409–4412 (2013). 19. D. Ramecourt, P. Niay, P. Bernage, I. Riant, and M. Douay, “Growth of strength of Bragg gratings written in H2 loaded telecommunication fibre during CW UV post-exposure,” Electron. Lett. 35, 329–331 (1999). 20. A. C. Thompson, P. J. Cadusch, D. F. Robertson, P. R. Stoddart, and S. A. Wade, “Origins of spectral changes in fiber Bragg gratings due to macrobending,” J. Lightwave Technol. 30, 3500–3511 (2012). 21. S. A. Wade, D. F. Robertson, A. C. Thompson, and P. R. Stoddart, “Changes in spectral properties of fibre Bragg gratings owing to bending,” Electron. Lett. 47, 558–559 (2011).
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In this study, a technique for measuring the grating visibility of the fiber Bragg grating (FBG) based on bent-spectral analysis is proposed. From varying ac and dc coupling coefficients at different bending radii, the grating visibility is estimated with the aid of a simple mathematical model. The investigation begins with the estimation of the grating visibility from the transmission spectra of the FBG during the inscription process. After that, the FBGs are subjected to a bending test with reducing radii, and again the transmission spectra are recorded. It is shown that the estimated grating visibility is in agreement with the result determined from the earlier inscription process. © 2015 Optical Society of America OCIS codes: (060.3735) Fiber Bragg gratings; (060.3738) Fiber Bragg gratings, photosensitivity; (060.2400) Fiber properties. http://dx.doi.org/10.1364/AO.54.001146
1. Introduction
Fiber Bragg gratings (FBGs) have a significant role in the field of optical communication and the sensing industries due to their numerous features, e.g., immunity to electromagnetic interference, high insulation, low fabrication cost, high sensitivity, and low weight [1–4]. With the increasing demand for FBGs, several grating inscription techniques have been used [5]. Notably, the phase mask technique is the most commonly used due to its simplicity and high efficiency in writing high-performance FBGs. With the assistance of an excimer laser, the formation of a grating structure can be attained within seconds. Hence, an excimer laser and phase mask is perceived as the best combination for the mass production of FBGs [6]. This technique engages a diffractive optical element to spatially modulate the UV writing beam [7]. Therefore, it is noticed that the effects of UV fluence and bending on the spectral properties of FBGs have largely been explored by various studies, 1559-128X/15/051146-06$15.00/0 © 2015 Optical Society of America 1146
APPLIED OPTICS / Vol. 54, No. 5 / 10 February 2015
e.g., macro bend losses for standard single mode fibers [8], wavelength measurement based on bending [9], axially offset FBGs [10], and index growth of germanosilicate fiber upon exposure to continuous UV light [11]. Generally, decreasing bend radius results in decreasing Bragg transmission depth (BTD). In order to reduce the losses created by the bends on optical fibers, a significant series of low bend loss fibers, especially for tight bend diameter applications, such as fiber to the home, are thoroughly studied and developed [12]. As a result of the immense usage of optical fibers in the telecommunication industry today, a comprehensive analysis on the spectral properties of bent FBG is still essential. The index growth of type-I FBGs is interpreted by the variation of the reflection spectrum of the grating during the inscription process [7,13]. The grating strength and reflectivity of an FBG rely on the ac coupling coefficient, which is associated with the grating visibility [14]. Despite the high UV fluence applied in the grating inscription process, the development of grating reflectivity may be appalling due to the poor interference visibility [15]. Thus, it would be beneficial to acquire the details about the interference and
