Abstract

We report our investigation on the correlation between glass viscosity and the lifetime of femtosecond laser written silica fiber Bragg gratings (FBGs) at high temperatures. The FBGs are made by a direct, point-by-point writing method using an 800-nm Ti:sapphire femtosecond laser. It shows that the femtosecond laser inscribed FBGs in the commercial silica fibers can survive under high-temperature up to 1150 °C. An empirical formula of FBG thermal lifetime τ (in second) versus glass viscosity η (in dPa·s), τ=0.27η0.32, is deduced. Both our experimental results and the previously reported work on femtosecond laser induced photo-defects is in good agreement with such a formula, indicating its effective prediction on the thermal stability and thermal decay of such a type of FBG at high temperatures.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Fiber Bragg gratings (FBGs), which are composed of a chain of one dimensional (1D) wavelength-scaled periodic refractive index variation along the axis of the fiber core, are important fiber optic components for many applications such as fiber lasers, spectral filters, telecommunications, distributed sensors of key physical parameters (e.g., temperature, pressure, strain, and refractive index) of the environment, and high-precision bio-chemical detection [15]. Such a type of fiber components is advantageous due to its low cost, compactness, immunity to electromagnetic interference, and fair resistance to harsh environments.

Silica FBGs were initially fabricated by ultraviolet (UV) light exposure, utilizing the UV-photosensitivity of the doped core of the silica fibers. Phase-mask method using relatively low-coherence UV light [6] and dual-beam interferometric technique using highly coherent UV laser [7] are developed. It is normally necessary for the core of the silica fibers having decent UV-photosensitivity when these two approaches are used. Germanium/boron doping and/or hydrogen-loading methods are the typical approaches to enhance the UV-photosensitivity of the core glass. The formed FBGs is normally called as Type-I FBGs. The refractive index change in Type-I FBGs is due to the oxygen-deficient color-center defects, which are formed when the high-photon-energy UV light breaks the weak oxygen-associated bonds, e.g., Ge–O bonds in Ge-doped photosensitive silica fibers [1].

With the rapid development of the ultrafast femtosecond (fs) laser sources in the past two decades, commercial turn-key infrared (IR) fs lasers become common laboratory tools for making FBGs [814]. Due to the high peak power of femtosecond laser pulses, multi-photon absorption and plasma explosion occur during the femtosecond laser inscription. When silica glass is exposed to femtosecond laser irradiation, the recombination of self-trapped excitons accompanies with the formation of molecular oxygen in the silica glass network:

$$Si{O_2} + X \to Si + {O_2}, $$
where X represents an exciton, and Si denotes the oxygen-deficient Si-O network unit, respectively [15]. The oxygen molecules is formed from the atomic oxygens decomposed from the Si-O network. Hence porous nanovoids filled with trapped molecular oxygen and the neighboring condensed glass with dissolved oxygen are formed within the localized area exposed by the fs-laser [16]. As a result, the index modulation Δn is therefore generated in the FBGs due to the index contrast between such nanoporous structures and the unchanged silica matrix. Moreover, the combination of the ultrafast reaction speed and the ultrahigh viscosity of the frozen glass prevents the reaction in Eq. (1) going towards the reverse direction so that the nanoporous structure can be maintained during the formation. This so-called Type-II FBGs can survive at high temperature above 1000 °C, because the collapse of such nanoporous structural defects requires relatively low viscosity for facilitating the diffusion of the atoms or ions to fill the nanovoids. On the other hand, Type-I FBG can be thermally stable up to only ∼700 °C [1], because electron- or ionic diffusion at such relatively low temperatures is fast enough to neutralize the color-center defects. Additionally, such a femtosecond-laser direct-writing method requires neither phase-masks nor photosensitized fibers and hence offers remarkably flexibility for the FBG fabrication. On the whole, femtosecond-laser-written FBGs are advantageous for the usages of high temperature applications or high laser power applications [17].

Chemical composition gratings (CCGs) or regenerated gratings [1829] are another type of FBG with ultrahigh thermal stability. CCGs are normally fabricated by first erasing UV-exposed Type-I FBGs and then annealed the sample at high temperatures close to 1000 °C. Due to the complex chemical reactions in the UV-exposed regions, the chemical nature of the silica glass within the local area of the regenerated FBGs is permanently changed. It is assumed that cristobalites, one type of the crystalline polymorph of silica group, nucleate and grow inside the vitreous silica, due to the high temperature (∼1000 °C) and high pressure (hundreds of MPa) inside the regenerated area [20,24]. According to the conventional crystal-growth theory [30], under appropriate high temperature and high pressure, space-selective heterogeneous nucleation occurs first, utilizing the erased Type-I FBGs as the aid interface of the heterogeneity. The crystalline phase then grows up from the nucleation centers. Due to the presence of the impurity sites on the heterogeneous interface, the free-energy barrier of nucleus formation in heterogeneous nucleation is significantly lower than that in homogeneous nucleation. Due to such a forming mechanism of the regenerated gratings, regenerated FBGs show high thermal stability at high temperatures. Indeed, the recorded highest temperature that regenerated FBGs can work at high temperatures up to 1500 °C [28], while regenerated FBGs also exhibit the recorded long-term stability at 890°C for 9000 hours of continuous use [29]. One should notice that the reflectivity of regenerated CCGs is much weaker than the original erased Type-I FBGs [18,19].

Although CCGs show promising for ultrahigh temperature sensing, their fabrication procedure at high-temperature normally reduces the mechanical strength of the fiber. In contrast, FBGs made by femtosecond laser direct-writing method, although less durable at high temperatures than the CCGs, should still be a decent solution, as the fiber integrity will not be degraded during the FBG fabrication [1].

So far, most of works on the femtosecond laser direct-written silica FBGs for high temperature usages mainly focus on characterizing the thermal stability and the performance of the FBGs, rather than on comprehensively understanding the dynamic mechanism of high-temperature stability and thermal decay of such a type of FBG, in particular when the temperature approaches the glass transition temperature Tg of silica [11,3135]. On the other hand, from the viewpoint of the material physics and chemistry, the thermal decay mechanism of the FBGs made by femtosecond laser direct-writing method is critical for comprehensively understanding and predicting how such a type of FBG behaves at any arbitrary time and temperature.

In this paper, we have investigated the thermal behaviors of femtosecond laser direct-written fiber Bragg gratings (FBGs) in various commercial silica optical fibers at the high temperature near the glass transition temperature Tg. It shows that the femtosecond laser inscribed FBGs in silica fibers can survive under high-temperature up to 1150 °C, in good agreement with the previous studies [11,3135]. At 1150 °C, the FBGs written in the fiber with a pure silica core can survive for ∼90 minutes before the FBG vanishes. The thermal behaviors, including the thermal stability and the thermal decay of such a type of FBG at high temperatures, are found to be dominated by the viscosity of the core glass. An empirical formula related to the thermal decay time and the glass viscosity has been deduced for such a type of FBG in silica fibers. And it is found that such a relation can well predict the thermal stability and the thermal decay behavior of silica FBGs inscribed by IR femtosecond laser.

2. Experiments

2.1. Fiber selection

Three commercial single-mode silica fibers were selected as the hosts for making femtosecond laser written FBGs. Fiber types 1#-3# are FiberCore SM1250SC, YOFC G652D (equivalent to Corning SMF28), and Nufern UHNA3, respectively. Table 1 lists the optical parameters and the glass systems of the core and the cladding of the selected fibers [3638]. The methodology of fiber selection is that the core or cladding of a selected fiber should be based on silica with a single dopant, i.e., F in the cladding of 1#, and Ge in the core of 2# & 3#; and the rest part of these fibers is based on pure silica. Therefore, complex discussion on the thermal diffusion and viscosity arising from multiple dopants in one glass matrix.

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Table 1. Parameters of selected single-mode silica fibers (dcore: core diameter; NA: numerical aperture; λc: cutoff wavelength of fundamental mode)

2.2. Stimulated Brillouin scattering (SBS) characterization of Ge-doped silica fibers

In order to determine the precise GeO2 content in the two GeO2-doped silica fibers (2# and 3#), stimulated Brillouin scattering (SBS) characterization was carried out. SBS is a nonlinear optical phenomenon, which occurs due to the interaction between a narrow-line laser and the acoustic wave propagating in the glass host. The acoustic velocity in the glass with a certain composition is only related to the chemical components composing the glass matrix [3942].

