Open Access
Add to BibSonomyAbstract
We demonstrate for the first time a possibility of fabrication of Bragg gratings in polymer microstructured fibers with multiple reflection peaks by using He-Cd laser (λ = 325 nm) and a phase mask with higher diffraction orders. We experimentally studied the growth dynamics of the grating with the primary Bragg peak at λB = 1555 nm, for which we also observed good quality peaks located at λB/2 = 782 nm and 2λB/3 = 1040 nm. Temperature response of all the Bragg peaks was also investigated. Detailed numerical simulations of the interference pattern produced by the phase mask suggests that the higher order Bragg peaks originate from interference of UV beams diffracted in ± 1st, ± 2nd orders. We also demonstrated the grating with the reflection peak at λB/2 = 659 nm, which is the shortest Bragg wavelength ever reported for polymer microstructured fibers. This peak was observed for the grating with primary Bragg wavelength at λB = 1309 nm.
©2013 Optical Society of America
1. Introduction
Over the past twenty years the technology of fabrication of Bragg gratings (FBGs) in silica fibers was very well refined and is now routinely used for production of fiber optic components for telecommunication, fiber lasers, and fiber sensing [1,2]. In recent years the manufacturing technology of Bragg gratings in polymer optical fibers (POFs) has been intensively developed. Due to specific material properties, POFs may have better parameters in a variety of applications than fibers made of silica glass. One of the advantages of polymer fibers is biological compatibility, which opens the possibility for medical applications. Moreover, Young's modulus of polymers is much lower (about 3 GPa) than the silica glass (72 GPa), which results in high flexibility and a much wider range of strain the POFs can withstand thus enabling applications of polymer fibers as elongation sensors in the range unattainable for silica fibers [3].
Fabrication of Bragg gratings in polymer fibers has been already reported in both standard [4–13] and microstructured fibers [14–22] made of different materials, including pure (methyl methacrylate) (PMMA) [4–16,19–22] and TOPAS [16–18]. In published literature one can find different methods of Bragg gratings inscription in POFs, including the phase mask technique [9–21], combination of the phase mask and the ring interferometry [4,6–8] and point by point direct writing using Ti:sapphire femtosecond laser [22]. Due to absorption characteristics of polymer materials, the most frequently used source for writing Bragg gratings is He-Cd laser, λ = 325 nm [9–12,14–21]. Successful fabrication of Bragg gratings in PMMA fibers has been demonstrated in the third and the second communication windows but practical significance of such devices is limited due to high material losses at these spectral ranges. Therefore, in recent years increasing efforts have been made to fabricate Bragg gratings in POFs for the first communication window and the visible range [9,16,18–21].
Phase masks for Bragg grating fabrication are typically designed to suppress a zero diffraction order. In case there are only ± 1st diffraction orders behind the phase mask with a period Λ, the intensity distribution in the interference pattern has a periodicity of Λ/2. However, the appearance of the 0th order diffraction beam (even with small efficiency), which interferes with ± 1st orders, causes formation of a periodic Talbot interference pattern behind the phase mask [5] and gives rise to intensity variations with a periodicity of Λ. The existence of these two periodicities in the diffraction field was experimentally confirmed by visual observation of corresponding index modulation imprinted in silica fibers [23–26] and polymer fibers [5,9,11,12]. Moreover, for Bragg gratings in silica fibers two reflection peaks at wavelengths λB and 2λB were observed, which are directly linked to effective index modulation with periodicity of Λ/2 and Λ [27–29]. It was also demonstrated for silica fibers that the presence of higher diffraction gives rise to Bragg reflection peaks located at λB/2 and 2λB/3 [26,30,31].
In this paper we demonstrate for the first time that higher order Bragg gratings can be inscribed also in microstructured polymer fibers (mPOFs) made of pure PMMA by using the phase mask with 0th, ± 1st, ± 2nd diffraction orders. We experimentally studied the growth dynamics of the grating with the primary Bragg peak at λB = 1555 nm, accompanied by higher order peaks placed at λB/2 = 782 nm and 2λB/3 = 1040 nm, and investigated the temperature response of all the peaks. We also demonstrated the Bragg reflection peak at shortest wavelength ever reported for mPOFs (λB/2 = 659 nm), which is the second order peak of the grating with λB = 1309 nm. Detailed numerical simulations of the interference pattern behind the phase mask points to the possible role of the ± 1st, ± 2nd diffraction orders in formation of the λB/2 and 2λB/3 Bragg reflection peaks.
