Simultaneous bend and temperature sensor using tilted FBG C. Caucheteur∗, K. Chah, F. Lhommé, M. Blondel, P. Mégret Faculté Polytechnique de Mons, Electromagnetism and Telecommunication Unit, 31 Boulevard Dolez, 7000 Mons, BELGIUM ABSTRACT We propose a simple, very reliable and fast optical sensor based on a tilted fiber Bragg grating for the simultaneous measurement of temperature and macro bending. The transmitted spectrum of a tilted Bragg grating is composed of numerous discrete dips which have two distinct origins : the dip at the longest wavelength comes from the self coupling of the core mode while the others are due to the backward coupling with the cladding modes. We apply a different demodulation technique to each of these two contributions in order to realize a dual sensor. This sensor allows the detection of small curvatures and provides a good accuracy. Keywords: Fiber Bragg gratings, tilted, sensor, temperature, bending
1. INTRODUCTION In recent years, a number of sensing schemes intended for the detection of physical parameters by use of fiber Bragg gratings have been proposed and discussed.1 Along with temperature and strain, mechanical bending is an important quantity in the diagnosis of structural damage. Tilted fiber Bragg gratings (TFBG), which are characterized by an index modulation pattern blazed by a certain angle with respect to the fiber axis, have demonstrated a great potential for macrobending measurement.2 In single mode fibers, TFBG enhance the backward couplings between the LP 01 core mode and the cladding modes. Hence, transmission spectra of TFBG exhibit discrete dips at wavelengths below the Bragg resonance wavelength which corresponds to the self backward coupling of the LP 01 mode. Among the cladding modes couplings, one is particularly strong and is called ‘ghost mode’ since the mode decays rapidly at the cladding-coating interface. The bending of a fiber containing a TFBG has previously been observed to result in a change in the depth of the ghost mode.2 This power variation allowed a sensitivity of about 5 cm in terms of the radius of the bending curvature. However, TFBG are also inherently sensitive to external temperature. It is thus important, especially in the case of realtime monitoring systems, to measure bending as well as temperature or, at least, to be sure that temperature does not affect bending measurements. In this paper, we first report a new bend induced effect and we secondly discriminate macro-bending and temperature effects by means of a 3° TFBG written into hydrogen-loaded single mode fiber. For that purpose, we dissociate the numerical treatment of the information contained in the transmitted spectrum of the 3° TFBG in order to realize a dual sensor. This sensor works very fast and offers a good accuracy.
2. CLADDING MODES COUPLINGS WITH TFBG In TFBG, two different couplings exist : one is the coupling between the forward core mode and the backward core mode, the other is the coupling between the core mode and the different cladding modes. If θ represents the angle of the TFBG with respect to the fiber axis and Λg is the nominal grating period (see Fig. 1), the resonance wavelength, corresponding to the self coupling of the core mode, is given by the following equation : λBragg =
2neff , core Λ g
(1)
cos θ
where neff,core is the effective refractive index of the LP01 mode. The wavelengths at which the couplings to contrapropagating cladding modes occur are obtained from the phase matching condition : λcoupling = ( neff ,cladding + neff , core ) ∗
Λg cos θ
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(2)
where neff,cladding is the effective refractive index of a particular cladding mode. The induced index change in the core of the fiber δn is also affected by the tilt angle leading to the following relationship : 3 2π δn( x, z ) = δn( z ' ) 1 + v cos( z ' ) Λg
(3)
where z’≅z cosθ since the “dc” index change δn can be considered as a slowly varying function. v is the fringe visibility of the index change. The expression of the backward coupling coefficient is then given by : K m ± ( z ) = σ ( z ) + 2κ m ± ( z ) cos(
2π z) Λ
(4)
In this expression, Λ is the grating period along the fiber axis. (+) and (-) denote the forward-going and backward-going modes, respectively. The “dc” and “ac” coupling coefficients σ and κ m ± depend both on the tilt angle and their expressions can be derived using the coupled mode theory formalism.3 From Fig. 2, which has been obtained by implementing the coupled mode equations reported in Ref. 4, the influence of the tilt angle on the backward coupling coefficient of the core mode is clearly observed. Hence, when the tilt angle increases, the value of the backward coefficient decreases and consequently, the grating reflectivity also decreases. The evolution of the backward coupling coefficient with the tilt angle has been computed with parameters corresponding to the fiber used during the experiments. Backward coupling coefficient
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Fig. 1. Parameters of a tilted fiber Bragg grating
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Fig. 3. Schematic of the bending system
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ilt an g le (d e g re e s) Fig. 2. Plot of the self coupling Tcoefficient of the core mode versus tilt angle for the parameters of the fiber used below : core radius a = 2.625 µm, cladding index ncl = 1.44 and core index nco = 1.448
Since we want to simultaneously measure bending and temperature, it is essential to have a transmitted spectrum of the TFBG exhibiting a dip at the resonance wavelength. It is the reason why we have written weakly tilted fiber Bragg gratings. In the following, we present the results obtained with a 3° TFBG. This choice has provided very good results. The grating was written into hydrogen-loaded single mode Corning Flexcore fiber by means of a frequency doubled Argon laser. We used a 1060 nm period phase mask mounted on a rotator so that it was possible to apply a tilt in the plane perpendicular to the laser beam. The grating had a physical length of 2 cm. The optical power on the phase mask was about 150 mW and the exposure time was equal to 10 minutes.