Figure 1 shows the experimental setup of heterodyne detection for SBS test. A 1.55-µm single frequency laser (Toptica photonics CTL-1550) with a linewidth <10 kHz was used as the pump. The laser output was split into two beams using a 70:30 fiber coupler (FC). One beam was sent to an erbium-doped fiber amplifier (EDFA) and served as the input pump in the fiber under test (FUT) through an optical circulator (OC), while the other beam was used as a reference beam or a local oscillator for heterodyne detection. The backscattered Brillouin signal coming back from the FUT was then mixed with the input laser using another 50:50 fiber coupler, generating a beat note signal which is further detected with an ultrafast photodiode. The Brillouin spectrum was finally recorded using an electrical signal spectrum analyzer (Agilent, N9030A PXA) with a resolution bandwidth of 10-kHz. Note that a fiber polarization controller (PC) was inserted to maximize the beat signal, and a power meter was also used in the experimental setup to accurately monitor the fiber transmission during measurements. The length of the FUTs was 25 km for G652D fiber and 0.12 km for UHNA3 fiber, respectively. Note that for the measurement on UHNA3 fiber, the output of the TLS source and the gain of the following EDFA were 30 mW and 10 dB, respectively. And for the measurement on G652D fiber, the output of the TLS source and the gain of the following EDFA were 30 mW and 0 dB, respectively.

 

Fig. 1. Experimental setup of heterodyne detection for measuring the Brillouin frequency and linewidth. FC, fiber coupler; EDFA, erbium-doped fiber amplifier; OC, optical circulator; FUT, fiber under test; PC, polarization controller; PD, photodiode detector; ESA, electrical signal spectrum analyzer.

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2.3. FBG writing

The grating inscription was then performed by using of an 800-nm Ti:sapphire laser system (Astrella, Coherent Inc.) with a pulse width of 80 fs and a repetition rate of 1-kHz. Point-by-point method was used for directly writing the uniform FBGs. To avoid the possible mechanical fracture and increase the fabrication yield, the protection polymer coating was stripped prior to the FBG fabrication. The fs laser spot was focused into the center of the fiber core and the array of the points was written along the central axis of the fiber core with high spatial precision of ±0.5 µm. The details of the high-precision FBG fabrication can be found elsewhere [43]. Table 2 summarizes the pulse energy of femtosecond laser used for writing FBGs and the key parameters of achieved FBGs.

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Table 2. Parameters of femtosecond laser used for writing FBG and spectral parameters of written FBGs.

Note that according to the Bragg equation:

$$m \cdot {\lambda _B} = 2 \cdot {n_{eff}} \cdot \Lambda , $$
where λB is the Bragg wavelength, m is the order of the grating, Λ is the period of the grating, neff is the effective index of the guided mode, respectively. For the FBGs made with the 800-nm fs laser source, due to the diffraction limit, the diameter of the laser spot focused into the fiber core was ∼1 µm. Hence, the order m of the FBGs in this work is 2.

2.4. Spectral characterization of FBGs at high temperatures

After the FBG inscription, the fiber sample with FBG was loaded into the central position of the hotzone in an electric resistance tube furnace (see the setup of high temperature characterization in Fig. 2). The uniform hotzone in the furnace was 50 mm long. Each FBG sample was first annealed in the tube furnace at temperature of 550 °C for 2 hours, in order to release the residual stress in the fiber. The sample was then cooled down to room temperature (RT) at the rate of 1 °C/min and ramped up again to high temperature with a ramp rate of 5 °C/min. A C-L band ASE (amplified spontaneous emission) source (Fiberlabs, ASE-FL7004) was used as the light source launching into the FBG. An optical spectrum analyzer (OSA, YOKOGAWA AQ6370C) was used to monitor and record the spectrum evolution of the FBG. The spectral resolution used for the measurement was set at 0.02 nm. During the heating process, the tube furnace was purged with dry nitrogen gas to avoid the attack of moisture in the air to the naked silica glass fiber. Note that the fiber sample with FBG was kept straight but unstressed during the thermal analysis. The FBG spectrum was recorded immediately when the furnace reached the scheduled temperature. And in the following, the shown temperature was the real temperature measured by a Type-K thermocouple.

 

Fig. 2. Experimental setup of spectral characterization of fs-laser written FBGs at high temperatures.

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3. Results and discussions

3.1. Determination of GeO2 content in silica fibers

According to the information of NA, cutoff wavelength and core diameter provided in Ref. [36], the cladding composition of fiber 1# was deduced to be 90.8SiO2-9.2F (mol.%).

The precise GeO2 concentrations in the core of fiber 2# and 3# are deduced from the relation between the Brillouin frequency νB of germanosilicate glass fibers and the germanium content [3942], according to the following equation:

$${\nu _B} = \frac{{2 \cdot {n_{eff}} \cdot {V_a}}}{{{\lambda _L}}}, $$
in which neff is the effective index of the guided fundamental mode, λL is the incident laser wavelength (i.e., 1.55 µm here), and Va is the acoustic velocity of the fiber core, respectively.

Using the setup shown in Fig. 1, the SBS frequencies νB of fiber 2# (G652D) and 3# (UHNA3) were measured to be 10.83 GHz and 8.92 GHz (see Fig. 3), respectively. Since there is a small deviation on the GeO2 content between the numerical models given by Ref. [42] and Ref. [44], the GeO2 contents here were calculated to be 4.4 mol. % and 44.6 mol. % respectively for G652D and UHNA3, by averaging the results from the two models.

 

Fig. 3. Experimental Brillouin spectra measured at 1550 nm in selected silica fibers with GeO2-doped core.

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Table 3 summarizes the determined compositions of the selected single-mode silica fibers.

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Table 3. Determined compositions of selected single-mode silica fibers.

3.2. Temperature coefficient of FBG spectrum in selected silica fibers

Figure 4 illustrates the shift of the Bragg wavelength λB with the temperature. According to Eq. (2), the effective index neff and the pitch Λ vary with the surrounding temperature T, the differential thermal shift of the Bragg wavelength λB is therefore deduced according to:

$$\frac{{\partial {\lambda _\textrm{B}}}}{{\partial T}} = \Lambda \frac{{\partial {n_{eff}}}}{{\partial T}} + {n_{eff}}\frac{{\partial \Lambda }}{{\partial T}}. $$

 

Fig. 4. Evolution of FBG spectrum during the temperature ramping in selected silica fibers: (a) SM1250SC; (b) G652D; (c) UHNA3.

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Dividing Eq. (4) by Eq. (2), one can obtain

$$\frac{{\Delta {\lambda _\textrm{B}}}}{{{\lambda _\textrm{B}}}} = (\frac{1}{{{n_{eff}}}} \cdot \frac{{\partial {n_{eff}}}}{{\partial T}} + \frac{1}{\Lambda } \cdot \frac{{\partial \Lambda }}{{\partial T}}) \cdot \Delta T, $$
in which ξ (=$\frac{1}{{{n_{eff}}}} \cdot \frac{{d{n_{eff}}}}{{dT}}$) is the thermo-optic coefficient, and α (=$\frac{1}{\Lambda } \cdot \frac{{d\Lambda }}{{dT}}$) is the coefficient of thermal expansion (CTE). Therefore, Eq. (5) can be converted to:
$$\frac{{\Delta {\lambda _\textrm{B}}}}{{\Delta T}} = (\xi + \alpha ) \cdot {\lambda _\textrm{B}}. $$
Equation (6) indicates that the thermal shift of FBG central wavelength λB depends on (i) the thermo-optic coefficient of the refractive index and (ii) the CTE of the fiber material, and (iii) the propagation constant of the LP01 mode. For the same silica fiber with certain glass core and cladding compositions, both ξ and α are approximately constant from RT to the temperature close to Tg. For example, in the range of RT-1000 °C, the thermo-optic coefficient dn/dT of the pure silica glass is +1.1 ± 0.1 × 10−5/°C, whereas its CTE is +5.5 ± 0.5 × 10−7/°C [1,45]. In addition, the variation of the waveguide constant of a single-mode silica fiber is negligible too when the temperature is below Tg. Therefore, the thermal shift of the FBG wavelength ΔλB ought to grow linearly with the temperature in the range of RT-Tg. In other words, any large deviation of dλB/dT away from such a linear relationship could be attributed to the following facts. First, it occurs when the silica glass transits from the solid state to the liquidus state when the temperature crosses the Tg and the CTE of the glass increases much faster with the temperature than the case below the Tg. Second, it could happen when the waveguide propagation constant of the LP01 mode changes dramatically. For example, when the core area expands largely due to the thermal diffusion of the dopant(s) inside the core towards the cladding or the dopant(s) inside the cladding towards the opposite direction. Therefore, the effective index neff changes significantly. Mind that the enhancement of thermal diffusion rate of the dopant ions inside glass also requires the temperature crossing beyond Tg so that the low viscosity of the glass could accelerate the motion of the small ions inside the glass matrix.

Figure 5 shows the evolution of the FBG wavelengths in various silica fibers with the temperature up to 1140 °C. Figures 5(a)–5(c) illustrates the normalized FBG wavelength λBB,RT in all the three selected silica fibers. A linear relationship is seen between λBB,RT and the temperature T, from RT up to 800 °C. Note that the λBB,RT of the FBG in the G652D fiber appears somehow nonlinear when the temperature is between 800 and 1150 °C.