2. Fabrication and characterization of Bragg gratings in mPOF
Fiber Bragg gratings studied in this work were inscribed in non-annealed microstructured poly(methyl methacrylate) (PMMA) fiber fabricated at Maria Curie-Sklodowska University, Lublin, Poland, by using a preform drilling method. For preform fabrication we used a commercially available PMMA (Plastics Group) with molecular weight of 135000 u. A cross-section of the fabricated fiber is shown in the inset to Fig. 1 . The fiber was drawn with a tension of 11.4 MPa at the temperature of 280°C. Its outer diameter was equal to 248 µm, while the averaged diameter of air holes and the pitch distance were equal respectively to 3.2 µm and 6.6 µm. The measured loss in the visible range for the fundamental mode was about 6 dB/m. Due to high attenuation of the first order mode, this fiber was effectively single mode in the first communication window.
Fig. 1 Schematic diagram of the experimental setup used for grating inscription in the mPOF shown in the inset.
For writing the Bragg gratings we used a single mode 30 mW CW He-Cd laser operating at 325 nm (IK3301R-G, Kimmon). The linearly polarized laser beam was focused on the fiber through the phase mask by plano-convex cylindrical lens with 100 mm focal length, located at a distance of 92 mm from the fiber. The focused beam formed on the fiber top surface a line of about 3 mm long and 50 µm wide. The electric vector of the laser beam was parallel to the phase mask’s grooves.
As Bragg gratings inscription in polymer fibers requires long irradiation time, a special care has to be taken to assure high mechanical stability of the experimental set-up. To avoid any movements of the fiber with respect to the phase mask, the mPOF was mounted in a specially designed base with V-groves. The phase mask was placed on the top of the base and held by two springs shown in the inset to Fig. 1. The gap of 80 μm between the fiber and the phase mask was adjusted by the distance plates with precision of about 10 μm. The base with the fiber and the phase mask was installed on a three-axis translation stage, allowing for a precise alignment of the fiber position with respect to the UV beam. Due to high attenuation of the polymer fibers in the third telecommunication window, we used a single mode fiber coupler, a supercontinuum source (NKT Photonics – SuperK Versa) and an optical spectrum analyzer (Ando AQ6317B) to monitor a re〉ection spectrum of the Bragg grating during the fabrication process. The light was coupled into the short piece (less than 20 cm) of mPOF from a single mode silica fiber using index matching gel to reduce Fresnel reflections.
In the fabrication process we used the phase mask from Ibsen Photonics with a period of Λ = 1.052 µm customized for 325 nm writing wavelength. This mask allows for inscription of the gratings in mPOFs with the primary Bragg peak at λB = 1555 nm. Its diffraction efficiency for the zero order was suppressed below 2%, however, as it is shown in Fig. 2 , the efficiencies for ± 1st, ± 2nd, and ± 3rd orders were significant. The measured values of the efficiency for all the diffraction orders are gathered in Table 1 .
Fig. 2 Diffraction orders behind the phase mask for He-Cd laser writing beam (325 nm) used for Bragg grating inscription.
Table 1. Diffraction efficiencies measured for the phase masks with period of 1052 nm and 855 nm used for Bragg gratings fabrication.
In Fig. 3 we show the reflection spectrum recorded in the spectral range 750-1600 nm, with clearly visible three Bragg peaks at wavelengths λB = 1555 nm, 2λB/3 = 1040 nm and λB/2 = 782 nm.
Fig. 3 Reflection spectrum recorded during the fabrication process (in 28th minute of exposure) of Bragg grating in microstructured polymer fiber with three reflection peaks.
We studied the evolution of all the Bragg peaks during the inscription process and after the He-Cd laser was turned-off. For this purpose we have fabricated more than ten Bragg gratings with higher order reflection peaks, which show repeatable growth dynamics illustrated in Figs. 4 and 5 for one selected grating. For this grating, we show in Fig. 4 the reflection spectra for the three peaks registered during irradiation by the He-Cd laser beam using OSA with resolution of 0.2 nm. In Fig. 5 we show a change in the Bragg wavelengths and peaks’ height during and after the writing process was finished. This change is defined as the difference between the actual position of the peak center and its initial position at the early stage of the grating development.
