# Reliable Lifetime Prediction for Passivated Fiber Bragg Gratings for Telecommunication Applications

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## Abstract

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## 1. Introduction

_{2}glasses was widely used for thw production of in-fibre/waveguide Bragg grating-based (BG) optical devices for the photonics industry. Indeed, photosensitivity allows for the fabrication of an outstanding number of in-Fiber Bragg Grating-based (FBG) optical devices like gain flattening filters (GFF), chromatic dispersion compensator (CDC) and 980 nm pump stabilization. These devices have found numerous applications in optical fiber telecommunication and all fiber laser systems. Most of these applications require long device lifetime (especially submarine optical networks) and the possibility of forecasting possible spontaneous degradation of the photo-induced index change. However, ageing experiments are always performed on a scale too short (<one month) to be extrapolated without a rational methodology. In 1998, Poumellec [1] established a general procedure based on the existence of a demarcation energy and the notion of Master Curve (MC); what he called Variable Reaction Pathways framework or VAREPA framework. This general procedure allows to identify and to check the necessary conditions leading to a reliable prediction of various physical quantities (e.g., laser-induced refractive index changes, photodarkening, radiation induced losses in harsh environment...).

_{anneal}at a temperature T

_{anneal}> T

_{use}. Now the question is how to perform a precise and reliable lifetime prediction of such passivated components? The usual procedure is to establish the master curve of simply outgassed components and perform the passivation FBG that have been previously out-gazed at low temperature to avoid any reactions with the remaining H

_{2}. The advantage is that this approach remains general since it can be applied to any passivation temperature provided that those are included in the master curve database and can lead to optimization of the passivation specification.

- To quickly recall the master curve approach and related physical hypotheses
- To report for the first time the passivation conditions uncertainty and their impact on the standard type I FBG lifetime prediction
- To report a reliable validation procedure of the lifetime prediction. This procedure is based on building of a “new” MC derivate from real passivated gratings.
- To highlight that building directly the MC on passivated FBG is less general but could be more reliable from an industrial point of view.

## 2. FBG Writing and Accelerated Ageing Experiments

_{w}at temperature T

_{w}produces a modulation of the RIC in space Δn(z, t

_{w}, T

_{w}) due to some physico-chemical reactions. The important features for the next discussion are 1) the mean index (Δn

_{mean}) which is the first component of the Fourier transform of Δn(z, t

_{w}, T

_{w}), 2) the refractive index modulation (Δn

_{mod}) at the Bragg wavelength which is the second component of the Fourier transform. Due to the linearity of the Fourier transform, the thermal stability of Δn

_{mean}, Δn

_{mod}, i.e., (the functions Δn

_{mean}(t, T)/Δn

_{mean}(t

_{w}, T

_{w}) and Δn

_{mod}(t, T)/Δn

_{mod}(t

_{w}, T

_{w})) are a weighted sum of the RIC stability at each point (i.e., of Δn(z, t, T)/Δn(z, t

_{w}, T

_{w}). In the simple case (like in slightly Ge-doped H

_{2}-loaded fibers), the stability does not depend on the RIC amplitude at the end of the writing process (e.g., Erdogan model of electron trapping [5]). Δn

_{mean}and Δn

_{mod}will have thus the same stability at any point of the grating and the index contrast will remain the same during the Bragg erasing. Outside of this simple case, the stability of Δn

_{mean}and Δn

_{mod}will be different.

#### 2.1. Fiber Bragg Gratings (FBG) Writing Method and Pre-Treatments

_{2}-loaded standard telecommunication optical fibers (H

_{2}loading conditions: 140 atm at room temperature for 15 days). To this purpose, the fibers were exposed through a phase mask (Lasiris; pitch = 1057 nm; diffraction power efficiency in the −1, +1 and 0 orders = 34%, 34% and 1% respectively) to a cw laser emitting at 244 nm. All the exposures were carried out at a mean power density ≈35 W/cm

^{2}. In this paper we will investigate two series of FBG. The first series was outgassed during 2 days at 50 °C and 2 days at 110 °C to ensure complete out-diffusion of the remaining hydrogen. The second series was first passivated during 10 min at 233 °C and then outgassed during 2 days at 50 °C and then 2 days at 110 °C to ensure complete out-diffusion of the hydrogen.