 

Fig. 5. Measured temperature dependence of FBG wavelength λB in selected silica fibers of (a) SM1250SC, (b) G652D, and (c) UHNA3. (d) Trend of thermal expansion of glasses with thermal history of rapid quenching and slow cooling.

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The temperature coefficients ΔλBT of the FBGs are summarized in Table 4. It is seen from Eq. (6) that ΔλBT is the sum of two coefficients of ξ and α. The linear relation between ΔλB/λB and T, from RT to 800 °C in all the three selected silica fibers in Figs. 5(a)–5(c) arises from the linear dependence of ξ and α [46,47] on the temperature.

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Table 4. Temperature parameters of FBGs made in various silica fibers.

As the sketch shown in Fig. 5(d), when a glass with the experience of rapid cooling is reheated with a slow ramp-up speed, the quenched sample is allowed to release the excess energy inside and such a relaxation exhibits as the nonlinear behavior of the thermal expansion, whilst the CTE of a well-annealed glass sample will only show the linear relationship with the increase of the temperature [48]. Therefore, the nonlinear relation of the λBB,RT of the FBG written in G652D fiber above 800 °C reveals the thermal history of rapid-cooling of such a fiber, probably due to the ultrafast drawing speed of the G652D fiber. Note that the typical drawing speed of conventional telecommunication silica SMF28 fiber (equivalent to G652D) is approximately 50 m/s, 1-2 order of magnitude faster than drawing other specialty fibers.

The nonlinear behavior of the normalized temperature dependence of FBG wavelength λBB,RT in G652D fiber [see Figs. 5(b) and (d)] can be supported by the recent discovery on the transition from purely elastic to viscoelastic behavior of SMF28 telecom fiber at high temperatures characterized using regenerated Bragg gratings [27]. The glass transition temperature Tg is defined as the transition between the viscous liquid and the solid glass state. At the temperature far below the glass Tg, the solid glass can be viewed as pure elastic, while the temperature approaching the Tg, which thermodynamically is typically a temperature range, the glass exhibits viscoelastic behavior. However, the turning point of ∼800°C, where the nonlinear behavior starts in G652D fiber, is quite far away from the Tg (1100-1300 °C) of silica glass. It can be explained that a rapidly quenched glass preserves the viscoelastic nature above the Tg, and when such a glass is reheated slowly to high temperature approaching the glass Tg, the relaxation of the glass structure occurs when the temperature is high enough but still far away from the Tg. This is why the transition from purely elastic to viscoelastic behavior can be observed in conventional SMF28 (or G652D) fiber at relatively low temperature [27].

3.3. Mechanism of thermal stability of fs-laser written FBGs

The reflectivity R of the FBG is calculated by:

$$\textrm{R} = \textrm{tanh}{(\kappa \textrm{L})^\textrm{2}}, $$
in which the product of κL ($\kappa = f\pi \Delta \textrm{n}/{\lambda _B}$, where f is the fraction of the guided mode power in the fiber core to the total guided mode power; Δn is laser induced refractive index change in the FBG) presents the strength of the FBG, and L is the FBG length, respectively.

Since the thermal expansion coefficient of silica glass is just ppm (parts per million), the variation of the FBG length L is nearly negligible. As κ is proportional to the index modulation Δn in the FBG, the change of κL with the temperature mainly represents the temperature dependence of the index modulation Δn in the written FBG.

Figure 6 plots the thermal decay of the normalized FBG strength κL against the time, when the fiber sample was kept at a constant temperature. Single exponential decay function

$$I = {I_0} \cdot exp ( - t/\tau ), $$
where the constant τ is the time t when the intensity I drops to 1/e (i.e., ∼37%) of the initial intensity I0, is used for fitting the time decay of the normalized κL in Fig. 6. Table 5 summarizes the thermal decay parameters of the FBGs written in the selected fiber types.

 

Fig. 6. Exponential#decay of FBGs in selected silica fibers ((a) SM1250SC; (b) G652D; (c) UHNA3) maintained at a certain temperature. Note that Y axis is in logarithmic scale.

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Table 5. Thermal decay parameters of FBGs made in various fibers.

In addition, it is seen from Figs. 6(a) and 6(c) that slight nonlinearity can be seen in the thermal decay of the FBGs in SM1250SC fiber and UHNA3 fiber at high temperatures when the decay time is in logarithmic scale. Such a nonlinear behaviors are believed to be due to the thermal diffusion of fluorine dopant in SM1250SC fiber cladding into the pure silica core, and germanium dopant in the UHNA3 fiber core into the pure silica cladding, respectively. In SM1250SC fiber with a pure silica core, because fluorine has a small radius, fluorine dopants diffuse much faster than other atoms in the silica glass network. In the case of UHNA3, the high content of GeO2 inside the glass matrix makes the Tg of the core glass reduce down to ∼800 °C. The high diffusion rate of germanium at the temperature above glass Tg facilitates the germanium moving into the pure silica cladding and leads into the expanding of the core area and also the reduction of the index difference between the core and the cladding. The change of the propagation constant of the fundamental mode therefore causes such a nonlinearity.

The glass viscosity η can be expressed as the function of the temperature T [49]:

$$\eta (T) = \textrm{A} \cdot \textrm{exp}(\frac{E}{{RT}}), $$
where A is the viscosity constant, E is the activation energy, and R is the gas constant, respectively. The A and E of the related pure silica, Ge-doped silica, and F-doped silica glasses are listed in Table 6, according to the information provided in Refs. [47,50]. In addition, such an Arrhenius dependence of viscosity has been proven valid for various melts, including silicates, fused salts, oxides, and organic liquids [51]. And either in high viscosity regime where η >107 dPa·s or in the low viscosity regime where η <102 dPa·s, the glass viscosity exhibits good Arrhenius-type behavior with a temperature-independent activation energy [51]. Figure 7 plots the viscosity curves of the glass compositions used in the selected silica fibers.

 

Fig. 7. Viscosity curves of glass compositions used for selected fibers.

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Table 6. Viscosity parameters of glasses used in selected fibers.

Figure 8 illustrates the exponential decay time τ of FBG strength versus the viscosity of the core glass, based on the six high-temperature experiments using the selected silica. An empirical relation of

$$\tau = 0.27{\eta ^{0.32}}$$
is fitted between the glass viscosity (in dPa·s) and the decay time τ (in second) of the FBGs written in silica fibers. In Fig. 8, the 95% prediction band of the fitting, which encloses the area that 95% of future data points should be enclosed with the prediction shadow area, is also plotted. The prediction band includes both the uncertainty in the true position of the fitting curve, and also accounts for scatter of data around the curve [52]. Note that for each data point (shown in Fig. 8) of the thermal decay of the FBG at a certain temperature in the selected fiber, at least one repeated experiment was done to check the repeatability and the measurement error was observed to be < ±10%.

 

Fig. 8. Fitted relation between FBG decay time τ and viscosity η of core glass in selected silica fibers.

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Moreover, the measured lifetimes of femtosecond laser induced nanostructures in bulk silica at high temperatures of 900 °C, 1000 °C, and 1100 °C [15] have been extracted and plotted in Fig. 8 as well. It is clearly seen that the three scatter data from this independent experiment distributes within the 95% prediction band of the empirical formula, indicating that the FBGs in the silica fibers written by the femtosecond laser are essentially the same kind of structure-related defects as the ones made in the bulk glass [15,16] and Eq. (10) can effectively predict the thermal stability and thermal decay of such a type of photo-induced nanostructured defects either in a fiber or in a bulk matrix at high temperatures. For example, given that the temperature of the FBG is 700 °C (i.e., 973.15 K), the viscosity of the pure silica glass is approximately at the order of 1024 dPa·s; the decay time of the FBG written in the fiber with a pure silica glass core is therefore estimated to be 1.6 × 107 s, equal to 185 days, close to the predicted decay time (208 days) of the nanogratings made by femtosecond laser in bulk silica glass [15].

In addition, one can expect that the FBG written in a pure silica based fiber, for example a photonic crystal fiber, could work under the temperature of 1450 °C for ∼5 minutes. Note that the regenerated FBGs can only work under 1500 °C for a few minutes [28]. It indicates that femtosecond laser inscribed FBGs in silica fibers can even be used for short-period under ultrahigh-temperature in the range of 1400-1500 °C.