Fig. 4 Evolution of reflection spectra at 1555 nm (a), 1040 nm (b) and 782 nm (c) during 41 min of inscription process for one of the fabricated gratings.
Fig. 5 Evolution of Bragg wavelengths (a) and peaks’ height (b) registered during and after the writing process.
Similarly as reported earlier for the primary peak [8,10,13,18,19], all the three peaks move towards shorter wavelengths during the writing process. This effect is induced by a change in the average mode effective index and by the temperature increase during the exposure to the UV beam, which results in partial relaxation of stress frozen in the fiber and causes a gradual reduction of the grating period [10,15]. An individual impact of each of the three factors responsible for the wavelength shift is difficult to estimate. However, by comparing the permanent shift of the Bragg peak after the fabrication process and after the thermal tests conducted for the gratings, we conclude that the fiber temperature during the inscription does not exceed 60°C.
We observed a certain level of randomness in the dynamics of the writing process between different gratings, which is most probably related to the fact that angular orientation of the fiber with respect to the UV writing beam was not controlled with sufficient precision. As demonstrated in [14,32], angular orientation of the fiber microstructure has a significant impact on the intensity distribution of the UV beam in the core region, which directly affects the growth dynamics. After switching off the He-Cd laser, all the Bragg peaks quickly shift towards longer wavelengths, which is most probably caused by reorientation of molecular chains to the initial positions they had before the writing process was started. This effect is not completely reversible because at increased temperature part of the frozen stress is released thus causing permanent shrinkage of the grating period. As a result the final positions of the Bragg peaks after finishing the inscription were shifted compared to their initial positions measured at the beginning of the inscription process. This shift is especially well pronounced for the peak at 1555 nm (0.8 nm) and is barely noticeable at 782 nm. The amount of the permanent Bragg wavelength shift depends on the exposure time and the fiber alignment. Longer exposure and faster grating growth result in greater permanent shift of the Bragg peaks. This effect is in agreement with earlier publications, which report on the Bragg wavelength return to the initial position after the writing process is stopped, when the local temperature of the fiber does not achieve the threshold level [10]. The threshold temperature is related to thermal history of the mPOF and the drawing conditions [15].
For most of the fabricated gratings, relative heights of all the reflected peaks measured with respect to the background increased with exposure time and saturated at certain level [10]. When the fiber was further irradiated, the peaks’ degradation was observed similarly as reported earlier in [7]. This observation is in contrast to Bragg gratings in silica fibers [26,27], in which the quickest saturation was reported for the primary peak. After turning off the He-Cd laser we often observed small changes in all the peaks’ height, which for the grating shown in Fig. 5 are equal respectively 0.6 dB for λB = 1555 nm, 2.6 dB for 2λB/3 = 1040 nm, and −0.1 dB for λB/2 = 782 nm.
The effect of degradation of the peaks’ heights after certain exposure time is most probably caused by material flow at increased temperature during the fabrication process, which leads to random variations of the gratings’ periodicity. As the same perturbation produces greater dephasing in the grating with a shorter period, the λB/2 peak reaches the maximum reflectivity the earliest, while the λB peak the latest. At the saturation level, the peak at λB = 1555 nm was always the highest, while the peak at 1040 nm the lowest. Full width at half maximum of all the peaks increased with exposure time and saturated after several minutes at the level of 3 nm for the peak at λB and at 1 nm for the λB/2 and 2λB/3 peaks. The absolute reflectivity measured on the transmission spectrum equals 43% for the λB peak. As suggested in [33], knowing the overlap coefficient of the fundamental mode with the grating (η = 1.0) and the gratings length (L = 3 mm), we determined the amplitude of the refractive index modulation responsible for the λB peak, which is 1.3 × 10−4.
