A detailed study of the dynamics during thermal regeneration of fiber Bragg gratings, written in hydrogen-loaded standard single-mode fibers using a ns pulsed 213 nm UV laser, is reported. Isothermal pre-annealing performed in the range 85 °C to 1100 °C, with subsequent grating regeneration at 1100 °C, resulted in a maximum refractive index modulation, Δnm ~1.4⋅10−4, for gratings pre-annealed near 900 °C while a minimum value of Δnm ~2⋅10−5 was achieved irrespective of pre-annealing temperature. This optimum denote an inflection point between opposing thermally triggered processes, which we ascribe to the reaction-diffusion mechanism of molecular water and hydroxyl species in silica. The results shed new light on the mechanisms underlying thermal grating regeneration in optical fibers.
© 2015 Optical Society of America
Optical fiber sensors employing fiber Bragg gratings (FBGs) have been found useful for a wide number of applications, in particular when strain or temperature is to be measured [1–3]. For sensing purposes, the variable being monitored is related to either the grating reflectivity (R) or the Bragg wavelength (λB), with the latter more commonly used. The Bragg condition corresponding to the peak reflectivity is given by λB = 2neffΛB, where neff is the effective refractive index seen by the optical mode and ΛB is the geometrical periodicity of the refractive index modulation. Both variables, neff and ΛB, are strain and temperature dependent through the stress-optic, thermo-optic and thermal expansion coefficients. The limitations in measurement range of FBG based sensors depend on the material properties of the optical fiber and, especially regarding strain measurements, the design and material properties of the transducer itself. For temperature sensing there is typically an upper limit at which FBGs show non-reversible changes, resulting in inaccurate measurements over time. The thermally induced decay of standard FBGs, referred to as type I gratings, typically follows a stretched-exponential behavior. Through accelerated ageing using suitable time and temperature conditions the measurement range can be extended to approximately 300 - 400 °C [4–6]. Due to this limitation significant efforts have been made over the years to extend the temperature range of FBG based sensors, resulting in several reports of different types of gratings including, e.g., type IIa [7,8], type II (formed by high-intensity single pulse exposure) , type I-IR and type II-IR (using ultrafast lasers) , and thermally regenerated gratings, e.g., chemical composition gratings (CCGs) .
A characteristic feature of many types of gratings showing an enhanced thermal stability, apart from type II gratings, is that they go through a regeneration process during grating formation. Following an initial growth in reflectivity characteristic of type I gratings, the reflectivity begins to decay before again increasing in strength. Except for type IIa gratings, where regeneration occurs during the irradiation process when inscribing the grating, most temperature enhanced FBGs require special thermal processing to trigger the regeneration process. A number of studies of thermally regenerated gratings have been reported, e.g., for fibers with different dopants, including Er-, and Yb-doped fibers [12,13], germanium-boron co-doped fibers [13–15], and multi-component silicates , or by using ultrashort pulsed lasers to write the initial grating [17,18]. In most cases hydrogen loading is used, while it was shown that grating regeneration is possible by hydrogen loading after grating inscription , as well as omitting hydrogen loading [20–22].
The physicochemical processes associated with hydrogen in glass are expected to be highly temperature dependent, following an Arrhenius type behavior, and therefore the dynamics of grating regeneration should be sensitive to how the thermal processing is performed. In the first report on thermally regenerated gratings , annealing was performed by ramping the temperature at a rate of 25 °C min−1 up to a regeneration temperature of 1000 °C. For a specially designed fluorine-doped fiber it was found that the regeneration dynamics was highly dependent on pre-annealing temperature, showing a peak in grating reflectivity when pre-annealed near 600 °C to 700 °C prior to regeneration at higher temperatures . No regeneration occurred when pre-annealing was omitted, i.e., when heating directly to 1000 °C. Pre-annealing at these intermediate temperatures, typically 600-700 °C, is now commonly used in many studies on thermal FBG regeneration, independently of the type and composition of fiber being used. While proven useful in several different high-temperature sensing applications, the mechanisms underlying grating regeneration are still not well understood and different types of regenerated gratings are likely to exist. Different models with significant disparity have been proposed to explain the formation of thermally regenerated gratings in hydrogen loaded fibers. In order to improve the grating properties and their reliability as sensors at elevated temperatures, further studies clarifying the different thermally driven physicochemical processes involved are needed in order to provide a sound and more complete understanding of grating regeneration process.