_{2}not consumed during FBG writing) either at room temperature (typically 1 month) or at a temperature low enough to avoid any interaction of the remaining H

_{2}with the glass matrix (typically a 2 days below 110 °C). If the passivation process (FBG stabilization) is achieved under the same conditions than the accelerated ageing process (MC determination), it is possible then to determine its duration for a given temperature to reach a specified lifetime. Thus, to remain general (i.e., any optical fiber chemical composition and any FBG writing conditions) this approach implies to outgass the FBG before to perform the passivation. This is the usual process described in the literature. However, in many cases, industrial manufacturers will passivate FBG before H

_{2}outgazing because it is simpler from the production point of view. In such a case, if there is a significant interaction of H

_{2}with the glass matrix (i.e., formation an H-bearing species or transformation of existing defects that significantly impact the refractive index changes) at the passivation temperature (typically above 220 °C), the lifetime of the passivated grating cannot be deduced from the MC. In such a case it is thus necessary to build a MC direcly with the real (i.e., passivated and outgassed) components.

#### 2.2. Accelerated Ageing Experiments

#### 2.3. How to Determine the Refractive Index Decay during the Accelerated Ageing Experiments

_{B}measurements was estimated to be about 0.2% and 10 pm respectively. Then, to deduce the changes in refractive index from these data, one usually starts by assuming a step-index fiber; a periodicity of the exposure-induced change in refractive index along the fiber axis ( ) and uniformity of this change across the core. The following formulae can then be used to calculate either Δn

_{mod}and Δn

_{mean}or the Normalized Integrated Coupling Constant (NICC) from the grating reflectivity R at λ = λ

_{B}[6]. Notice that those formulae are given for a simple grating [6].

_{max}at λ = λ

_{B}, T is the fixed temperature at which the BG has been held for an annealing time t. Notice that provided the FBG is uniform and the integral overlap η (the fraction of the total optical power propagating along the core) does not depend on T and does not change too much during annealing, NICC is the same quantity as the normalized modulation index: [2], where Δn

_{mod}(0,296K) and Δn

_{mod}(t, T) are the modulation at the beginning of the annealing and after annealing at T for t respectively. In most experiments, both R and λ

_{B}are measured at the temperature T of the isothermal ageing. However, this practice can sometimes be an error source if temperature-induced reversible changes in reflectivity are not taken into account. The extent of these changes is known to be significant in some kind of FBG like non-H

_{2}-loaded Ge-doped fibers [7]. As these reversible changes can spoil the analysis of the isothermal annealing experiments, it proves necessary to correct the raw data to account for these changes by means of relations similar to those established in [7]. This correction procedure will be applied in the following.

## 3. The Lifetime Prediction Theory: The Master Curve Formalism and the VAREPA Framework

_{w}, T

_{w}) arises from several physical phenomena directly proportional to each other’s [2,3]: creation of species with a polarizability different from the non-irradiated matter polarizability, some re-organization of the matter (e.g., glass density changes) and stress redistribution. All these phenomena can thus be reduced to only one species that we will call B in such a way that the question of stability of the RIC restricts only to the stability of B.

**(A) First group of assumptions (the application field)**

_{0}like k(E, T) = k

_{0}exp(−E/k

_{B}T) where k

_{B}is the Boltzman constant and [B] is the concentration of the B species.

**(B) The second group of assumptions (on the reaction towards the computation of time dependence)**

_{d}

_{0}(E) is the initial population produced by the FBG writing.