We have also fabricated a few gratings with the primary Bragg peak at λB = 1309 nm using a phase mask with a period of Λ = 0.885 µm. For this grating we observed in the far-field behind the phase mask a weak 0th diffraction order, strong 1st diffraction order and moderate 2nd diffraction order. The measured efficiencies for all the diffraction orders are listed in Table 1. In Fig. 6(a) we show the reflection spectrum of the grating for the primary peak at λB = 1309 nm registered during the fabrication process, while in Fig. 7 we present the evolution of the central wavelength and the peak height during and after the fabrication process was finished. The growth dynamics of this grating is similar as in the previous case. After 43 minutes of exposure the height of the primary peak reached the saturation level of about 15 dB with respect to the background while the FWHM was about 2 nm. We registered the reflection spectrum for the peak placed at λB/2 = 659 nm (Fig. 6(b)). Due to a high noise level of the OSA at this spectral range, the reflection spectrum was recorded using Ocean Optics Spectrometer with 1.5 nm resolution after finishing the fabrication process. For this grating, we did not observe the peak at 2λB/3. To our knowledge this is the shortest Bragg wavelength ever reported for polymer microstructured fibers. A successful fabrication of this grating was possible thanks to high mechanical stability of our inscription set-up and application of a single-mode He-Cd laser with high spatial coherence. In earlier experiments reported in literature [9–11,18–21] the multimode He-Cd lasers were used.
Fig. 6 Evolution of the primary reflection spectra at λB = 1309 nm during 41 min of the inscription process (a) and the secondary Bragg peak at λB/2 = 659 nm registered after the inscription process was finished (b).
Fig. 7 Evolution of the Bragg wavelength and the peak’s height registered for the grating at λB = 1309 nm during and after the writing process was finished.
To measure the temperature response of the fabricated gratings, we used a Peltier element installed in a specially designed temperature chamber of a small size, equipped with a thermocouple. We subjected the gratings to several temperature cycles with a gradually increasing range, respectively from ambient temperature to 30°C, 40°C, 50°C, 60°C, 70°C, 80°C, and 90°C. The temperature around the grating was measured by the thermocouple with the accuracy of 0.1°C. Following the suggestions from [10,15], we waited about fifteen minutes to obtain stable readings of the reflection spectrum. The displacement of all the peaks registered for full temperature cycles is shown Fig. 8 . In all the series, a hysteresis increasing with the measurement range was observed. As a result, the reflected peaks were permanently shifted towards shorter wavelength after completing successive temperature cycles. At the end of the first cycle, the hysteresis was lower than 0.2 nm for all peaks, while in the sixth cycle up to 80°C, it reached 69.8 nm for the λB peak, 46.7 nm for the 2λB/3 peak, and 35 nm for the λB/2 peak. No significant variations in the peaks’ height were observed during successive temperature cycles up to 80°C. All the peaks started to degradate at the temperature above 80°C. The 2λB/3 peak disappeared completely at 84°C, the λB/2 peak at 88°C, and the λB peak at 90°C. The probable cause of the quickest vanishing of the 2λB/3 peak is its lowest initial height.
Fig. 8 Shift of Bragg wavelength induced by increasing and decreasing temperature in successive seven cycles registered for λB peak (a), 2λB/3 peak (b), λB/2 peak (c).
In the first two temperature cycles up to 30°C and 40°C, the gratings response was linear for increasing and decreasing temperature in the whole measurement range. In the next cycle (up to 50°C) the position of all the peaks started to shift rapidly towards shorter wavelengths at the temperature of 46°C. In successive cycles we observed similar behaviour, however, as reported already for the primary Bragg peak in [10,15], the linear response range gradually increased in successive cycles. In contrast to Bragg gratings in silica fibers, the thermo-optic effect for gratings in POFs has greater impact on a wavelength shift than the thermal expansion [6], which results in negative sign of the temperature sensitivity for all the peaks. The change in the Bragg wavelength was greater for heating than for cooling. Moreover, the sensitivity coefficients decreased in successive cycles and in the last heating up to 90°C were equal in the linear part of the characteristics −59 pm/°C for the λB peak, −40.9 pm/°C for the 2λB/3 peak, and −31.1 pm/°C for the λB/2 peak.
For another grating with no thermal history prior to the test, we registered a response to a step-like increase in temperature from 24°C to 71°C. As it is shown in Fig. 9(a) after four hours from the temperature change the peaks were still drifting towards shorter wavelengths, however, with a gradually decreasing rate. Next we changed the temperature to the initial value (24°C). After about one hour the peaks reached a stable position shifted towards shorter wavelengths respectively by 56.7 nm for the λB peak, 37.9 nm for the 2λB/3 peak, and 28.5 nm for the λB/2 peak. In Fig. 9(b) the corresponding variations of the peaks’ height are presented.
Fig. 9 Response of all the Bragg peaks to step-like temperature change (a) with corresponding variation of the peaks’ heights (b).