3. BENDING MEASUREMENT Since the effective variation in the tilt angle depends on the bending direction with respect to the tilt angle direction, the side of the fiber facing the UV beam was marked during the inscription of the grating. This precaution allows the right positioning of the grating tilt direction with respect to the bending direction so that the grating exhibits the maximum sensitivity.2 In order to eliminate axial strain, the bend sensitivity measurements were made by loosely fixing the two ends of the fiber containing the TFBG on two blocks, whose one was mounted on a translation stage in order to bend the fiber, as shown on Fig. 3. When the TFBG is placed midway between the two mounting blocks, the resulting curvature R is simply given by the following expression : R=
2h h + ( d / 2) 2 2
(5)
where d is the distance between the two blocks and h is the bending displacement. The effect of bending on the transmitted spectrum of the 3° TFBG can be observed on Fig. 4. The measurements were obtained by means of a
Amplitude of the resonant dip (dB)
broadband ASE source and an optical spectrum analyzer ANDO AQ6317C. The transmitted spectra were recorded with a wavelength resolution of 15 pm. The main effect of a small bending is indicated by an arrow on the transmitted spectrum presented in Fig. 4b. The dips corresponding to the high effective index cladding modes, i.e. the cladding modes situated near the resonance wavelength, are very sensitive to small bending and their peak to peak amplitudes decrease as a function of curvature whereas the amplitude of the dip corresponding to the resonant wavelength remains nearly unchanged (Fig. 4c). This behavior can be explained owing to the coupling strengths of the cladding modes. The couplings with the highest effective index cladding modes are much stronger and thus more sensitive to small curvatures than the other ones.5 The highest effective cladding modes become radiated, which is spectrally marked by a smoothing around the longest wavelengths. To correlate the spectral evolution with the bending strength, we have chosen to monitor the evolution of the area delimited by the upper and lower envelopes of the part of the transmitted spectrum corresponding to the cladding modes (see Fig. 5). We use the normalized area which is defined as the ratio between the area of a perturbed spectrum (i.e. subjected to some bending) and the area of the reference grating (without bending). 6 Since the effect of bending is to smooth the spectrum, the normalized area decreases with increasing bending. The evolution of the normalized area with respect to curvature, which can be approached by a second order polynomial, is observed on Fig. 6. Hence, applying this demodulation technique to the 3° TFBG allows us to accurately detect curvatures as small as 1 or 2 cm-1. The accuracy on the detection of small curvatures has been measured equal to ± 0.5 cm-1. To test the repeatability of the method, we have applied a constant bending on the grating and we have measured the transmitted spectrum 100 times. 90 % of the measurements gave the same curvature to within 1 cm-1. So, the monitoring of the evolution of the normalized area provides both a good accuracy and a good repeatability for the detection of curvatures. 1 .0 0 .8 0 .6
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Fig. 4. Transmitted spectrum of the 3° TFBG with R=0 m-1 (a) and R=0.2 m-1 (b); Evolution of the resonant dip with respect to bending (c) : R=0 m-1 (solid), R=0.5 m-1 (dash) and R=1 m-1 (dot) 1 .0
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Fig. 5. Envelope curves of the transmitted spectrum of the 3° TFBG measured without bending
Fig. 6. Normalized area versus curvature
4. THERMAL EFFECTS To study the temperature influence on the transmitted spectrum of the 3° TFBG, we have placed the grating inside an oven regulated by a thermoelectric temperature controller. Temperature was set from 25°C to 80°C with an accuracy of 0.1°C. In response to temperature variations, the transmitted spectrum was subjected to a wavelength shift without significant change in amplitude. We have then computed the temperature sensitivities of the cladding modes. These sensitivities as well as the errors made during the computation of the linear regressions are shown on Fig. 7. The cladding resonances were numbered with respect to their coupling wavelength λcoupling,i so that the number i=1 represented the smallest value of λcoupling,i.