In this work we present a detailed study of the dynamics during isothermal pre-annealing and thermal regeneration of gratings, written in hydrogen loaded standard single-mode fibers using a nanosecond pulsed UV laser at 213 nm wavelength. The aim of the study is to clarify the role of hydrogen during thermal regeneration, and to provide a thermal recipe for fabrication of regenerated gratings in standard telecommunications fiber. With regeneration performed at 1100 °C, a maximum growth in reflectivity was achieved for gratings pre-annealed near 900 °C, with resulting refractive index modulation as high as Δnm ~1.4⋅10−4, while a minimum refractive index modulation of Δnm ~2⋅10−5 was achieved independently of pre-annealing temperature. The dynamics during thermal processing show a highly complex behavior, indicating that several different processes are involved in the grating regeneration. Based on the experimental results presented here, we ascribe one of these processes to the reaction-diffusion mechanism of molecular water and hydroxyl species in silica.
2. Background - mechanisms of thermal grating regeneration
In the following section we provide as background, a brief review and critical discussion of the most cited models that have been proposed regarding the mechanisms of thermal grating regeneration in hydrogen loaded fibers. The purpose of the present paper is provide new evidence regarding the role of hydrogen during thermal regeneration in support of one of the mechanisms (section 2.1) initially proposed by one of the authors.
2.1. Chemical composition gratings
The initially proposed mechanisms for the regeneration dynamics during thermal processing of gratings written in hydrogen loaded fibers was ascribed to photolytic and chemical interaction of hydrogen related species, resulting in locally enhanced diffusion of dopants within the fiber. More details can be found in ref [11,13]. The gratings were labeled chemical composition gratings (CCGs) as the final refractive-index modulation was due partly to a spatially modified composition along the fiber axis. The proposed dopants involved in the process, having an enhanced diffusivity when associated with hydrogen species, were fluorine  and oxygen . In the case of fluorine-CCGs specialty fiber is required as fluorine is typically not used as a core-dopant in standard fiber manufacturing. However, in the case of oxygen-CCGs any silica based fiber can be used as oxygen is the main dopant. The locally enhanced diffusivity of fluorine in hydroxyl rich silica was initially proposed by Kirchhoff et al  and was attributed to the formation of HF molecules having an enhanced mobility through interstitial diffusion, in part due to the small chemical diameter of the HF molecule. Fluorine doping is commonly used to reduce detrimental water related absorption in optical fibers during fiber preform fabrication. For CCGs the opposite approach is applied, i.e., hydroxyl groups are used to locally, with high spatial resolution, reduce the fluorine concentration. For oxygen-CCGs the enhanced mobility of oxygen was ascribed to the reaction-diffusion mechanism of hydroxyl groups in silica, proposed by Doremus . Here two hydroxyl groups combine to form molecular water having an increased diffusivity compared to hydroxyl groups and consequently also having significantly higher diffusivity compared to network oxygen atoms.
A pre-annealing step at intermediate temperatures was proposed in order to thermally activate the locally enhanced hydrogen related diffusion, whereas the final step comprising the thermal treatment process at temperatures near the glass transition region, i.e., the thermal regeneration process, was required in order to restructure and stabilize the matrix of the modified glass through structural relaxation . The high-temperature treatment can also be considered necessary in order to remove the less stable components of the refractive index modulation associated with the type I grating, i.e., the regeneration step is similar to accelerated ageing of FBGs, after which the final high-temperature stable components of the grating can be distinguished.