3. Numerical simulations of the inscription process
In order to understand the origin of higher order Bragg peaks, we numerically modeled an intensity distribution behind the phase mask, which is transferred into longitudinal modulation of an effective index by the inscription process. The electric field distribution behind the mask can be represented as a sum of plane waves corresponding to different diffraction orders [5,25,34]:
where m is an integer number denoting diffraction order, Cm is the amplitude of the electric field, is a reciprocal vector of the phase mask, mG is a z-component of wave vector k, and is an x-component of wave vector (according to coordinate system as shown Fig. 2). The wave vector is calculated for the refractive index of PMMA estimated at 1.527 for λ = 325 nm.In Fig. 10 we show the intensity distributions calculated for different combinations of diffracted waves and the final pattern obtained as a result of the interference of 0th, ± 1st, ± 2nd, ± 3rd diffraction orders with relative amplitudes as shown in Table 1. The resulting interference pattern is rather complex, however, one can notice periodicities corresponding to Talbot lengths XT given by [24,34]:
where m and n are integers denoting diffraction orders. To determine periodicities present in the inscribed grating, we replaced the microstructured fiber by a slab waveguide and assumed that change in the material refractive index induced by the writing process is proportional to the intensity distribution in the interference pattern. Subsequently, to evaluate a change in the effective index of the mode at a given point along the waveguide, we integrated numerically the material refractive index along t direction [34] with Gaussian weight function representing the mode intensity distribution (Fig. 11 ). Finally, we performed Fourier analysis of the longitudinal variations of the effective index to identify spatial frequencies present in the inscribed grating.This simplified model does not take into account the effect of microstructure on the interference pattern in the core, which may change the relative amplitudes of respective harmonics. Quantitative analysis of the role played by the microstructured cladding and the fiber orientation was presented in [32]. The numerical studies carried out using the finite difference time domain method showed that for specific angular orientations of the microstructured fiber a higher concentration of the UV beam in the core region may be achieved, which facilitates the inscription process. As in our experiments the angular orientation of the fiber was not controlled with a sufficient precision, we assumed in the numerical simulations that the core is uniformly irradiated by the UV beam. The effect of the microstructure was taken into account by making the 1/e2 width of the Gaussian weight function equal to the mode field diameter in the investigated mPOF (τ = 10.4 μm).
Figure 12 presents the simulation results obtained with the proposed approach. Following cases were considered (from left to right): only ± 1st diffraction order interfere; then also 0th order was accounted for; subsequently ± 2nd order was added and finally all diffraction orders (from 0th to ± 3rd) were taken into account. The change in the material refractive index weighted with Gaussian shape of the mode is presented in Fig. 12(a), the change in the mode effective index is shown in Fig. 12(b), while the absolute value of the Fourier transform calculated with FFT algorithm (Fast Fourier Transform) is presented in Fig. 12(c).
Fig. 12 Refractive index change in the core of the slab waveguide weighted with Gaussian mode shape (a), corresponding change in the mode effective index (b), absolute value of Fourier transform showing spatial frequencies present in the Bragg grating (c).
The simulation results help to understand the origin of different Bragg peaks observed in the reflected spectrum. The periodicities in z direction are determined by the following formula:
where m and n are the integers denoting diffraction orders. The above formula allows to identify spatial frequencies in effective index modulation produced by interference of selected diffraction orders.The primary Bragg peak at λB is associated with effective index periodicity of Λ/2 (spatial frequency 2/Λ). This periodicity occurs as a result of interference between ± 1st diffraction orders (black cell in Table 2 ). Accounting for the 0th diffraction order leads to the appearance of spatial frequency 1/Λ (periodicity Λ) (dark gray cells in Table 2) corresponding to the Bragg reflection peak at 2λB = 3110 nm, which is behind the reach of our OSA.
Table 2. Spatial frequencies expressed in 1/Λ corresponding to interference of m and n diffraction orders.
Including the ± 2nd orders leads to the appearance of shorter periods Λ/3 and Λ/4. Interference of the + 2nd and the −2nd orders results in the periodicity of Λ/4 (spatial frequency 4/Λ), which produces the Bragg peak at λB/2. Interference of the + 1st and the −2nd orders and the −1st and the + 2nd orders results in periodicity of Λ/3 (spatial frequency 3/Λ) and the corresponding Bragg reflection peak at 2λB/3. The ± 2nd orders contribute also to other periodicities. For example, interference of the 0th and the + 2nd orders contributes to Λ/2 periodicity, while interference of the + 1st and the + 2nd orders to Λ periodicity (gray cells in Table 2).