The empirical formula [Eq.(10)] implies that the thermal decay speed of a fs laser written FBG in silica fibers is dominated by the glass viscosity rather than other factors (e.g., surface tension). It is known that the index modulation of UV-induced FBGs are due to the formation of the oxygen-deficient color-center defects on the oxygen-associated bonds in the silica glass network [53,54]. Different from the UV-induced FBGs, the index modulation of femtosecond laser written FBGs arises from the nanostructures involved with O2-filled nanovoids [15,16]. The inner pressure of O2-filled nanovoids can be estimated using Young-Laplace equation [55]

$$\Delta P = 4\sigma /d, $$
in which σ is the surface tension of the liquid and d is the diameter of the bubble, respectively. Note that vitreous silica melt has positive temperature coefficient of surface tension, for example, the surface tension of silica melt is ∼0.28 N/m at 1200 °C and ∼0.30 N/m at 1800 °C [56]. Because the nanovoids are formed inside the core glass due to the plasma explosion with a localized temperature far above the glass Tg, it can therefore be estimated that the pressure inside the nanovoids with the effective diameter of 10 nm is at least at the level of 100 MPa. Under such a high pressure, the molecule oxygen inside will quickly dissolute into the glass melt when the melt is liquidus enough, i.e., its viscosity is sufficiently low. The nanovoids will then collapse and the modulated index change will completely vanish. This can quantitatively explain why the thermal decay of a femtosecond laser inscribed FBG is dominated by the glass viscosity.

4. Conclusion

In conclusion, we have investigated the thermal behaviors of femtosecond laser direct-written fiber Bragg gratings (FBGs) in a variety of commercial silica optical fibers. The observation shows that the fabricated FBGs in the silica fibers can be highly stable at high temperatures around the glass transition temperature. The thermal decay behavior of the FBGs at high temperatures is dominated by the viscosity of the core glass. The deduced empirical formula of the decay rate versus the viscosity indicates that the femtosecond laser inscribed FBGs and the femtosecond laser written nanostructures in the bulk silica are essentially the same type of photo-induced defects. According to the empirical formula, one can expect the short-period usage of such a type of FBG under ultrahigh temperature above 1400 °C, when the FBG is made in a single pure-silica material based photonic crystal fiber.

Funding

Graduate Research and Innovation Projects of Jiangsu Province (KYCX20_2346); Jiangsu Collaborative Innovation Centre of Advanced Laser Technology and Emerging Industry; Priority Academic Program Development of Jiangsu Higher Education Institutions.

Acknowledgments

Jindan Shi thanks Dr. M. Beresna in Optoelectronic Research Centre of University of Southampton (UK) for the useful discussions. The authors thank Dr. Lei Li and Miss Xuan Wang from Jiangsu Normal University for the use of the setup of measuring fiber SBS.

Disclosures

The authors declare no conflicts of interest.

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8. R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999). [CrossRef]  

9. S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, “Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation,” Opt. Lett. 28(12), 995–997 (2003). [CrossRef]  

10. S. J. Mihailov, D. Grobnic, C. W. Smelser, P. Lu, R. B. Walker, and H. Ding, “Bragg grating inscription in various optical fibers with femtosecond infrared lasers and a phase mask,” Opt. Mater. Express 1(4), 754–765 (2011). [CrossRef]  

11. Y. Li, M. Yang, D. N. Wang, J. Lu, T. Sun, and K. T. V. Grattan, “Fiber Bragg gratings with enhanced thermal stability by residual stress relaxation,” Opt. Express 17(22), 19785–19790 (2009). [CrossRef]  

12. M. Becker, J. Bergmann, S. Brückner, M. Franke, E. Lindner, M. W. Rothhardt, and H. Bartelt, “Fiber Bragg grating inscription combining DUV sub-picosecond laser pulses and two-beam interferometry,” Opt. Express 16(23), 19169–19178 (2008). [CrossRef]  

13. M. Gagné, S. Loranger, J. Lapointe, and R. Kashyap, “Fabrication of high quality, ultra-long fiber Bragg gratings: up to 2 million periods in phase,” Opt. Express 22(1), 387–398 (2014). [CrossRef]  

14. A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004). [CrossRef]  

15. J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014). [CrossRef]  

16. M. Lancry, B. Poumellec, J. Canning, K. Cook, J.-C. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser Photonics Rev. 7(6), 953–962 (2013). [CrossRef]  

17. R. G. Krämer, F. Möller, C. Matzdorf, T. A. Goebel, M. Strecker, M. Heck, D. Richter, M. Plötner, T. Schreiber, A. Tünnermann, and S. Nolte, “Extremely robust femtosecond written fiber Bragg gratings for an ytterbium-doped fiber oscillator with 5 kW output power,” Opt. Lett. 45(6), 1447–1450 (2020). [CrossRef]  

18. M. Fokine, “Thermal stability of chemical composition gratings in fluorine–germanium-doped silica fibers,” Opt. Lett. 27(12), 1016–1018 (2002). [CrossRef]  

19. M. Fokine, “Growth dynamics of chemical composition gratings in fluorine-doped silica optical fibers,” Opt. Lett. 27(22), 1974–1976 (2002). [CrossRef]  

20. J. Canning, M. Stevenson, S. Bandyopadhyay, and K. Cook, “Extreme Silica Optical Fibre Gratings,” Sensors 8(10), 6448–6452 (2008). [CrossRef]  

21. S. Bandyopadhyay, J. Canning, M. Stevenson, and K. Cook, “Ultrahigh-temperature regenerated gratings in boron-codoped germanosilicate optical fiber using 193 nm,” Opt. Lett. 33(16), 1917–1919 (2008). [CrossRef]  

22. B. Zhang and M. Kahrizi, “High-Temperature Resistance Fiber Bragg Grating Temperature Sensor Fabrication,” IEEE Sens. J. 7(4), 586–591 (2007). [CrossRef]  

23. K. Chah, K. Yüksel, D. Kinet, N. S. Yazd, P. Mégret, and C. Caucheteur, “Fiber Bragg grating regeneration at 450°C for improved high temperature sensing,” Opt. Lett. 44(16), 4036–4039 (2019). [CrossRef]  

24. D. S. Gunawardena, O. K. Law, Z. Liu, X. Zhong, Y.-T. Ho, and H.-Y. Tam, “Resurgent regenerated fiber Bragg gratings and thermal annealing techniques for ultra-high temperature sensing beyond 1400°C,” Opt. Express 28(7), 10595–10608 (2020). [CrossRef]  

25. K. Chah, D. Kinet, and C. Caucheteur, “Negative axial strain sensitivity in gold-coated eccentric fiber Bragg gratings,” Sci. Rep. 6(1), 38042 (2016). [CrossRef]  

26. H. Chikh-Bled, K. Chah, Á González-Vila, B. Lasri, and C. Caucheteur, “Behavior of femtosecond laser-induced eccentric fiber Bragg gratings at very high temperatures,” Opt. Lett. 41(17), 4048–4051 (2016). [CrossRef]  

27. M. Lindner, D. Bernard, F. Heilmeier, M. Jakobi, W. Volk, A. W. Koch, and J. Roths, “Transition from purely elastic to viscoelastic behavior of silica optical fibers at high temperatures characterized using regenerated Bragg gratings,” Opt. Express 28(5), 7323–7340 (2020). [CrossRef]  

28. M. L. Åslund, J. Canning, H. Fu, and H. Tam, “Single-mode optical fibre thermocoupler based on regenerated fibre Bragg gratings evaluated at ∼1500 °C,” Proc. SPIE 7839, 78391F (2010). [CrossRef]  

29. G. Laffont, R. Cotillard, and P. Ferdinand, “9000 hours-long high temperature annealing of regenerated fiber Bragg gratings,” Proc. SPIE 8794, 87941X (2013). [CrossRef]  

30. C. H. L. Goodman, Crystal Growth: Theory and Techniques, Volume 1, 1st ed. Springer, 1974.

31. A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41(4), 176–178 (2005). [CrossRef]  

32. C. Zhang, Y. Yang, C. Wang, C. Liao, and Y. Wang, “Femtosecond-laser-inscribed sampled fiber Bragg grating with ultrahigh thermal stability,” Opt. Express 24(4), 3981–3988 (2016). [CrossRef]  

33. Y. Zhang, X. Ding, Y. Song, M. Dong, and L. Zhu, “Characterization of a fiber Bragg grating in pure-silica-core and Ge-doped-core optical fiber under high-temperature strain,” Meas. Sci. Technol. 29(3), 035102 (2018). [CrossRef]  

34. Y. Wang, Z. Li, S. Liu, C. Fu, Z. Li, Z. Zhang, Y. Wang, J. He, Z. Bai, and C. Liao, “Parallel-Integrated Fiber Bragg Gratings Inscribedby Femtosecond Laser Point-by-Point Technology,” J. Lightwave Technol. 37(10), 2185–2193 (2019). [CrossRef]  

35. N. Abdukerim, D. Grobnic, C. Hnatovsky, and S. J. Mihailov, “High-temperature stable fiber Bragg gratings with ultrastrong cladding modes written using the phase mask technique and an infrared femtosecond laser,” Opt. Lett. 45(2), 443–446 (2020). [CrossRef]  