2.2. Seeded crystallization
A number of different mechanisms have been proposed by Canning et al. [28–30] relating the thermal grating regeneration to different processes arising at the core-cladding interface or within the inner-cladding of the fiber. The proposed mechanisms include, e.g., a high-pressure induced phase transition of a signature remaining in the glass structure after the grating has been erased, and seeded crystallization or amorphization from pressure buildup during UV exposure. The proposed mechanisms were based on the simultaneous observation of two gratings during the regeneration process ; one grating is decreasing in reflectivity, while simultaneously a second grating is regenerated, increasing in reflectivity. The regenerated grating is red-shifted in relation to the initial grating referred to as the seed grating, which they claim is not spatially collocated with the regenerated grating. The effect of such dynamics, however, can easily be explained by a temperature gradient along the grating during thermal processing. The peak to peak wavelength separation reported for the two gratings (Fig. 1 in ref ) is 0.5 to 0.8 nm and assuming a wavelength-temperature response of δλB/ δT ~9 - 12 pm/°C equates to a temperature difference along the grating on the order of 50 °C to 90 °C. This temperature difference has a significant effect on the decay and growth dynamics during grating regeneration (see e.g., section 3 of this paper). The “hot” part of the grating will decay faster and then regenerate while the “cold” part of the grating is still decreasing in reflectivity. This double-peak behavior was observed during initial studies by one of the present authors, but vanished when using a micro-furnace specially designed to minimize the temperature gradients across the fiber grating when heated . The proposed mechanisms of seeded crystallization seem unlikely for several reasons. In [29,30] it was proposed that a seed grating induces nucleation, followed by crystal growth of a “cristobalite-like” phase at the core-cladding interface when heated to 900 °C. With a crystalline phase present in combination with continued thermal treatment at even higher temperatures, one would expect continued growth of these crystals. For similar conditions in silica glass, the growth rates are expected to be on the order 10−11 to 10−13 cms−1 or higher . However, the refractive index modulation of the regenerated grating quickly reaches a limiting value on the order of Δnm ~10−5 - 10−4, followed by a slow decay rate that accelerates with temperature. Several reports show that when heated at sufficiently high temperatures, regenerated gratings decay following a diffusion based decay model [11,14,33]. With a sinusoidal variation in the chemical composition the decay in refractive index modulation, Δnm, can be accurately described using the following Eq :Eq. (1) it is clear that FBGs with a shorter grating period, i.e., shorter Bragg wavelength, will decay more rapidly than FBGs at longer wavelengths due to the smaller distance for inter-fringe diffusion, which has also been verified experimentally [14,33]. In a recent report by Yang et al.  grating regeneration was studied in etched fiber. Here gratings were written in hydrogen loaded fibers and prior to thermally induced grating regeneration the cladding was removed by chemical etching in hydrofluoric acid. The final diameter of the etched fiber prior thermal regeneration was d ~5.6 µm, smaller than the original core (d ~8 - 10 µm), clearly showing that the grating regeneration mechanism is not related to mechanisms occurring specifically at the core-cladding interface or in the inner cladding.
2.3. Trapped water molecules
A model proposed by Zhang et al.  suggests that the refractive index modulation of thermally regenerated gratings is due to periodic formation of molecular water, with the high-temperature stability of the grating ascribed to water molecules being trapped within interstitial voids of the glass. However this model contradicts the widely accepted model for diffusion of water in silica glass, as proposed by Doremus . The interaction of hydrogen, hydroxyl and molecular water in silica glass has been extensively studied over time due to the industrial and scientific significance of silica glass, in addition to related research regarding the mechanisms of oxidation of silicon , where molecular water acts as an oxygen carrier. There are also a number of reports discussing molecular water in relation to photosensitivity. Following UV exposure of H2 loaded preforms Poumellec et al  showed that there is a significant migration of hydroxyl groups, indicating a high mobility of molecular water even at low temperatures. Although shown to be more stable at higher temperatures, gratings written in hydrogen loaded fibers are often reported to be less stable at low- to intermediate temperatures compared to gratings written in pristine fibers [38,39] which could be associated to the high mobility of molecular water.