The ± 3rd diffraction orders produce the periodicities of Λ/5 and Λ/6 in the grating. Interference of the + 3rd and the −3rd orders results in the Λ/6 periodicity (spatial frequency 6/Λ) with corresponding Bragg peak at λB/3, while interference of + 2nd and −3rd orders and −2nd and + 3rd produces the Bragg reflection peak at 2λB/5. As it is shown in Table 2 the ± 3rd orders contribute also to other periodicities. For example, interference of 0th and + 3rd orders contributes to Λ/3 periodicity and interference of + 1st and + 3rd orders contributes to Λ/2 periodicity (light gray cells in Table 2).
The results of numerical simulations presented in this section suggest that the Bragg reflection peaks observed at λB/2 = 782nm and 2λB/3 = 1040 nm appear due to periodicities induced by the interference of relatively strong 2nd diffraction order with itself and with the 1st order. It is also possible that the peak at λB/2 represents in part the 2nd order Bragg reflection from the grating with Λ/2 periodicity, while the peak at 2λB/3 can be partially attributed to the 3rd order reflection from the grating with periodicity of Λ. Such a situation was previously observed for Bragg gratings in silica fibers [24]. The analysis presented in [26] shows that in silica fibers a relative contribution of the two possible mechanisms of generation of the higher order Bragg reflection peaks depends on the fabrication process. Further research is needed to determine the contribution of the two possible mechanisms in formation of the λB/2 and 2λB/3 peaks for the Bragg gratings in mPOFs.
In the conducted experiments, we did not observe the peaks at λB/3 = 518 nm and 2λB/5 = 622 nm, which according to our simulations should appear in the reflection spectra. The possible explanation can be linked to stronger scattering of the ± 3rd diffraction orders by the microstructured cladding than the ± 2nd orders. As a result, a spatial resolution reached in the inscription process for the ± 3rd diffraction orders is not enough to reproduce so high frequencies.
4. Conclusions
In this work we demonstrate a possibility of fabrication of high quality Bragg gratings with the primary Bragg peak at λB = 1555 nm and additional peaks located at λB/2 = 782 nm and 2λB/3 = 1040 nm by using a phase mask with higher diffraction orders. We also demonstrated the grating with the reflection peak at λB/2 = 659 nm, which is the shortest Bragg wavelength ever reported for polymer microstructured fibers. The temperature response of all the peaks shows similar behavior as reported earlier for the primary peak in [10,15] i.e., a hysteresis increasing with the temperature range and an increasing linearity in successive temperature cycles. All the peaks disappeared at the temperature above 80°C.
The formation of the peaks at λB/2 and 2λB/3 can be attributed to the first order reflection from the gratings with periodicity of Λ/4 and Λ/3 or to the 2nd and 3rd order reflection from the grating of period of Λ. Further research is necessary to determine the contribution of the two mechanisms in formation of the higher order peaks.
Acknowledgment
This work was supported by Wroclaw Research Center EIT + Ltd. in the frame of the NanoMat project Application of Nanotechnology in Advanced Materials, within the European Funds for Regional Development, POIG, Sub-action 1.1.2.
References and links
1. K. O. Hill and G. Meltz, “Fiber Bragg grating technology - fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]
2. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997). [CrossRef]
3. D. Webb and K. Kalli, “Polymer fiber Bragg gratings,” in Fiber Bragg Grating Sensors: Recent Advancements, Industrial Applications and Market Exploitation, A. Cusano, A. Cutolo, and J. Albert, Eds. Sharjah (Bentham Science Publishers 2011), pp. 292−312.
4. Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Highly tunable Bragg gratings in single-mode polymer optical fibers,” IEEE Photon. Technol. Lett. 11(3), 352–354 (1999). [CrossRef]
5. Z. Xiong, G. D. Peng, B. Wu, and P. L. Chu, “Effects of the zeroth-order diffraction of a phase mask on Bragg gratings,” J. Lightwave Technol. 17(11), 2361–2365 (1999). [CrossRef]
6. H. Y. Liu, G. D. Peng, and P. L. Chu, “Thermal tuning of polymer optical fiber Bragg gratings,” IEEE Photon. Technol. Lett. 13(8), 824–826 (2001). [CrossRef]
7. H. B. Liu, H. Y. Liu, G. D. Peng, and P. L. Chu, “Novel growth behaviors of fiber Bragg gratings in polymer optical fiber under UV irradiation with low power,” IEEE Photon. Technol. Lett. 16(1), 159–161 (2004). [CrossRef]
8. H. Y. Liu, H. B. Liu, G. D. Peng, and P. L. Chu, “Observation of type I and type II gratings behavior in polymer optical fiber,” Opt. Commun. 220(4-6), 337–343 (2003). [CrossRef]
9. Z. F. Zhang, Ch. Zhang, X. M. Tao, G. F. Wang, and G. D. Peng, “Inscription of polymer optical fiber Bragg grating at 962 nm and its potential in strain sensing,” IEEE Photon. Technol. Lett. 22(21), 1562–1564 (2010). [CrossRef]
10. W. Yuan, A. Stefani, M. Bache, T. Jacobsen, B. Rose, N. Herholdt-Rasmussen, F. K. Nielsen, S. Andresen, O. B. Sørensen, K. S. Hansen, and O. Bang, “Improved thermal and strain performance of annealed polymer optical fiber Bragg gratings,” Opt. Commun. 284(1), 176–182 (2011). [CrossRef]
11. X. Chen, C. Zhang, D. J. Webb, G. D. Peng, and K. Kalli, “Bragg grating in a polymer optical fibre for strain, bend and temperature sensing,” Meas. Sci. Technol. 21(9), 094005 (2010). [CrossRef]
12. K. Kalli, H. L. Dobb, D. J. Webb, K. Carroll, C. Themistos, M. Komodromos, G. D. Peng, Q. Fang, and I. W. Boyd, “Development of an electrically tunable Bragg grating filter in polymer optical fibre operating at 1.55 μm,” Meas. Sci. Technol. 18(10), 3155–3164 (2007). [CrossRef]
13. N. G. Harbach, “Fiber Bragg gratings in polymer optical fibers,” Thesis, EPFL, Lausanne (2008).
14. H. Dobb, D. J. Webb, K. Kalli, A. Argyros, M. C. J. Large, and M. A. van Eijkelenborg, “Continuous wave ultraviolet light-induced fiber Bragg gratings in few- and single-mode microstructured polymer optical fibers,” Opt. Lett. 30(24), 3296–3298 (2005). [CrossRef] [PubMed]
15. K. E. Carroll, Ch. Zhang, D. J. Webb, K. Kalli, A. Argyros, and M. C. J. Large, “Thermal response of Bragg gratings in PMMA microstructured optical fibers,” Opt. Express 15(14), 8844–8850 (2007). [CrossRef] [PubMed]
16. I. P. Johnson, D. J. Webb, K. Kalli, W. Yuan, A. Stefani, K. Nielsen, H. K. Rasmussen, and O. Bang, “Polymer PCF Bragg grating sensor based on poly(methyl methacrylate) and TOPAS cyclic olefin copolymer,” Proc. SPIE 8073, 80732V, 80732V-8 (2011). [CrossRef]
17. I. P. Johnson, W. Yuan, A. Stefani, K. Nielsen, H. Rasmussen, L. Khan, D. J. Webb, K. Kalli, and O. Bang, “Optical fibre Bragg grating recorded in TOPAS cyclic olefin copolymer,” Electron. Lett. 47(4), 271–272 (2011). [CrossRef]
18. W. Yuan, L. Khan, D. J. Webb, K. Kalli, H. K. Rasmussen, A. Stefani, and O. Bang, “Humidity insensitive TOPAS polymer fiber Bragg grating sensor,” Opt. Express 19(20), 19731–19739 (2011). [CrossRef] [PubMed]
19. A. Stefani, W. Yuan, C. Markos, and O. Bang, “Narrow bandwidth 850-nm fiber Bragg gratings in few-mode polymer optical fibers,” IEEE Photon. Technol. Lett. 23(10), 660–662 (2011). [CrossRef]