_{d}and thus we can read:

_{d}is properly defined by . For a first order reaction E

_{d}= k

_{B.}T.ln(k

_{0}t). The reaction properties (i.e., k

_{0}) are appearing in E

_{d}only, the disorder (relevant of the glass) appears in g(E). Finally, [B](t, T) is the area under the red dotted curve in Figure 1. The advancement degree x(E, t, T) in progressing erases the B distribution.

**(C) Some consequences:**

_{d}). The curve [B](E

_{d}) is called master curve as it is unique whatever the (t, T) couple may be. We can note that T is equivalent to ln(t) in E

_{d}and thus isochronal ageing data are equivalent to isothermal ageing data for establishing MC. Notice that from practical point of view most people consider that NICC(E

_{d}) is the master curve. This is discussed in Section 4. Now the MC plot allows the user to predict the grating lifetime, providing that the anticipated conditions of BG use E

_{d}= f(t

_{use}, T

_{use}) correspond to a point on the MC that has been actually sampled during the annealing experiment.

## 4. Results

#### 4.1. Step 1: Build the MC with Data Obtained after Accelerated Ageing of Non-Passivated Gratings and Determine the Lifetime in the Conditions of Use

_{2}-loaded Ge-doped optical fiber core using a cw244 nm laser. Figure 2 displays the isothermal decays of the Normalized Integrated Coupling Constant NICC(t, T) corresponding to the decays of two or three gratings for each of the five chosen temperatures (406 K, 452 K, 508 K, 560 K and 610 K). The choice of using up to five different temperatures and more than one grating per temperature has been dictated by the necessity to determine and to minimize the error on k

_{0}. Figure 3 shows those data series plotted against k

_{B}.T.ln(t). Then, as shown in Figure 4, collapsing the data series into a single curve is achieved by adjusting k

_{0}(and its uncertainty) in the demarcation energy expression and gives rise to the master curve (MC) [1,5,9].

**Figure 2.**Isothermal decays of identical uniforms Fiber Bragg gratings (FBG) written in an H

_{2}-loaded standard telecommunication fiber.

**Figure 3.**Normalized Integrated Coupling Constant (NICC) as a function of the intermediate variable k

_{B}.T.ln(t).

**Figure 4.**Normalized Integrated Coupling Constant (NICC) as a function of the demarcation energy E

_{d}= k

_{B}.T.ln(k

_{0}t) (in eV), i.e., the master curve. k

_{0}in s

^{−1}.

_{0}and its confidence interval. This has been made in Figure 4 yielding ln(k

_{0}in s

^{−1}) = 21.5 ± 2.0. We can here check that it was possible to find a frequency factor (k

_{0}) so that the earlier assumptions are reasonable. Indeed it can be shown that if one assumption is not verified in the investigated range of (t, T) and for the expression of E

_{d}that has been previously defined, no collapse is possible. In addition, a key assumption in using these MCs is that the decay in the change of refractive index is just defined by E

_{d}[11]. To check quickly this hypothesis at high temperature, one has to carry out isochronal and isothermal measurements for one quantity (here NICC) and secondly to plot data versus k

_{B}.T.ln(Δt

_{isoc}) for the first set and k

_{B}.T

_{isot}.ln(t) for the second set. If curves are parallel and if they collapse into a MC by k

_{0}optimization, the hypotheses are then fulfilled [4]. In the opposite situation, there may be several parallel or serial limiting reactions with different k

_{0}and different distributions. The analysis is thus more complex for achieving lifetime prediction but it is still possible to perform a VAREPA approach [1,11]. However, no MC exists anymore.

_{d}= f(t

_{use}, T

_{use}) correspond to a point on the MC that has been actually sampled during the annealing experiment. Furthermore, the shape of the distribution of activation energies can be extracted from the slope of the MC by simple differentiation as we mentioned in Section 3C. Since the life function is now available, it is possible to calculate the lifetime for a maximum working temperature. For example for gratings measured in Figure 4, NICC will decrease to 0.82 at 45 °C and 25 years (18% erasure) or 10% erasure over 4.2 years at 45 °C. This lifetime may be not suitable for the most applications and especially for sub-marine networks. However due to the distribution of the activation energies, it is possible to increase the lifetime of our grating by performing a passivation process that suppresses the less stable sites. This is called “the passivation process” and this is the main topic of the following sections.