The general procedure for grating regeneration follows that of ref . and can be summarized in the following steps: (1) hydrogen loading, (2) fringed UV exposure, (3) out diffusion of remaining hydrogen, (4) annealing at intermediate temperature, and (5) grating regeneration at elevated temperature. A standard telecommunications fiber (Corning SMF-28) was used throughout this study.
3.1. Hydrogen loading
Hydrogen loading was performed by placing the fibers in a hydrogen atmosphere at 12 MPa, for the duration of 12 days at room temperature. After removing the fibers from the pressure chamber they were stored at −62 °C to prevent hydrogen out-diffusion prior to grating inscription.
3.2. Fringed UV-exposure
Grating fabrication was performed using a diode-pumped solid-state Q-switched Nd:VO4 laser operating at 213 nm (Impress 213, Xiton-Photonics GmbH). The pulse duration and repetition rate was τp ~6 ns and 15 kHz, respectively. A two-beam interferometric setup using dielectric mirrors and a phase mask as a beam splitter was used, with the zero order blocked. The beam was focused onto the core using two cylindrical fused silica lenses having a focal length of f = 500 and f = 50 mm, respectively. The focal spot along the fiber axis was approximately 160 µm. The length of the FBG was controlled by scanning the UV beam across the phase-mask, using a motorized translation stage. The total UV power launched onto the fiber was 20 mW with a difference in power between the arms of the interferometer below 1%.
The grating length used in this study was 9 mm, with a center Bragg wavelength at λB ~1554 nm. The gratings were written using a translation speed of 15 µms−1 resulting in a peak reflectivity near 100%, having a full-width half-maximum (FWHM) of approximately 2 nm. Calculated refractive index modulation after grating inscription was estimated to be Δnm ~1.8⋅10−3. The refractive index modulation of the FBGs monitored during fabrication, annealing and regeneration was estimated from the peak grating reflectivity (R) using the following relation:38]:Eq. (2) for Δnm ~1⋅10−4. The spectral response of the FBGs during inscription and thermal processing was monitored in reflection using a super continuum white-light source (Koheras SuperK), an optical circulator and an optical spectrum analyzer (OSA, BaySpec FBG-IRS) having a Bragg wavelength readout resolution of 1 pm and optical resolution of 0.15 nm. For increased optical resolution, measurements were also performed using a spectrum analyzer with 0.06 nm resolution (Agilent 86140B) and in transmission when possible. A reference grating placed outside the furnace was used to monitor the stability of the white-light source. In Fig. 1, the reflection spectra are shown for one grating before and after annealing, and after thermal regeneration. The grating was annealed at 700 °C during 60 min and subsequently regenerated at a temperature of 1100 °C.
3.3. Out diffusion of remaining hydrogen
In order to avoid thermally induced reactions, the remaining hydrogen within the fiber was out-diffused after grating inscription by heating in an oven at a temperature and duration of 85 °C and 72 hours, respectively.
3.4. Annealing and thermal regeneration of gratings
Thermal processing of FBGs was performed using a box furnace (Carbolite CWF1100). In order to reduce the insertion time of the FBGs, while maintaining the pre-set temperature of the furnace, a hole was drilled horizontally into the furnace chamber and fitted with two ceramic tubes (Mullite). The FBG was placed in a quartz capillary to avoid damaging the fiber and grating when quickly inserted into one of the ceramic tubes. A K-type thermocouple inserted into a similar quartz capillary was placed in the second ceramic tube for continuous monitoring of the temperature near the location of the FBG. The time required for the FBG to reach 90% of the furnace temperature when rapidly inserted at 1100 °C was approximately 20 seconds, while 98% of the final temperature was typically achieved within 50 seconds.