36. https://www.fibercore.com/product/pure-silica-core-sm-fiber

37. https://www.thefoa.org/tech/smf.htm

38. https://www.nufern.com/pam/optical_fibers/984/UHNA3/#

39. P. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45(5), 256–257 (2009). [CrossRef]  

40. P. Dragic, “Estimating the effect of Ge doping on the acoustic damping coefficient via a highly Ge-doped MCVD silica fiber,” J. Opt. Soc. Am. B 26(8), 1614–1620 (2009). [CrossRef]  

41. P. Dragic, “The acoustic velocity of Ge-doped silica fibers: a comparison of two models,” Int. J. Appl. Glass Sci. 1(3), 330–337 (2010). [CrossRef]  

42. M. Deroh, B. Kibler, H. Maillotte, T. Sylvestre, and J.-C. Beugnot, “Large Brillouin gain in Germania-doped core optical fibers up to a 98 mol% doping level,” Opt. Lett. 43(16), 4005–4008 (2018). [CrossRef]  

43. Y. Yu, J. Shi, F. Han, W. Sun, and X. Feng, “High-precision fiber Bragg gratings inscription by infrared femtosecond laser direct-writing method assisted with image recognition,” Opt. Express 28(6), 8937–8948 (2020). [CrossRef]  

44. J.-C. Beugnot and V. Laude, “Electrostriction and guidance of acoustic phonons in optical fibers,” Phys. Rev. B 86(22), 224304 (2012). [CrossRef]  

45. H. Gao, Y. Jiang, Y. Cui, L. Zhang, J. Jia, and L. Jiang, “Investigation on the Thermo-Optic Coefficient of Silica Fiber Within a Wide Temperature Range,” J. Lightwave Technol. 36(24), 5881–5886 (2018). [CrossRef]  

46. M. Cavillon, P. D. Dragic, and J. Ballato, “Additivity of the coefficient of thermal expansion in silicate optical fibers,” Opt. Lett. 42(18), 3650–3653 (2017). [CrossRef]  

47. E. F. Riebling, “Nonideal mixing in binary GeO2-SiO2 glasses,” J. Am. Ceram. Soc. 51(7), 406–407 (1968). [CrossRef]  

48. W. Vogel, Glass Chemistry, 2nd ed. (Springer-Verlag, 1994).

49. Y. I. Frenkel, Kinetic Theory of Liquids (Oxford University Press, 1946).

50. D. Hewak, Ed., Properties, Processing and Applications of Glass and Rare Earth-Doped Glasses for Optical Fibres, (EMIS Datareview Series No. 22), London, (The Institute of Electrical Engineers, 1998).

51. M. I. Ojovan, “Viscosity and Glass Transition in Amorphous Oxides,” Adv. Condens. Matter Phys. 2008, 1–23 (2008). [CrossRef]  

52. https://www.graphpad.com/guides/prism/8/curve-fitting/reg_graphing_confidence_and_predic.htm

53. T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet-induced fiber Bragg gratings,” J. Appl. Phys. 76(1), 73–80 (1994). [CrossRef]  

54. R. M. Atkins, V. Mizrahi, and T. Erdogan, “248 nm induced vacuum UV spectral changes in optical fibre preform cores: support for a colour centre model of photosensitivity,” Electron. Lett. 29(4), 385–387 (1993). [CrossRef]  