grating visibilities of a particular FBG, as it would provide accurate information about the grating strength of the fiber. The other factor that also gives the motivation to conduct this investigation is to clarify the picture of visibility for the user who purchases different FBGs to be used in various applications, which does not have any information of their visibilities. Therefore, in this work a unique measurement technique for measuring the grating visibility based on bent-spectral analysis is proposed. Mathematical models are presented and used in the analysis. FBGs with different grating visibilities are fabricated and employed in the measurement to justify the validity of this work. The mathematical formulation for the proposed technique is carried out in Section 2. Section 3 elaborates on the experimental procedure for inscription of FBGs and then their respective bending tests. Section 4 provides a detailed analysis of the experimental results. This section is further divided into two subsections to facilitate better understanding of each part of the experiment: visibility analysis before bending and after bending. Finally, the conclusions are drawn out in Section 5. 2. Mathematical Model for Proposed Technique
The present study describes the effect of the grating and interference visibilities considered as parameters when analyzing the properties of an FBG at different conditions such as bending. The applied UV fluence on an FBG can be used to analyze the grating strength of a fiber [14]. This applied UV fluence is also used to investigate mechanical properties of the Bragg grating such as axial strength [16]. Additional UV fluence is necessitated in the inscription of FBG with equivalent grating strength. A red shift in the Bragg wavelength will be induced when the average refractive index is large and positive. This relationship can be well explained by the ac and dc coupling coefficients in which the growth of the grating strength is influenced by κ, which is called the ac coupling coefficient, and the Bragg wavelength is influenced by σ, which is called the dc coupling coefficient. Their relationship is denoted by [14] κ vg σ∕2;
(1)
where vg is the grating visibility. In an ideal scenario, both interference and grating visibilities are unity, but it is practically challenging due to several factors, e.g., unsuppressed zeroth order and low spatial and spectral coherences. Such limitations can be alleviated by placing the fiber as close as possible to the phase mask to obtain maximum interference visibility. The interference visibility vi of this fringe is estimated using the curve-matching technique, which is discussed further in this study. The factors 1 vi and 1 − vi describe the intensities of the interference fringe spectrum with reference to the average fluence F. The outcome can be represented as
Δnmax Δn1 vi F;
(2)
Δnmin Δn1 − vi F;
(3)
where Δnmax and Δnmin represent the maximum and minimum refractive index change, respectively, and F indicates the cumulated UV fluence. These equations can be related to the average index change Δnave and index modulation Δnmod in the following manner: Δnmax Δnave Δnmod ;
(4)
Δnmin Δnave − Δnmod :
(5)
The parameters Δnave and Δnmod can be obtained experimentally using the equations Δnave λc F∕λD − 1neff ;
(6)
p Δnmod λc Ftanh−1 R∕ηπL;
(7)
where λc F is the center wavelength, which is a function of F, R the reflectivity of the grating, λD the design Bragg wavelength, η the mode overlap parameter, L the grating length, and neff the effective index of the fiber. A relationship between the BTD and the center wavelength is built up. The ultimate result of this approach is estimating the grating visibility of the fiber after the bending process: λcenter 1 εδn∕neff λB ;
(8)
δn λ : λcenter R ∞ 1 neff B
(9)
The equation below can be derived from Eqs. (8) and (9) as 1−η
1 − εδn ; neff
(10)
where δn represents the index modulation amplitude and ε represents the relative coupling coefficient, which is a function based on bending radius and has a value between 0 and 1. Furthermore, η
λcenter R : λcenter R ∞
(11)
The values of left hand side (LHS) of Eq. (10) are calculated using the data of center wavelengths while the right hand side (RHS) of Eq. (10) are calculated using the BTD data. In order to acquire the best fitting graph of these two functions, the visibility value is adjusted until the curves of the functions overlapped with each other and the optimum cross correlation coefficient is achieved. The cross correlation coefficient can be computed with 10 February 2015 / Vol. 54, No. 5 / APPLIED OPTICS
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P x − x¯ y − y¯ ρ q ; P 1 1 y − y¯ 2 x − x¯ 2 K1 K1 1 K1
(12)