3.5. Experimental parameters
A total of 21 gratings were used in this study. The gratings were written in two batches under similar conditions. Isothermal annealing was performed at 100 °C increments ranging from 200 °C to 1100 °C, with an additional annealing performed at 950 °C. The furnace temperature was allowed to stabilize at each set temperature prior to fiber insertion. The duration of annealing was either 0, 15, 30 or 60 minutes, where 0 minutes correspond to annealing at 85 °C, i.e. the hydrogen out-diffusion step. After completion of an annealing cycle the FBG was removed from the furnace and further characterized at room temperature. The experimental parameters are summarized in Table 1. In the following sections we use the set temperature value when discussing the results while calculations and processed data are based on the measured temperature values.
4. Experimental results
4.1. Pre-annealing data
The measured results of grating decay during 30 minute isothermal annealing are summarized in Fig. 2, showing the decay in refractive index modulation (Δnm) as a function of time. For annealing temperatures between 200 °C and 800 °C, Fig. 2(a), the decay in Δnm follows a stretched exponential behavior that is typical for type I FBGs. For higher annealing temperatures, shown in Fig. 2(b), the dynamics change character. Above 900 °C, grating regeneration started within the 30 minute duration of the pre-annealing step. When the annealing time was extended to 60 minutes, grating regeneration also occurred for the grating annealed at 900 °C. After an initial rapid decrease in Δnm, and prior to regeneration, the dynamics approaches that of single exponential decay, which is highlighted by re-plotting the data in a lin-log plot in Fig. 3(a). Time constants could be extracted by curve fitting using a single exponential function when omitting the data points corresponding to the initial rapid decay shown in Fig. 3(a). In Fig. 3(b) the changes in grating wavelength during annealing are shown. For comparison with the decay dynamics in Δnm in Fig. 3(a), curve fitting was also applied to the changes in wavelength shown in Fig. 3(b). Here curve fitting using a single exponential function was also possible when omitting the data points prior to reaching the maximum wavelength for each temperature, data points corresponding to the temperature ramping window were a steady-state temperature had not yet been reached. The fitted curves for the wavelength dynamics, also included in Fig. 3(b), extend across the decay as well as the regeneration process of the gratings. Curve fitting could not be performed reliably for annealed gratings at 1100 °C, as most of the grating was erased during the temperature ramping window.
In Fig. 4, time constants extracted from the measurements in Fig. 3 are presented in an Arrhenius plot. As seen in Fig. 4 there is a significant difference in slope between the rate of change in refractive index modulation, from Fig. 3(a), and changes in Bragg wavelength, from Fig. 3(b), with activation energies of Ea(Δnm) = 294.5 ( ± 19.9) kJmol−1 and Ea(ΔλB) = 86.2 ( ± 0.8) kJmol−1, respectively. Activation energies were extracted from the slope of the fitting, which was performed using linear regression analysis. In Fig. 5 a summary of the normalized refractive index modulation and change in Bragg wavelength after 30 minutes isothermal annealing is presented. The measurements are performed at room temperature and the changes in Bragg wavelength are shown in relation to the starting wavelength prior to annealing, i.e., ΔλB = 0 at time t = 0. The results show a continuous blue-shift of the Bragg wavelength with increasing temperature, although for temperatures below 600 °C changes in Bragg wavelength are minor. The largest blue-shift, ΔλB = 2.5 nm, is measured for the grating annealed at 1100 °C.