#### 4.2. The Passivation Process: A Method Used to Enhance the Thermal Stability of BG Written in A Standard Telecommunication Fiber

_{anneal}at a temperature T

_{anneal}> T

_{use}. A coherent rationale of this method is formulated from the above-mentioned approach [5]: the treatment wipes out the portion of the index change that would normally decay over the lifetime of the device and keeps only the stable portion of the index change [5]. Notice that this method proves to be effective for enhancing the stability of index changes in either non-hydrogenated or H

_{2}-loaded Ge-doped fibers.

_{f}after a time t

_{use}at temperature T

_{use}by the index change Δn

_{1}after burning in process. If we impose that after a given time at a given temperature (let us say 25 years at 40 °C for instance), the lifetime ratio Δn

_{f}/Δn

_{1}has to remain within a given range with ε < 10% for instance, we obtain the passivation parameters (time t

_{a}and temperature T

_{a}). Notice that in general we estimate the uncertainty on k

_{0}based on the data uncertainty, then we chose the worst case value and we added an extra safety margin (typically ε < 1% instead of 10%).

**Figure 5.**Scheme of the passivation process (also called burn in process in this figure) [12]. Δn

_{0}is the FBG index modulation (or its reflectivity) before the passivation process at the temperature T

_{a}for a given time t

_{a}. Δn

_{1}is the FBG index modulation after the passivation process. Δn

_{f}is the final value of the index change after its life for a time t

_{use}at a given temperature T

_{use}. Δn

_{0}/Δn

_{1}is called the passivation (or annealing) ratio. Δn

_{f}/Δn

_{1}is called the lifetime ratio.

_{0}/Δn

_{1}that is defined by the FBG index modulation Δn

_{1}(or its reflectivity) after a passivation time t

_{a}at a given passivation temperature T

_{a}by the FBG index modulation Δn

_{0}(or its reflectivity) before the passivation process. So if the end user imposes that after a given time t

_{use}at a given temperature T

_{use}(let us say 25 years at 45 °C for instance), the lifetime ratio Δn

_{f}/Δn

_{1}has to remain within a given range with ε < 1% for instance, we determined the related passivation ratio Δn

_{0}/Δn

_{1}, e.g., 2. This means that the passivated FBG at a chosen passivation temperature T

_{a}(e.g., 220 °C in our study) has to be erased of about a factor 2 to respect the above mentioned lifetime criteria (ε < 1% during 25 years at 45 °C).

#### 4.3. Uncertainties in the passivation conditions and impact in the lifetime prediction of passivated FBG:

_{0}) to an uncertainty of at least 1% of this prediction.

**Figure 6.**Simulation of accelerated ageing during 2000 h at 125 °C for a passivated grating during 10 min at different temperatures around 233.5 °C.

**Figure 7.**An example of comparison between qualification data (i.e., accelerated isothermal ageing) at 125 °C and the lifetime prediction for 11 passivated identical FBG using the Master Curve (MC). The passivation ratio Δn

_{0}/Δn

_{1}was about 1.9 ± 0.1.

## 5. A Critical Study of the Passivation Method and How to Perform A Reliable Prediction

#### 5.1. How to Verify the Validity of the FBG Passivation Conditions and Related FBG Lifetime Prediction from Industrial Point of View

_{0}coefficient, i.e., the optimum value for k

_{0}obtained by least square optimization (here ln(k

_{0}) = 21.5) but also the upper and the lower bounds corresponding to its confidence interval (ln(k

_{0}) = 19.5 and 23.5) that have been estimated based on ageing data uncertainty. As it can be seen, there is a good agreement between qualification data and the lifetime predictions at 125 °C. Indeed, the worst case of the qualification data remains higher than the prediction’s lower bound. It must be mentioned that this approach based on “only” one isotherm is not reliable from a lifetime prediction point of view, but this is only a first step. It could be useful in such a manner and it has the merit to detect some potential failure in the lifetime predictions.