where x and y represent the data of LHS and RHS of Eq. (7). x¯ and y¯ denote P the respective mean values, and the summations are taken over a segment of length K 1 [17]. Subsequently, the grating visibilities before the bending process vgi and after the bending process vgb are compared and analyzed. It is observed that the final value of vgi is the same as the value of vgb , which is obtained after bending. The misalignment of LHS and RHS only occurs after the critical bend radius of FUD-2300, which is 0.63 cm. NA, core, and cladding radii are important parameters in this experiment. It is observed that a smaller bending radius results in high optical losses due to the leakage of wave power from the core to the cladding. 3. Experimental Setup for FBG Inscription and Bending
The experiment discussed in this study consists of two stages. Firstly, the FBGs are fabricated using the excimer–phasemask technique. When fabricating the FBG, the size of the UV beam is set to 2 cm with the aid of a beam expander and the grating length is adjusted using an adjustable vertical slit. Pulse energy in the range of 10-20 mJ and a repetition rate of 2 Hz are used in this experiment. During the grating formation process, the transmission spectra are recorded using an Optical Spectrum Analyzer controlled by Labview program via GPIB. By analyzing the data obtained for the grating growth process, the grating and interference visibilities after FBG inscription are determined. Subsequently, the obtained results aid in estimating the value of the grating visibility, which will be used for comparison after the bending process. Secondly, the FBG is recoated with a UV curable acrylate because it has the capability of increasing the flexibility of the fiber so that the fiber can be bent to achieve small bending radii, limiting the breakage of the fiber. The fiber is bent into a knot without the usage of any additional tool, which is a complete circle that consists of a 360° bending angle, as demonstrated in Fig. 1. This technique is used to keep the fiber stable for a long period of time throughout the experiment [18]. Therefore, the experimental setup would not be disturbed in any circumstance when the reading at each decreasing bending radius
Fig. 1. Schematic experimental setup for the proposed FBG bending technique. OSA: optical spectrum analyzer, ASE: amplified spontaneous emission source. 1148
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is recorded. Gradually, the bending radius is decreased till the fiber reaches its saturation level, and the corresponding transmission spectra are recorded. The recorded data are used to calculate the grating visibility of the bent FBG. The FBGs used in this experiment are fabricated in low bending loss photosensitive fibers (Nufern FUD-2300) with the employment of a KrF excimer laser and phase mask method. The UV beam is split into two components that are subsequently recombined to form an interference pattern. The enhanced spatial coherence length of the excimer laser provides an interference field with good contrast behind the mask. The gratings are formed in the fiber by exposing it to the overlapping region of the two beams. In this technique, vi is predicted in such a way that it is almost equal to the starting grating visibility value vg of the fiber, which is close to the ideal grating visibility value. In order to obtain accurate values for vg and vi , small single-pulse energy is used, particularly at the beginning of the FBG inscription process, so that the BTD induced by the first pulse fluence is small and the design wavelength of the FBG can be accurately estimated. 4. Experimental Results and Analysis
In this section the experimental data obtained during the inscription of Bragg gratings is analyzed, and the visibilities before bending are obtained. Similarly the visibilities after bending are also found and compared with the previously obtained results. A. Grating Inscription and Visibility Analysis
FUD-2300 FBGs at different reflectivity values are fabricated in order to analyze the effect on the grating visibilities. Figure 2 indicates the transmission spectra of a FUD-2300 fiber. It is observed that each of the subsequent transmission spectra shifts towards the right, which means that the center wavelength and the BTD of the grating gradually increase with increasing fluence. The FUD-2300 fiber in Fig. 2 indicates a BTD of 23.9 dB. Figure 3 shows the relationship of the center wavelength and the BTD against increasing fluence of a FUD-2300 fiber. Both center wavelength and BTD show similar trends of progression.
Fig. 2. Transmission spectra of a 2 cm long grating written in FUD-2300 fiber.
Fig. 3. Overlaid graph of center wavelength shift and variation of BTD with increasing UV fluence.