55. R. Finn, Capillary Surface Interfaces, Vol. 46 (Springer, 1999), pp. 770–781.

56. H. Scholze, Glass - Nature, Structure, and Properties, (Springer-Verlag, 1991).

References

  • View by:
  • |
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  • |

  1. R. Kashyap, Fiber Bragg Gratings, 2nd ed. (Academic Press, 2009).
  2. C. A. F. Marques, V. de Oliveira, H. J. Kalinowski, and R. N. Nogueira, “Production of optical notch filters with fine parameter control using regenerated fiber Bragg gratings,” Opt. Lett. 37(10), 1697–1699 (2012).
    [Crossref]
  3. C. Broadway, R. Min, A. G. Leal-Junior, C. Marques, and C. Caucheteur, “Toward Commercial Polymer Fiber Bragg Grating Sensors: Review and Applications,” J. Lightwave Technol. 37(11), 2605–2615 (2019).
    [Crossref]
  4. J. K. Sahota, N. Gupta, and D. Dhawan, “Fiber Bragg grating sensors for monitoring of physical parameters: a comprehensive review,” Opt. Eng. 59(06), 1 (2020).
    [Crossref]
  5. A. K. Sharma and C. Marques, “Design and performance perspectives on fiber optic sensors with plasmonic nanostructures and gratings: A review,” IEEE Sens. J. 19(17), 7168–7178 (2019).
    [Crossref]
  6. G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14(15), 823–825 (1989).
    [Crossref]
  7. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62(10), 1035–1037 (1993).
    [Crossref]
  8. R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
    [Crossref]
  9. S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, “Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation,” Opt. Lett. 28(12), 995–997 (2003).
    [Crossref]
  10. S. J. Mihailov, D. Grobnic, C. W. Smelser, P. Lu, R. B. Walker, and H. Ding, “Bragg grating inscription in various optical fibers with femtosecond infrared lasers and a phase mask,” Opt. Mater. Express 1(4), 754–765 (2011).
    [Crossref]
  11. Y. Li, M. Yang, D. N. Wang, J. Lu, T. Sun, and K. T. V. Grattan, “Fiber Bragg gratings with enhanced thermal stability by residual stress relaxation,” Opt. Express 17(22), 19785–19790 (2009).
    [Crossref]
  12. M. Becker, J. Bergmann, S. Brückner, M. Franke, E. Lindner, M. W. Rothhardt, and H. Bartelt, “Fiber Bragg grating inscription combining DUV sub-picosecond laser pulses and two-beam interferometry,” Opt. Express 16(23), 19169–19178 (2008).
    [Crossref]
  13. M. Gagné, S. Loranger, J. Lapointe, and R. Kashyap, “Fabrication of high quality, ultra-long fiber Bragg gratings: up to 2 million periods in phase,” Opt. Express 22(1), 387–398 (2014).
    [Crossref]
  14. A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
    [Crossref]
  15. J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014).
    [Crossref]
  16. M. Lancry, B. Poumellec, J. Canning, K. Cook, J.-C. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser Photonics Rev. 7(6), 953–962 (2013).
    [Crossref]
  17. R. G. Krämer, F. Möller, C. Matzdorf, T. A. Goebel, M. Strecker, M. Heck, D. Richter, M. Plötner, T. Schreiber, A. Tünnermann, and S. Nolte, “Extremely robust femtosecond written fiber Bragg gratings for an ytterbium-doped fiber oscillator with 5  kW output power,” Opt. Lett. 45(6), 1447–1450 (2020).
    [Crossref]
  18. M. Fokine, “Thermal stability of chemical composition gratings in fluorine–germanium-doped silica fibers,” Opt. Lett. 27(12), 1016–1018 (2002).
    [Crossref]
  19. M. Fokine, “Growth dynamics of chemical composition gratings in fluorine-doped silica optical fibers,” Opt. Lett. 27(22), 1974–1976 (2002).
    [Crossref]
  20. J. Canning, M. Stevenson, S. Bandyopadhyay, and K. Cook, “Extreme Silica Optical Fibre Gratings,” Sensors 8(10), 6448–6452 (2008).
    [Crossref]
  21. S. Bandyopadhyay, J. Canning, M. Stevenson, and K. Cook, “Ultrahigh-temperature regenerated gratings in boron-codoped germanosilicate optical fiber using 193 nm,” Opt. Lett. 33(16), 1917–1919 (2008).
    [Crossref]
  22. B. Zhang and M. Kahrizi, “High-Temperature Resistance Fiber Bragg Grating Temperature Sensor Fabrication,” IEEE Sens. J. 7(4), 586–591 (2007).
    [Crossref]
  23. K. Chah, K. Yüksel, D. Kinet, N. S. Yazd, P. Mégret, and C. Caucheteur, “Fiber Bragg grating regeneration at 450°C for improved high temperature sensing,” Opt. Lett. 44(16), 4036–4039 (2019).
    [Crossref]
  24. D. S. Gunawardena, O. K. Law, Z. Liu, X. Zhong, Y.-T. Ho, and H.-Y. Tam, “Resurgent regenerated fiber Bragg gratings and thermal annealing techniques for ultra-high temperature sensing beyond 1400°C,” Opt. Express 28(7), 10595–10608 (2020).
    [Crossref]
  25. K. Chah, D. Kinet, and C. Caucheteur, “Negative axial strain sensitivity in gold-coated eccentric fiber Bragg gratings,” Sci. Rep. 6(1), 38042 (2016).
    [Crossref]
  26. H. Chikh-Bled, K. Chah, Á González-Vila, B. Lasri, and C. Caucheteur, “Behavior of femtosecond laser-induced eccentric fiber Bragg gratings at very high temperatures,” Opt. Lett. 41(17), 4048–4051 (2016).
    [Crossref]
  27. M. Lindner, D. Bernard, F. Heilmeier, M. Jakobi, W. Volk, A. W. Koch, and J. Roths, “Transition from purely elastic to viscoelastic behavior of silica optical fibers at high temperatures characterized using regenerated Bragg gratings,” Opt. Express 28(5), 7323–7340 (2020).
    [Crossref]
  28. M. L. Åslund, J. Canning, H. Fu, and H. Tam, “Single-mode optical fibre thermocoupler based on regenerated fibre Bragg gratings evaluated at ∼1500 °C,” Proc. SPIE 7839, 78391F (2010).
    [Crossref]
  29. G. Laffont, R. Cotillard, and P. Ferdinand, “9000 hours-long high temperature annealing of regenerated fiber Bragg gratings,” Proc. SPIE 8794, 87941X (2013).
    [Crossref]
  30. C. H. L. Goodman, Crystal Growth: Theory and Techniques, Volume 1, 1st ed. Springer, 1974.
  31. A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41(4), 176–178 (2005).
    [Crossref]
  32. C. Zhang, Y. Yang, C. Wang, C. Liao, and Y. Wang, “Femtosecond-laser-inscribed sampled fiber Bragg grating with ultrahigh thermal stability,” Opt. Express 24(4), 3981–3988 (2016).
    [Crossref]
  33. Y. Zhang, X. Ding, Y. Song, M. Dong, and L. Zhu, “Characterization of a fiber Bragg grating in pure-silica-core and Ge-doped-core optical fiber under high-temperature strain,” Meas. Sci. Technol. 29(3), 035102 (2018).
    [Crossref]
  34. Y. Wang, Z. Li, S. Liu, C. Fu, Z. Li, Z. Zhang, Y. Wang, J. He, Z. Bai, and C. Liao, “Parallel-Integrated Fiber Bragg Gratings Inscribedby Femtosecond Laser Point-by-Point Technology,” J. Lightwave Technol. 37(10), 2185–2193 (2019).
    [Crossref]
  35. N. Abdukerim, D. Grobnic, C. Hnatovsky, and S. J. Mihailov, “High-temperature stable fiber Bragg gratings with ultrastrong cladding modes written using the phase mask technique and an infrared femtosecond laser,” Opt. Lett. 45(2), 443–446 (2020).
    [Crossref]
  36. https://www.fibercore.com/product/pure-silica-core-sm-fiber
  37. https://www.thefoa.org/tech/smf.htm
  38. https://www.nufern.com/pam/optical_fibers/984/UHNA3/#
  39. P. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45(5), 256–257 (2009).
    [Crossref]
  40. P. Dragic, “Estimating the effect of Ge doping on the acoustic damping coefficient via a highly Ge-doped MCVD silica fiber,” J. Opt. Soc. Am. B 26(8), 1614–1620 (2009).
    [Crossref]
  41. P. Dragic, “The acoustic velocity of Ge-doped silica fibers: a comparison of two models,” Int. J. Appl. Glass Sci. 1(3), 330–337 (2010).
    [Crossref]
  42. M. Deroh, B. Kibler, H. Maillotte, T. Sylvestre, and J.-C. Beugnot, “Large Brillouin gain in Germania-doped core optical fibers up to a 98  mol% doping level,” Opt. Lett. 43(16), 4005–4008 (2018).
    [Crossref]
  43. Y. Yu, J. Shi, F. Han, W. Sun, and X. Feng, “High-precision fiber Bragg gratings inscription by infrared femtosecond laser direct-writing method assisted with image recognition,” Opt. Express 28(6), 8937–8948 (2020).
    [Crossref]
  44. J.-C. Beugnot and V. Laude, “Electrostriction and guidance of acoustic phonons in optical fibers,” Phys. Rev. B 86(22), 224304 (2012).
    [Crossref]
  45. H. Gao, Y. Jiang, Y. Cui, L. Zhang, J. Jia, and L. Jiang, “Investigation on the Thermo-Optic Coefficient of Silica Fiber Within a Wide Temperature Range,” J. Lightwave Technol. 36(24), 5881–5886 (2018).
    [Crossref]
  46. M. Cavillon, P. D. Dragic, and J. Ballato, “Additivity of the coefficient of thermal expansion in silicate optical fibers,” Opt. Lett. 42(18), 3650–3653 (2017).
    [Crossref]
  47. E. F. Riebling, “Nonideal mixing in binary GeO2-SiO2 glasses,” J. Am. Ceram. Soc. 51(7), 406–407 (1968).
    [Crossref]
  48. W. Vogel, Glass Chemistry, 2nd ed. (Springer-Verlag, 1994).
  49. Y. I. Frenkel, Kinetic Theory of Liquids (Oxford University Press, 1946).
  50. D. Hewak, Ed., Properties, Processing and Applications of Glass and Rare Earth-Doped Glasses for Optical Fibres, (EMIS Datareview Series No. 22), London, (The Institute of Electrical Engineers, 1998).
  51. M. I. Ojovan, “Viscosity and Glass Transition in Amorphous Oxides,” Adv. Condens. Matter Phys. 2008, 1–23 (2008).
    [Crossref]
  52. https://www.graphpad.com/guides/prism/8/curve-fitting/reg_graphing_confidence_and_predic.htm
  53. T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet-induced fiber Bragg gratings,” J. Appl. Phys. 76(1), 73–80 (1994).
    [Crossref]
  54. R. M. Atkins, V. Mizrahi, and T. Erdogan, “248 nm induced vacuum UV spectral changes in optical fibre preform cores: support for a colour centre model of photosensitivity,” Electron. Lett. 29(4), 385–387 (1993).
    [Crossref]
  55. R. Finn, Capillary Surface Interfaces, Vol. 46 (Springer, 1999), pp. 770–781.
  56. H. Scholze, Glass - Nature, Structure, and Properties, (Springer-Verlag, 1991).

2020 (6)

J. K. Sahota, N. Gupta, and D. Dhawan, “Fiber Bragg grating sensors for monitoring of physical parameters: a comprehensive review,” Opt. Eng. 59(06), 1 (2020).
[Crossref]

R. G. Krämer, F. Möller, C. Matzdorf, T. A. Goebel, M. Strecker, M. Heck, D. Richter, M. Plötner, T. Schreiber, A. Tünnermann, and S. Nolte, “Extremely robust femtosecond written fiber Bragg gratings for an ytterbium-doped fiber oscillator with 5  kW output power,” Opt. Lett. 45(6), 1447–1450 (2020).
[Crossref]

D. S. Gunawardena, O. K. Law, Z. Liu, X. Zhong, Y.-T. Ho, and H.-Y. Tam, “Resurgent regenerated fiber Bragg gratings and thermal annealing techniques for ultra-high temperature sensing beyond 1400°C,” Opt. Express 28(7), 10595–10608 (2020).
[Crossref]

M. Lindner, D. Bernard, F. Heilmeier, M. Jakobi, W. Volk, A. W. Koch, and J. Roths, “Transition from purely elastic to viscoelastic behavior of silica optical fibers at high temperatures characterized using regenerated Bragg gratings,” Opt. Express 28(5), 7323–7340 (2020).
[Crossref]

N. Abdukerim, D. Grobnic, C. Hnatovsky, and S. J. Mihailov, “High-temperature stable fiber Bragg gratings with ultrastrong cladding modes written using the phase mask technique and an infrared femtosecond laser,” Opt. Lett. 45(2), 443–446 (2020).
[Crossref]

Y. Yu, J. Shi, F. Han, W. Sun, and X. Feng, “High-precision fiber Bragg gratings inscription by infrared femtosecond laser direct-writing method assisted with image recognition,” Opt. Express 28(6), 8937–8948 (2020).
[Crossref]

2019 (4)

2018 (3)

2017 (1)

2016 (3)

2014 (2)

M. Gagné, S. Loranger, J. Lapointe, and R. Kashyap, “Fabrication of high quality, ultra-long fiber Bragg gratings: up to 2 million periods in phase,” Opt. Express 22(1), 387–398 (2014).
[Crossref]

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014).
[Crossref]

2013 (2)

M. Lancry, B. Poumellec, J. Canning, K. Cook, J.-C. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser Photonics Rev. 7(6), 953–962 (2013).
[Crossref]

G. Laffont, R. Cotillard, and P. Ferdinand, “9000 hours-long high temperature annealing of regenerated fiber Bragg gratings,” Proc. SPIE 8794, 87941X (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (2)

P. Dragic, “The acoustic velocity of Ge-doped silica fibers: a comparison of two models,” Int. J. Appl. Glass Sci. 1(3), 330–337 (2010).
[Crossref]