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Fig. 7. Temperature sensitivity of the cladding modes
Fig. 8. Temperature sensitivity of the resonance wavelength
With a very good approximation, we can consider that the different cladding modes exhibit the same temperature sensitivity and that the global shape of the transmitted spectrum remains always the same under any thermal fluctuations. In the same way, we can assume that the envelope curves and the normalized area are not affected by changes of external temperature. We have also compared the normalized areas computed when the grating was subjected to a constant bending and a variable temperature. We have not found any significant change in the normalized area. We have verified that it does not affect the accuracy on the bending measurements, which proves the validity of our approximation. Hence, to detect temperature effects, we have simply used the wavelength shift of the resonant dip since we have demonstrated that it is not sensitive to macro bending in the ranges of interest. The evolution of the resonance wavelength can be observed on Fig. 8. The temperature sensitivity was measured to be equal to 9.94 ± 0.05 pm/°C. The accuracy on the measurement of temperature with this simple set-up was computed equal to ± 1.5°C. Our set-up allows us to simultaneously detect bending and curvature by means of a very simple detection scheme including only a broadband light source and an optical spectrum analyzer. This last one is controlled by a computer in which the demodulation algorithm for the bending measurement is implemented. More than its accuracy and repeatability, our sensor provides very fast measurements, which is particularly useful for real-time monitoring systems.
5. CONCLUSIONS We studied the influences of macro-bending and temperature on the transmitted spectrum of a 3° TFBG. We showed that the main effect of small bending was to smooth the transmitted spectrum around the highest effective cladding modes and that the resonance wavelength was not affected. In order to detect curvatures, we chose to monitor the evolution of the area delimited by the cladding modes of the transmitted spectrum. This demodulation technique allows the proper detection of very small curvatures. We also showed that temperature did not affect this demodulation technique. The monitoring of the temperature induced shift of the Bragg resonance wavelength allowed to simultaneously measure bending and temperature. The accuracies were equal to 0.5 cm -1 and 1.5°C for bending and temperature, respectively.
ACKNOWLEDGMENTS Christophe Caucheteur is supported by the ‘Fonds National de la Recherche Scientifique’ (FNRS). Patrice Mégret is supported by the ‘Belgian Science Policy’. The authors are grateful to Damien Kinet from Multitel ASBL for the hydrogenation of the fiber used in this work.
REFERENCE 1. 2. 3. 4. 5. 6.
Y.J. Rao, “Recent progress in application of in-fibre Bragg grating sensors”, Optics and Lasers in Engineering 31, pp 297-324, 1999. S. Baek, Y. Jeong, B. Lee, “Characteristics of short-period blazed fiber Bragg gratings for use as macro-bending sensors”, Applied Optics 41, pp 631-636, 2002. T. Erdogan, “Fiber grating spectra”, Journal of Lightwave Technology 15, pp 1277-1294, 1997. C. Tsao, Optical Fibre Waveguide Analysis, Oxford U. Press, Oxford, 1992. A. Yariv, Optical Electronics (fourth edition), HRW Saunders, USA, 1991. G. Laffont, P. Ferdinand, “Tilted short-period fibre-Bragg-grating-induced coupling to cladding modes for accurate refractometry”, Measurement Science and Technology 12, pp 765-770, 2001.