4.2. Regeneration – developing the grating
After the pre-annealing step described in section 4.1, grating regeneration was performed by rapidly inserting the pre-annealed grating into the furnace set to 1100 °C. At this temperature the reflectivity of all the gratings decay rapidly reach zero reflectivity within 55 to 65 seconds. Figure 6 summarize the regeneration dynamics of the gratings, showing the change in refractive index modulation as a function of time. The labeling in Fig. 6 refers to the temperature at which the grating was pre-annealed following the heat treatment for hydrogen out-diffusion at 85 °C, which was the same for all gratings. Figure 6(a) includes gratings annealed at temperatures from 200 °C to 900 °C, in 100 °C increments. Figure 6(b) shows the dynamics for the gratings annealed at 900 °C, 950 °C, 1000 °C, and 1100 °C. The starting values of the index modulation for the different gratings prior to regeneration, being partly obscured in Fig. 6, are also shown in shown in Fig. 5. It should be noted that the data points labeled 1100 °C in Fig. 6(b) also correspond to a grating pre-annealing at 85 °C, since the pre-annealing temperature and regeneration temperature are the same. When increasing pre-annealing temperature, the regenerated index modulation increases, reaching a peak value of Δnm ~1.4⋅10−4 for the grating annealed at 900 °C. For annealing temperatures above 900 °C there is an opposite behavior compared to lower temperatures, showing a continuous decrease in peak index modulation with increasing temperature. After reaching the peak value of the regenerated refractive index modulation, all the regenerated gratings in this study showed a decay before the reflectivity stabilized after approximately 10 minutes.
All the gratings used in this study, including gratings that regenerated during the pre-annealing step, were completely erased prior to the onset of grating regeneration, i.e., the reflectivity dropped below the noise floor of the measurements. Due to the quadratic dependence on the refractive index modulation of the reflectivity (see Eq. (2) there is an uncertainty regarding the sign of the refractive index modulation. However, in order to preserve continuity of the refractive index modulation at the point of erasure, and considering the exponential decay behavior shown in Fig. 3(a), the regenerated grating is expected to have a negative refractive index modulation compared to the initial type I grating, as pointed out in ref . This is more apparent in Fig. 7 where the refractive index modulation for the gratings during isothermal annealing and regeneration are plotted in sequence, with a reversal in sign when passing through Δnm = 0, i.e., at the point of erasure of the initial grating. A subsequent question now arise regarding the sign of the initial decay component of the regenerated grating, occurring within the first 10 minutes after reaching the peak index modulation. If the change occurs in the UV exposed regions (fringes) there is a positive contribution (Δn > 0) to the refractive index modulation, while if the change occurs in the non-exposed inter-fringe regions, the unstable component is also negative, i.e., Δn < 0 with the change being π out of phase with grating fringes. A summary of the final refractive index modulation of the regenerated gratings isothermally pre-annealed for 30 minutes at different temperatures is shown in Fig. 8. The figure shows the absolute values of the peak index modulation (ΔnP) of the regenerated grating, as well as the stable (ΔnS) and unstable (ΔnU) components. The magnitude of the stable component was defined as the extrapolated value of a linear fit to the stable refractive index modulation at the time corresponding to ΔnP. The unstable component is taken as the difference between the two, i.e., ΔnU = ΔnP - ΔnS. The dynamics for gratings isothermally annealed for 15 and 60 minutes show the same behavior as for 30 minute annealing, shown in Fig. 8. A trend of increasing refractive index with increasing annealing time was noted for annealing temperatures up to 800 °C, while the data was not conclusive for higher temperatures. Both the stable and unstable components show a non-zero reflectivity, independent of annealing temperatures, including when only annealed at 85 °C. No additional conclusive results could be drawn from the 15 and 60 minute annealing studies.
In Fig. 9 the regeneration dynamics are presented for gratings pre-annealed at 800 °C, 900°C and 1000 °C, as well as the grating annealed at 85 °C. Here the time axis for the different curves has been shifted so that time t = 0 corresponds to complete erasure of the type I grating, i.e., when Δnm = 0. Similar to isothermal annealing shown in Fig. 3, the dynamics during grating regeneration at 1100 °C display substantial differences in magnitude and direction when comparing changes in the refractive index modulation with changes in Bragg wavelength. A similar behavior during high-temperature grating regeneration was also observed in ref . When estimating the mean refractive index change, ΔnDC, during grating inscription the following relation is often applied :Eq. (4) can provide valuable information regarding the grating qualities and also regarding the type of photosensitivity through intercomparison of the different variables (Δnm, ΔλB, Δneff, and ΔnDC) . However, considering the grating dynamics displayed in Fig. 3 and Fig. 9, Eq. (4) is less suitable for use in thermal decay studies. The equation is derived assuming that the grating period, ΛB, is constant, which may not always be the case considering the high temperatures involved during grating regeneration. In Fig. 10 we have plotted the changes in refractive index modulation in Fig. 9(a) as a function of the changes in Bragg wavelength, shown in Fig. 9(b), to highlight the complex dynamics during regeneration. Besides the difference in the relative magnitudes there is also a directional change with the turning point for pre-annealing temperatures near 900 °C.