M. L. Åslund, J. Canning, H. Fu, and H. Tam, “Single-mode optical fibre thermocoupler based on regenerated fibre Bragg gratings evaluated at ∼1500 °C,” Proc. SPIE 7839, 78391F (2010).
[Crossref]

2009 (3)

2008 (4)

2007 (1)

B. Zhang and M. Kahrizi, “High-Temperature Resistance Fiber Bragg Grating Temperature Sensor Fabrication,” IEEE Sens. J. 7(4), 586–591 (2007).
[Crossref]

2005 (1)

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41(4), 176–178 (2005).
[Crossref]

2004 (1)

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
[Crossref]

2003 (1)

2002 (2)

1999 (1)

R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
[Crossref]

1994 (1)

T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet-induced fiber Bragg gratings,” J. Appl. Phys. 76(1), 73–80 (1994).
[Crossref]

1993 (2)

R. M. Atkins, V. Mizrahi, and T. Erdogan, “248 nm induced vacuum UV spectral changes in optical fibre preform cores: support for a colour centre model of photosensitivity,” Electron. Lett. 29(4), 385–387 (1993).
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K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62(10), 1035–1037 (1993).
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1989 (1)

1968 (1)

E. F. Riebling, “Nonideal mixing in binary GeO2-SiO2 glasses,” J. Am. Ceram. Soc. 51(7), 406–407 (1968).
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Albert, J.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62(10), 1035–1037 (1993).
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M. L. Åslund, J. Canning, H. Fu, and H. Tam, “Single-mode optical fibre thermocoupler based on regenerated fibre Bragg gratings evaluated at ∼1500 °C,” Proc. SPIE 7839, 78391F (2010).
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R. M. Atkins, V. Mizrahi, and T. Erdogan, “248 nm induced vacuum UV spectral changes in optical fibre preform cores: support for a colour centre model of photosensitivity,” Electron. Lett. 29(4), 385–387 (1993).
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Ballato, J.

Bandyopadhyay, S.

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A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41(4), 176–178 (2005).
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A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
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J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014).
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Bernard, D.

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Bilodeau, F.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62(10), 1035–1037 (1993).
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M. Lancry, B. Poumellec, J. Canning, K. Cook, J.-C. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser Photonics Rev. 7(6), 953–962 (2013).
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Brownlow, D. L.

R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
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Canning, J.

M. Lancry, B. Poumellec, J. Canning, K. Cook, J.-C. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser Photonics Rev. 7(6), 953–962 (2013).
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M. L. Åslund, J. Canning, H. Fu, and H. Tam, “Single-mode optical fibre thermocoupler based on regenerated fibre Bragg gratings evaluated at ∼1500 °C,” Proc. SPIE 7839, 78391F (2010).
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Cook, K.

M. Lancry, B. Poumellec, J. Canning, K. Cook, J.-C. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser Photonics Rev. 7(6), 953–962 (2013).
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de Oliveira, V.

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Y. Zhang, X. Ding, Y. Song, M. Dong, and L. Zhu, “Characterization of a fiber Bragg grating in pure-silica-core and Ge-doped-core optical fiber under high-temperature strain,” Meas. Sci. Technol. 29(3), 035102 (2018).
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Y. Zhang, X. Ding, Y. Song, M. Dong, and L. Zhu, “Characterization of a fiber Bragg grating in pure-silica-core and Ge-doped-core optical fiber under high-temperature strain,” Meas. Sci. Technol. 29(3), 035102 (2018).
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R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
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M. L. Åslund, J. Canning, H. Fu, and H. Tam, “Single-mode optical fibre thermocoupler based on regenerated fibre Bragg gratings evaluated at ∼1500 °C,” Proc. SPIE 7839, 78391F (2010).
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Gao, H.

Gecevicius, M.

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014).
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Glodis, P. A.

R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
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K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62(10), 1035–1037 (1993).
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K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62(10), 1035–1037 (1993).
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B. Zhang and M. Kahrizi, “High-Temperature Resistance Fiber Bragg Grating Temperature Sensor Fabrication,” IEEE Sens. J. 7(4), 586–591 (2007).
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Kashyap, R.

Kazansky, P. G.

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014).
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A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
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A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41(4), 176–178 (2005).
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G. Laffont, R. Cotillard, and P. Ferdinand, “9000 hours-long high temperature annealing of regenerated fiber Bragg gratings,” Proc. SPIE 8794, 87941X (2013).
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M. Lancry, B. Poumellec, J. Canning, K. Cook, J.-C. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser Photonics Rev. 7(6), 953–962 (2013).
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K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62(10), 1035–1037 (1993).
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A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
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T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet-induced fiber Bragg gratings,” J. Appl. Phys. 76(1), 73–80 (1994).
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T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet-induced fiber Bragg gratings,” J. Appl. Phys. 76(1), 73–80 (1994).
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M. Lancry, B. Poumellec, J. Canning, K. Cook, J.-C. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser Photonics Rev. 7(6), 953–962 (2013).
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R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
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R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
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R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
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Windeler, R. S.

R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
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B. Zhang and M. Kahrizi, “High-Temperature Resistance Fiber Bragg Grating Temperature Sensor Fabrication,” IEEE Sens. J. 7(4), 586–591 (2007).
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Zhang, J.

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014).
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Zhang, Y.

Y. Zhang, X. Ding, Y. Song, M. Dong, and L. Zhu, “Characterization of a fiber Bragg grating in pure-silica-core and Ge-doped-core optical fiber under high-temperature strain,” Meas. Sci. Technol. 29(3), 035102 (2018).
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Y. Zhang, X. Ding, Y. Song, M. Dong, and L. Zhu, “Characterization of a fiber Bragg grating in pure-silica-core and Ge-doped-core optical fiber under high-temperature strain,” Meas. Sci. Technol. 29(3), 035102 (2018).
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Adv. Condens. Matter Phys. (1)

M. I. Ojovan, “Viscosity and Glass Transition in Amorphous Oxides,” Adv. Condens. Matter Phys. 2008, 1–23 (2008).
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Appl. Phys. Lett. (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62(10), 1035–1037 (1993).
[Crossref]

Electron. Lett. (4)

A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion, “Direct writing of fibre Bragg gratings by femtosecond laser,” Electron. Lett. 40(19), 1170–1172 (2004).
[Crossref]

A. Martinez, I. Y. Khrushchev, and I. Bennion, “Thermal properties of fibre Bragg gratings inscribed point-by-point by infrared femtosecond laser,” Electron. Lett. 41(4), 176–178 (2005).
[Crossref]

P. Dragic, “Simplified model for effect of Ge doping on silica fibre acoustic properties,” Electron. Lett. 45(5), 256–257 (2009).
[Crossref]

R. M. Atkins, V. Mizrahi, and T. Erdogan, “248 nm induced vacuum UV spectral changes in optical fibre preform cores: support for a colour centre model of photosensitivity,” Electron. Lett. 29(4), 385–387 (1993).
[Crossref]

IEEE Photonics Technol. Lett. (1)

R. P. Espindola, R. M. Atkins, N. P. Wang, D. A. Simoff, M. A. Paczkowski, R. S. Windeler, D. L. Brownlow, D. S. Shenk, P. A. Glodis, T. A. Strasser, J. J. DeMarco, and P. J. Chandonnet, “Highly reflective fiber Bragg gratings written through a vinyl ether coating,” IEEE Photonics Technol. Lett. 11(7), 833–835 (1999).
[Crossref]

IEEE Sens. J. (2)

A. K. Sharma and C. Marques, “Design and performance perspectives on fiber optic sensors with plasmonic nanostructures and gratings: A review,” IEEE Sens. J. 19(17), 7168–7178 (2019).
[Crossref]

B. Zhang and M. Kahrizi, “High-Temperature Resistance Fiber Bragg Grating Temperature Sensor Fabrication,” IEEE Sens. J. 7(4), 586–591 (2007).
[Crossref]

Int. J. Appl. Glass Sci. (1)

P. Dragic, “The acoustic velocity of Ge-doped silica fibers: a comparison of two models,” Int. J. Appl. Glass Sci. 1(3), 330–337 (2010).
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J. Am. Ceram. Soc. (1)

E. F. Riebling, “Nonideal mixing in binary GeO2-SiO2 glasses,” J. Am. Ceram. Soc. 51(7), 406–407 (1968).
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J. Appl. Phys. (1)

T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet-induced fiber Bragg gratings,” J. Appl. Phys. 76(1), 73–80 (1994).
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J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

M. Lancry, B. Poumellec, J. Canning, K. Cook, J.-C. Poulin, and F. Brisset, “Ultrafast nanoporous silica formation driven by femtosecond laser irradiation,” Laser Photonics Rev. 7(6), 953–962 (2013).
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Meas. Sci. Technol. (1)