20. W. Yuan, A. Stefani, and O. Bang, “Tunable polymer fiber Bragg grating (FBG) inscription: fabrication of dual-FBG temperature compensated polymer optical fiber strain sensors,” IEEE Photon. Technol. Lett. 24(5), 401–403 (2012). [CrossRef]
21. A. Stefani, S. Andresen, W. Yuan, N. Herholdt-Rasmussen, and O. Bang, “High sensitivity polymer optical fiber-Bragg-grating-based accelerometer,” IEEE Photon. Technol. Lett. 24(9), 763–765 (2012). [CrossRef]
22. A. Stefani, M. Stecher, O. Bang, and G. Town, “Direct writing of fiber Bragg grating in microstructured polymer optical fiber,” IEEE Photon. Technol. Lett. 24(13), 1148–1150 (2012). [CrossRef]
23. N. M. Dragomir, C. M. Rollinson, S. A. Wade, A. J. Stevenson, S. F. Collins, G. W. Baxter, P. M. Farrell, and A. Roberts, “Nondestructive imaging of a type I optical fiber Bragg grating,” Opt. Lett. 28(10), 789–791 (2003). [CrossRef] [PubMed]
24. C. M. Rollinson, S. A. Wade, N. M. Dragomir, G. W. Baxter, S. F. Collins, and A. Roberts, “Reflections near 1030 nm from 1540 nm fibre Bragg gratings: evidence of a complex refractive index structure,” Opt. Commun. 256(4-6), 310–318 (2005). [CrossRef]
25. B. P. Kouskousis, C. M. Rollinson, D. J. Kitcher, S. F. Collins, G. W. Baxter, S. A. Wade, N. M. Dragomir, and A. Roberts, “Quantitative investigation of the refractive-index modulation within the core of a fiber Bragg grating,” Opt. Express 14(22), 10332–10338 (2006). [CrossRef] [PubMed]
26. C. M. Rollinson, S. A. Wade, B. P. Kouskousis, D. J. Kitcher, G. W. Baxter, and S. F. Collins, “Variations of the growth of harmonic reflections in fiber Bragg gratings fabricated using phase masks,” J. Opt. Soc. Am. A 29(7), 1259–1268 (2012). [CrossRef] [PubMed]
27. W. X. Xie, M. Douay, P. Bernage, P. Niay, J. F. Bayon, and T. Georges, “Second order diffraction efficiency of Bragg gratings written within germanosilicate fibres,” Opt. Commun. 101(1-2), 85–91 (1993). [CrossRef]
28. S. P. Yam, Z. Brodzeli, B. P. Kouskousis, C. M. Rollinson, S. A. Wade, G. W. Baxter, and S. F. Collins, “Fabrication of a π -phase-shifted fiber Bragg grating at twice the Bragg wavelength with the standard phase mask technique,” Opt. Lett. 34(13), 2021–2023 (2009). [CrossRef] [PubMed]
29. H. K. Bal, F. Sidiroglou, Z. Brodzeli, S. A. Wade, G. W. Baxter, and S. F. Collins, “Fibre Bragg grating transverse strain sensing using reflections at twice the Bragg wavelength,” Meas. Sci. Technol. 21(9), 094004 (2010). [CrossRef]
30. B. Malo, D. C. Johnson, F. Bilodeau, J. Albert, and K. O. Hill, “Single-excimer-pulse writing of fiber gratings by use of a zero-order nulled phase mask: grating spectral response and visualization of index perturbations,” Opt. Lett. 18(15), 1277–1279 (1993). [CrossRef] [PubMed]
31. S. A. Wade, W. G. Brown, H. K. Bal, F. Sidiroglou, G. W. Baxter, and S. F. Collins, “Effect of phase mask alignment on fiber Bragg grating spectra at harmonics of the Bragg wavelength,” J. Opt. Soc. Am. A 29(8), 1597–1605 (2012). [CrossRef] [PubMed]
32. T. Baghdasaryan, T. Geernaert, F. Berghmans, and H. Thienpont, “Geometrical study of a hexagonal lattice photonic crystal fiber for efficient femtosecond laser grating inscription,” Opt. Express 19(8), 7705–7716 (2011). [CrossRef] [PubMed]
33. B. J. Eggleton, P. S. Westbrook, R. S. Windeler, S. Spälter, and T. A. Strasser, “Grating resonances in air-silica microstructured optical fibers,” Opt. Lett. 24(21), 1460–1462 (1999). [CrossRef] [PubMed]
34. J. D. Mills, C. W. J. Hillman, B. H. Blott, and W. S. Brocklesby, “Imaging of free-space interference patterns used to manufacture fiber bragg gratings,” Appl. Opt. 39(33), 6128–6135 (2000). [CrossRef] [PubMed]