5. Discussion – Experimental results
The final refractive index modulation of the regenerated gratings, shown in Fig. 8, increase with temperature reaching a maximum when isothermal pre-annealing is performed near 900 °C, and decreases rapidly for higher temperatures. The observed optimum in pre-annealing temperature indicates an inflection point between different opposing mechanisms.
Measurements of the decay in refractive index modulation (Δnm) and the Bragg wavelength shift (ΔλB) during isothermal annealing, as well as during thermal regeneration at 1100 °C (Fig. 10) display a highly complex behavior, which further indicate that multiple mechanisms are involved during thermal processing. In addition, the reflectivity of regenerated gratings show an initial rapid decay at 1100 °C before stabilizing, which may be related to different types of regenerated gratings having significantly different thermal stability. A common feature for the dynamics shown in Figs. 2 and 3, 6, 8, and 10, is that two temperature regimes can be identified having a coinciding crossover point near 900 °C.
In the Arrhenius plot shown in Fig. 4, a linear regression fit to the time constants for the decay in refractive index modulation and changes in Bragg wavelength intersect at a temperature of 895 °C. For the low temperature region (T < 895 °C) the activation energy is Ea(ΔλB) = 86.2 kJmol−1 (0.89 eV), while for the high-temperature region (T > 895 °C) the activation energy is Ea(Δnm) = 294.5 kJmol−1 (3.05 eV). The overall behavior during annealing correlate very well with the temperature dependent structural changes and diffusion-reaction dynamics of molecular water in silica glass, reported by Davis and Tomozawa . Here, water diffusion in silica is separated into two regimes; a high-temperature extreme and a low-temperature extreme, with the transition between the two occurring at a temperature near 850 °C. The reported activation energies for the low-temperature and high-temperature regimes are 83 kJmol−1 (0.86 eV), and 237 kJmol−1 (2.45 eV) respectively. Molecular water is the diffusing species, which migrates within the glass matrix until encountering reactive sites forming nearly immobile hydroxyl groups. The concentration of the different hydrogen-related species depends on the local equilibrium conditions determined by the water diffusion-reaction mechanism according to the Doremus model , schematically described as:
The formation and diffusion of molecular water at lower temperatures is in agreement with the proposed model discussed in section 2.1 and ref [11,13], suggesting locally enhanced mobility of network oxygen as a possible route to the formation of a periodic change of the glass composition. As the annealing temperature increases, the diffusivity of molecular water increases, and subsequently also the removal rate of oxygen from the UV exposed regions. With increasing temperature, the refractive index modulation of the regenerated grating should increase, which is the case for T< 900 °C, as shown in Fig. 8. The activation energy in the low temperature regime for the Bragg wavelength dynamics, derived from Fig. 4, and the diffusion of molecular water, reported in ref , are in excellent agreement. However, further experimental verification linking the two mechanisms is needed. A possible mechanism for the change in Bragg wavelength dynamics, e.g., shown in Fig. 10, can be linked with the effect of hydroxyl concentration on glass density [43,44]. For silica glass an increase in hydroxyl concentration results in a decrease in density, and subsequently a decrease in refractive index, provided that the temperature is sufficiently high for structural relaxation to occur.