Y. Zhang, X. Ding, Y. Song, M. Dong, and L. Zhu, “Characterization of a fiber Bragg grating in pure-silica-core and Ge-doped-core optical fiber under high-temperature strain,” Meas. Sci. Technol. 29(3), 035102 (2018).
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Opt. Eng. (1)

J. K. Sahota, N. Gupta, and D. Dhawan, “Fiber Bragg grating sensors for monitoring of physical parameters: a comprehensive review,” Opt. Eng. 59(06), 1 (2020).
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Opt. Express (7)

Y. Li, M. Yang, D. N. Wang, J. Lu, T. Sun, and K. T. V. Grattan, “Fiber Bragg gratings with enhanced thermal stability by residual stress relaxation,” Opt. Express 17(22), 19785–19790 (2009).
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M. Becker, J. Bergmann, S. Brückner, M. Franke, E. Lindner, M. W. Rothhardt, and H. Bartelt, “Fiber Bragg grating inscription combining DUV sub-picosecond laser pulses and two-beam interferometry,” Opt. Express 16(23), 19169–19178 (2008).
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M. Gagné, S. Loranger, J. Lapointe, and R. Kashyap, “Fabrication of high quality, ultra-long fiber Bragg gratings: up to 2 million periods in phase,” Opt. Express 22(1), 387–398 (2014).
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M. Lindner, D. Bernard, F. Heilmeier, M. Jakobi, W. Volk, A. W. Koch, and J. Roths, “Transition from purely elastic to viscoelastic behavior of silica optical fibers at high temperatures characterized using regenerated Bragg gratings,” Opt. Express 28(5), 7323–7340 (2020).
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D. S. Gunawardena, O. K. Law, Z. Liu, X. Zhong, Y.-T. Ho, and H.-Y. Tam, “Resurgent regenerated fiber Bragg gratings and thermal annealing techniques for ultra-high temperature sensing beyond 1400°C,” Opt. Express 28(7), 10595–10608 (2020).
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C. Zhang, Y. Yang, C. Wang, C. Liao, and Y. Wang, “Femtosecond-laser-inscribed sampled fiber Bragg grating with ultrahigh thermal stability,” Opt. Express 24(4), 3981–3988 (2016).
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Y. Yu, J. Shi, F. Han, W. Sun, and X. Feng, “High-precision fiber Bragg gratings inscription by infrared femtosecond laser direct-writing method assisted with image recognition,” Opt. Express 28(6), 8937–8948 (2020).
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Opt. Lett. (12)

M. Deroh, B. Kibler, H. Maillotte, T. Sylvestre, and J.-C. Beugnot, “Large Brillouin gain in Germania-doped core optical fibers up to a 98  mol% doping level,” Opt. Lett. 43(16), 4005–4008 (2018).
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M. Cavillon, P. D. Dragic, and J. Ballato, “Additivity of the coefficient of thermal expansion in silicate optical fibers,” Opt. Lett. 42(18), 3650–3653 (2017).
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S. Bandyopadhyay, J. Canning, M. Stevenson, and K. Cook, “Ultrahigh-temperature regenerated gratings in boron-codoped germanosilicate optical fiber using 193 nm,” Opt. Lett. 33(16), 1917–1919 (2008).
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H. Chikh-Bled, K. Chah, Á González-Vila, B. Lasri, and C. Caucheteur, “Behavior of femtosecond laser-induced eccentric fiber Bragg gratings at very high temperatures,” Opt. Lett. 41(17), 4048–4051 (2016).
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K. Chah, K. Yüksel, D. Kinet, N. S. Yazd, P. Mégret, and C. Caucheteur, “Fiber Bragg grating regeneration at 450°C for improved high temperature sensing,” Opt. Lett. 44(16), 4036–4039 (2019).
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N. Abdukerim, D. Grobnic, C. Hnatovsky, and S. J. Mihailov, “High-temperature stable fiber Bragg gratings with ultrastrong cladding modes written using the phase mask technique and an infrared femtosecond laser,” Opt. Lett. 45(2), 443–446 (2020).
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M. Fokine, “Thermal stability of chemical composition gratings in fluorine–germanium-doped silica fibers,” Opt. Lett. 27(12), 1016–1018 (2002).
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C. A. F. Marques, V. de Oliveira, H. J. Kalinowski, and R. N. Nogueira, “Production of optical notch filters with fine parameter control using regenerated fiber Bragg gratings,” Opt. Lett. 37(10), 1697–1699 (2012).
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S. J. Mihailov, C. W. Smelser, P. Lu, R. B. Walker, D. Grobnic, H. Ding, G. Henderson, and J. Unruh, “Fiber Bragg gratings made with a phase mask and 800-nm femtosecond radiation,” Opt. Lett. 28(12), 995–997 (2003).
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Opt. Mater. Express (1)

Phys. Rev. B (1)

J.-C. Beugnot and V. Laude, “Electrostriction and guidance of acoustic phonons in optical fibers,” Phys. Rev. B 86(22), 224304 (2012).
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Phys. Rev. Lett. (1)

J. Zhang, M. Gecevičius, M. Beresna, and P. G. Kazansky, “Seemingly unlimited lifetime data storage in nanostructured glass,” Phys. Rev. Lett. 112(3), 033901 (2014).
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Proc. SPIE (2)

M. L. Åslund, J. Canning, H. Fu, and H. Tam, “Single-mode optical fibre thermocoupler based on regenerated fibre Bragg gratings evaluated at ∼1500 °C,” Proc. SPIE 7839, 78391F (2010).
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G. Laffont, R. Cotillard, and P. Ferdinand, “9000 hours-long high temperature annealing of regenerated fiber Bragg gratings,” Proc. SPIE 8794, 87941X (2013).
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Sci. Rep. (1)

K. Chah, D. Kinet, and C. Caucheteur, “Negative axial strain sensitivity in gold-coated eccentric fiber Bragg gratings,” Sci. Rep. 6(1), 38042 (2016).
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Sensors (1)

J. Canning, M. Stevenson, S. Bandyopadhyay, and K. Cook, “Extreme Silica Optical Fibre Gratings,” Sensors 8(10), 6448–6452 (2008).
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Figures (8)

Fig. 1.
Fig. 1. Experimental setup of heterodyne detection for measuring the Brillouin frequency and linewidth. FC, fiber coupler; EDFA, erbium-doped fiber amplifier; OC, optical circulator; FUT, fiber under test; PC, polarization controller; PD, photodiode detector; ESA, electrical signal spectrum analyzer.
Fig. 2.
Fig. 2. Experimental setup of spectral characterization of fs-laser written FBGs at high temperatures.
Fig. 3.
Fig. 3. Experimental Brillouin spectra measured at 1550 nm in selected silica fibers with GeO2-doped core.
Fig. 4.
Fig. 4. Evolution of FBG spectrum during the temperature ramping in selected silica fibers: (a) SM1250SC; (b) G652D; (c) UHNA3.
Fig. 5.
Fig. 5. Measured temperature dependence of FBG wavelength λB in selected silica fibers of (a) SM1250SC, (b) G652D, and (c) UHNA3. (d) Trend of thermal expansion of glasses with thermal history of rapid quenching and slow cooling.
Fig. 6.
Fig. 6. Exponential#decay of FBGs in selected silica fibers ((a) SM1250SC; (b) G652D; (c) UHNA3) maintained at a certain temperature. Note that Y axis is in logarithmic scale.
Fig. 7.
Fig. 7. Viscosity curves of glass compositions used for selected fibers.
Fig. 8.
Fig. 8. Fitted relation between FBG decay time τ and viscosity η of core glass in selected silica fibers.

Tables (6)

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Table 1. Parameters of selected single-mode silica fibers (dcore: core diameter; NA: numerical aperture; λc: cutoff wavelength of fundamental mode)

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Table 2. Parameters of femtosecond laser used for writing FBG and spectral parameters of written FBGs.

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Table 3. Determined compositions of selected single-mode silica fibers.

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Table 4. Temperature parameters of FBGs made in various silica fibers.

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Table 5. Thermal decay parameters of FBGs made in various fibers.

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Table 6. Viscosity parameters of glasses used in selected fibers.

Equations (11)

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S i O 2 + X S i + O 2 ,
m λ B = 2 n e f f Λ ,
ν B = 2 n e f f V a λ L ,
λ B T = Λ n e f f T + n e f f Λ T .
Δ λ B λ B = ( 1 n e f f n e f f T + 1 Λ Λ T ) Δ T ,
Δ λ B Δ T = ( ξ + α ) λ B .
R = tanh ( κ L ) 2 ,
I = I 0 e x p ( t / τ ) ,
η ( T ) = A exp ( E R T ) ,
τ = 0.27 η 0.32
Δ P = 4 σ / d ,

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