#### 5.2. Potential Failure in the Prediction of Passivation Effect and Subsequent FBG Lifetime due to H_{2} Reactions at “high” Temperature

_{2}, T-OH with T = Si or Ge) can be transformed under the effect of a rise in temperature (e.g., passivation at temperatures higher than 150 °C). These chemical reactions affect the index modulation and thus FBG reflectivity; specifically it can lead to an “amplification” of the erasure of photo-induced index changes compared to the erasure predicted using the master curve. To conclude, it is important to remember that the master curve is established for FBG prepared under specific conditions and it does not apply a priori if FBG were conditioned (i.e., H

_{2}out-gazing and passivation conditions) in a different manner.

#### 5.3. How to Predict the Lifetime of a Passivated FBG in a Reliable Manner

- (1)
- Establish the master curve of simply outgassed components and perform the passivation of FBG after H
_{2}outgazing at low temperature (below 100 °C) to avoid any reactions with the remaining H_{2}. The advantage is that this approach remains general since it can be applied to any passivation temperature provided that those are included in the master curve database and can lead to optimization of the passivation specification. - (2)
- An alternative solution is to simply build a mastercurve on the real components (i.e., the gratings written, outgassed and passivated under fixed conditions) that we will called “restricted” master curve. The major advantage is that the master curve is built on components that went through the whole fabrication process and is therefore necessarily representative of the final product’s behavior.

_{B}T

_{isot}ln(t) are the same (parallel curves) and if their collapse into a MC is possible by fitting k

_{0}), the obtained mastercurve can then be used to predict the behaviour of annealed gratings with time and temperature in a reliable manner. An example of such a “restricted” mastercurve built on passivated gratings is shown in Figure 8 together with its prediction deduced from the initial master curve [12]. The good agreement between those curves allows then the user to validate the FBG lifetime prediction.

**Figure 8.**Normalized Integrated Coupling Constant (NICC) as a function of the demarcation energy E

_{d}= k

_{B}T.ln(k

_{0}t) (in eV), i.e., the master curve for passivated FBG written in H

_{2}-loaded germanosilicate core optical fibers. The black lines correspond to the MC prediction based on non-passivated gratings using a non-temperature dependent (black dotted line) and a temperature dependent (black full line) approach.

## 6. Conclusions

_{2}degassing for instance) determination of the lifetime for a given temperature is no longer possible. In that case, the lifetime can be checked by establishing a “restricted” MC related to the passivated gratings. The major advantage of this approach is that this “restricted” master curve is built on components that went through the whole fabrication process and is therefore necessarily representative of the final product’s behavior. This eliminates hydrogen-related issues mentioned above, for instance. The major drawback is that the master curve and the related predictions are available only for the chosen passivation conditions and cannot be transposed to different passivation conditions. However, this may not be a limitation if a controlled fabrication process is followed.

## Acknowledgments

## Conflicts of Interest

## References

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## Share and Cite

**MDPI and ACS Style**

Lancry, M.; Poumellec, B.; Costes, S.; Magné, J. Reliable Lifetime Prediction for Passivated Fiber Bragg Gratings for Telecommunication Applications. *Fibers* **2014**, *2*, 92-107.
https://doi.org/10.3390/fib2010092

**AMA Style**

Lancry M, Poumellec B, Costes S, Magné J. Reliable Lifetime Prediction for Passivated Fiber Bragg Gratings for Telecommunication Applications. *Fibers*. 2014; 2(1):92-107.
https://doi.org/10.3390/fib2010092

**Chicago/Turabian Style**

Lancry, Matthieu, Bertrand Poumellec, Sylvain Costes, and Julien Magné. 2014. "Reliable Lifetime Prediction for Passivated Fiber Bragg Gratings for Telecommunication Applications" *Fibers* 2, no. 1: 92-107.
https://doi.org/10.3390/fib2010092