In the high temperature regime the results are more difficult to interpret. Grubsky et al.  found similar values for the Δnm-decay showing a single exponential decay behavior for grating regeneration using SMF-28 fiber (Ea = 2.8 eV) while a lower value was found for Ge/B-doped photosensitive fiber (Ea = 2.2 eV). The difference in activation energy was ascribed to a lower viscosity of the Ge/B doped fiber. The activation energy for the high-temperature regime, derived from Fig. 4, is approximately 0.5 eV larger than the activation energy for water related relaxation and diffusion in the high-temperature regime for pure silica . An additional mechanism likely to occur at higher temperatures is the removal of water related species from the core as well as the fiber cladding [44–46]. In ref , e.g., an activation energy for dehydroxylation of silica glass of Ea = 254 kJmol−1 (2.63 eV) was found for the temperature range 700 °C to 900 °C, corresponding to the binding energy of the SiO-H bond, while for 900 °C to 1200 °C the activation energy decreased to 32 kJmol−1, corresponding to the activation energy for hydrogen diffusion in silica glass. The analysis is further complicated by the peak position of defect distributions reported in non-hydrogenated fibers by, e.g, Erdogan et al. (2.9 eV) , Vasiliev et al. (2.9 eV) , Pal et al. (3.1 eV) , and Violakis et al. (3.15 eV) , as well as in hydrogen loaded fibers (3.15 eV) .
The stable component of the regenerated grating is believed to be related to changes in the composition within the core (O-CCG), although further high-temperature decay studies are required in order to determine the activation energy for grating decay . Further studies are also required in order to accurately assess the mechanisms for the unstable component of the regenerated grating. However, considering the long time constants (τ ~10 min) for the decay of the unstable component at 1100 °C, close to the glass transition region for fused silica, the mechanism is likely associated with structural changes of the glass matrix.
A significant difference in our results, compared to previous studies, is the formation of a regenerated grating independently of annealing temperature, as shown in Fig. 8, with minimum refractive index modulation of Δnm ∼0.2⋅10−4. Generally when pre-annealing is omitted, grating regeneration does not occur. The non-zero component could be linked to the required time to reach the set temperature of the furnace when inserting the fiber and fiber holder, effectively pre-annealing the grating for a short time. However, from previous experience using different types of lasers, including pulsed laser operating at 242 nm, and CW lasers operating at 244 nm and 266 nm, and under similar conditions grating regeneration did not occur. In this work we have used, for the first time, a ns Q-switched Nd:VO4 laser operating at 213 nm for fabrication of thermally regenerated gratings. As shown the laser is highly suitable for fabrication of thermally regenerated gratings. This type of laser has previously been shown to be very efficient for writing strong gratings in non-hydrogen loaded fibers associated with glass compaction, and for writing type IIa gratings associated with UV induced stress relaxation . It seems therefore likely that the non-zero component of the grating is a result of strong grating formation, resulting in the formation of molecular water during grating fabrication , in combination with UV induced structural changes of the glass matrix resulting in partial regeneration during the grating inscription process.
In this work we have presented a detailed study on thermally regenerated fiber Bragg gratings in hydrogen loaded optical fibers. Isothermal pre-annealing was performed from 85 °C up to 1100 °C, with the subsequent grating regeneration performed at 1100 °C. A maximum refractive index modulation of Δnm = 1.4⋅10−4 was achieved when the grating was pre-annealed near 900 °C prior to regeneration. Furthermore we show that the dynamics during pre-annealing and grating regeneration in hydrogen loaded standard telecommunications fiber correlate strongly with the diffusion-reaction mechanism of molecular water and hydroxyl species in silica glass. These results are in agreement with previously proposed model for regenerated gratings, ascribing the high thermal stability of the gratings to compositional and structural changes following chemical interaction and diffusion of hydrogen species within the glass matrix.
We acknowledge financial support from the Swedish Research Council (VR) through the Linnæus Center of Excellence ADOPT (P. Holmberg), Ångpanneföreningen's Foundation for Research and Development (Project 10-150) and the Richertska Foundation to promote research (M. Fokine).
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