The gradual increment of the two parameters, BTD and center wavelength, is due to the increment of the ac and dc coupling of the fiber. With reference to Eq. (8), it can be explained that λcenter can be influenced by bending due to its relationship with the relative coupling coefficient of the fiber. Figure 4(a) displays two functions Δnave and Δnmod , which are represented in terms of fluence. These two functions initiate from the same locality at the commencement of the grating inscription process, and eventually Δnave deviates from Δnmod as the UV fluence increases. Figure 4(b) indicates the functions of Δnmax and Δnmin . The array F of these two functions is subsequently multiplied by the factors 1 vi and 1 − vi [see Fig. 4(c)], where vi is the interference visibility that lies within the range of (0, 1]. The interference visibility is estimated by adjusting the value of vi in such a way that the positions of the two curves in Fig. 4(c) vary and overlap with each other. The best fit value for vi is 0.86.
Fig. 4. (a) Growth of Δnave and Δnmod and (b) Δnmax and Δnmin represented as a function of cumulated fluence F. (c) The points of Δnmax and Δnmin are shifted to the new points Δn1 vi F; and Δn1 − vi F.
Fig. 5. Variation of the grating visibility during FBG inscription process.
The grating visibility of the FBG gradually drops as shown in Fig. 5 with increasing UV fluence. The grating visibility is assumed to be as close as possible to the ideal grating visibility. Therefore, it initiates at 0.86 and decays till 0.37 at the end of the inscription process. The index modulation is directly associated with the grating strength. During the grating inscription process, the Bragg wavelength red-shifts due to the increment of Δnave, and the BTD also increases due to the increment in Δnmod . Since the refractive index change increases at the beginning of the grating inscription process and gradually slows down, the rate of increase of Δn also decreases with increasing UV fluence. The result of the gradual decrement of the grating visibility is closely associated with Δn [19]. B. Determination of Grating Visibility via Bending
After the inscription process, the bending investigation is carried out to analyze the spectral response of the FBG. Figure 6 presents the transmission spectra of FBG at different bending radii in the range of 0.55–1.5 cm. The center wavelength and the BTD of the spectra gradually decrease, which is the exact opposite behavior of Fig. 2. Even though the shift in the center wavelength is approximately 0.1 nm in FUD-2300 FBG, there is a significant change in the BTD. The reason behind this decrement is the increased bending loss that takes place with decreasing bending radius. It is observed in several studies that higher bend losses in different fibers result in larger changes in BTD [20,21]. Figure 7 shows the results
Fig. 6. Transmission spectra of FBG inscribed in FUD-2300 at decreasing bending radii. 10 February 2015 / Vol. 54, No. 5 / APPLIED OPTICS
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Fig. 7. Values of LHS and RHS calculated using data of center wavelength shift and BTD against the variation of bending radius based on Eq. (10).
obtained based on Eq. (10). The two graphs are matched by varying the grating visibility of the fiber. The graphs in Fig. 7 are obtained when vgb 0.37, which is almost the same as the final value of the grating visibility vgi obtained during the FBG inscription process, as shown in Fig. 5. This result indicates that the grating visibility of an FBG can be determined from the variation in the transmission spectrum with decreasing bending radius. This concept is further tested for FUD-2300 fibers at different ranges of grating visibilities by repeating the same procedure described above. Figures 8(a)–8(c)
show the overlaid graphs for the data calculated from LHS and RHS of Eq. (10). The best fitting graphs are obtained by setting the values of vgb as 0.19, 0.29, and 0.4. The fibers are bent starting from a bending radius of 1.55 cm until it reached 0.55 cm. It is observed that the disagreement between LHS and RHS only occurs when the bending radius reaches 0.63, which is the critical bending radius of FUD-2300 fiber. The accuracy of the overlapping of these two functions is assessed based on the calculation of the cross correlation coefficient. The best grating visibility value is attained when the optimum cross correlation coefficient is achieved. Table 1 summarizes the grating visibilities determined from the transmission spectra obtained during FBG inscription vgi; the measured result based on bent-spectral analysis vgb, and the corresponding optimum cross-correlation coefficients. Apparently, the measurement based on bentspectral analysis is in good agreement with that of acquired data from the earlier inscription process. Four different grating visibilities (acquired from inscription process) ranging between 0.18 and 0.39 are investigated and a small error of ∼0.01 is observed in the measurement with cross correlation coefficients greater than 0.9. The experiment was repeated for grating visibility values above 0.5 as well. The difficulty at this stage is that vgb does not take the same value as vgi . In order to achieve a high value for vgi , the grating inscription with lower cumulative fluence should be carried out. Nevertheless, it may result in a lower Δn and BTD. This increases the difficulty in achieving accurate results due to low values in Δnave and Δnmod . The variations in the spectral characteristics with decreasing bending radius are relatively smaller if compared with the experimental uncertainty. This results in larger error in the measurement. Therefore, this study concentrates on a specific range of the grating visibility (0.1–0.4), and the results obtained justify the goal mentioned at the beginning of this paper. The increased probability of fiber breakage due to smaller bending radii during the bending process is the major challenge in the measurement. Besides, accurate measurements rely on several other factors, such as the uniformity of the fiber bent radius when the fiber is bent into a knot of 360° bending angle and stress incurred along the fiber or twisting of the fiber. It is beneficial to acquire the grating visibility that reflects the performance of the grating inscription system. Moreover, these measurement results provide information that can be incorporated in the performance optimization of the grating inscription Table 1. Grating Visibility Values Obtained after FBG Inscription and Bending Including the Respective Cross Correlation Coefficients
Fig. 8. (a)–(c) Values of LHS and RHS calculated using data of center wavelength shift and BTD against the variation of bending radius based on Eq. (10). 1150
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vgi
vgb
Cross Correlation Coefficient ρ
0.18 0.30 0.37 0.39
0.19 0.29 0.37 0.40
0.91 0.96 0.99 0.94
system. It is particularly useful for the FBG manufacturers in achieving efficient production of quality FBGs and preventing excessive UV irradiation that would weaken the fiber glass strength and lead to glass brittleness. In future works, the investigation will be extended to the grating visibility measurement for nonuniform grating structures such as apodized, phase-shifted, and chirped gratings. 5. Conclusion
In conclusion, the technique for the measurement of FBG visibility has been proposed by estimating the interference as well as grating visibilities of FUD2300 FBGs under applied UV fluence and bending conditions. The spectral properties of the FBGs during these two stages have also been analyzed. The curve matching technique has been used to estimate the interference visibility during the inscription process. Measurements of the grating visibility after inscription and with decreasing bending radius are compared by representing the two functions on an overlaid graph. The experiment is repeated for different visibility ranges to verify the validity of the results. The accuracy of these results has been verified by investigating the cross correlation coefficient of the functions. Hence, because of cost effectiveness and the importance in calculating the interference and grating visibilities, it can be considered that this method is more appealing to be used in practical applications. This work was supported by University of Malaya HIR (UM.C/625/1/HIR/181, a/c no. J-21001-73860), FRGS (FP002-2013B), and PPP (PG004-2014A). References 1. M. Lancry and B. Poumellec, “UV laser processing and multiphoton absorption processes in optical telecommunication fiber materials,” Phys. Rep. 523, 207–229 (2013). 2. J. M. López-Higuera, L. R. Cobo, A. Q. Incera, and A. Cobo, “Fiber optic sensors in structural health monitoring,” J. Lightwave Technol. 29, 587–608 (2011). 3. I. Riant, “Fiber Bragg gratings for optical telecommunications,” C. R. Phys. 4, 41–49 (2003). 4. C. R. Dennison, P. M. Wild, D. R. Wilson, and P. A. Cripton, “A minimally invasive in-fiber Bragg grating sensor for intervertebral disc pressure measurements,” Meas. Sci. Technol. 19, 1–12 (2008). 5. R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Academic, 2009).
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