We demonstrate the use of fiber Bragg gratings (FBGs) as a monolithic temperature sensor from ambient to liquid nitrogen temperatures, without the use of any auxiliary embedding structure. The Bragg gratings, fabricated in three different types of fibers and characterized with a high density of points, confirm a nonlinear thermal sensitivity of the fibers. With a conventional interrogation scheme it is possible to have a resolution of 0.5 K for weak pure-silica-core FBGs and 0.25 K using both boron-doped and germanium-doped standard fibers at 77 K. We quantitatively show for the first time that the nonlinear thermal sensitivity of the FBG arises from the nonlinearity of both thermo-optic and thermal expansion coefficients, allowing consistent modeling of FBGs at low temperatures.
© 2014 Optical Society of America
Fiber Bragg-grating sensors, although extensively used for temperature sensing at room and high temperatures [1–5], are less ubiquitous at temperatures below the ice point. Since the intrinsic value of the FBG sensitivity can drop significantly as the temperature decreases, previous works on FBGs at low temperatures [4, 6, 7] concentrated efforts on increasing the temperature sensitivity by embedding the FBG in a material with different thermal expansion coefficients. The surrounding material applies a tension/stress to the FBG, which translates into a higher effective Bragg wavelength thermal coefficient of the sensing head. While this approach can result in an impressive increase in the sensitivity, it increases significantly the sensor footprint and complexity. This can give rise to further nonlinearities, risk of de-lamination, hysteresis , or other unwanted phenomena which will depend upon the system used. Although this approach can be beneficial for some applications, it nullifies the advantages for the use of a monolithic, high-purity dielectric, with a small footprint and thermal mass.
While packaging has been critical in real systems using FBGs, it is not always necessary and sometimes even undesirable. For the cases where packaging is desirable, it can still benefit from the knowledge of the individual contributions of the FBG itself and the contributions of the embedding material to the overall sensor response. While the FBG integration into a high-CTE, hard embedding material can mask the individual contribution of the FBG itself, its effect must be taken in account when the FBG is embedded in a thin, soft, or of similar CTE, e.g. a coated FBG measuring gas temperature. In some applications, the packaging is rather undesirable, such as in experiments with gases at hundreds of degrees temperatures , as well as in optical refrigeration  and optical calorimetry . In addition, packaging is not required in most of the cases where the FBG is free to move, i.e. in measurements on liquids and gases, or in solids provided the fiber is allowed to slide, e.g. in the present work. The understanding of the thermo-opto-elastic properties of fiber optics materials is essential to the modeling of more diverse FBGs, whether they are embedded, coated, bare or etched. This understanding should start from the simplest case of these, which is the bare fiber.
One subtle, but very important characteristic of FBGs is the unique material in which it is fabricated. The workhorse material for FBGs sensors is telecom-grade silica, which has a loss below 2.5 dB/km at ~800 nm and sub-dB/km in the 1300-1600 nm wavelength range. Bare FBG sensors are immune to electromagnetic noise, have a small footprint and thermal load, are inert to a wide range of chemicals, to cite but a few. This inertness is desirable in harsh environments such as in plasmas , intense radiation , and magnetic fields, although conditions can be tailored to sense the latter  as well. The single-lead multiplexing capability of FBGs also reduces the experimental complexity by facilitating thermal, electrical and chemical insulation. Its small and tailorable footprint and thermal mass , and lack of self-heating makes bare FBGs ideal for temperature measurement of small loads such as gases. Combined with its cryogenic capability, it may be used in optical refrigeration of solids, which also benefits from the FBG small footprint and high transparency to the intense optical fields present in such experiments as we recently demonstrated at room temperature [9, 10].
It has been noticed that sensitivity to temperature of the wavelength of a standard FBG is around five-fold smaller at 77 K (LNT) than it is at 295 K (RT), in addition to being a nonlinear function [7, 14]. The values presented in the literature vary widely [6, 7, 14, 15], and could be attributed to the use of different fabrication processes and coatings, to the different compositions of the fibers, or in some cases, poor resolution of the bare FBG measurements. For FBGs to become ubiquitous in the cryogenic regime, further studies must be performed. Here we use three different fibers – including one with no dopant in the core, and take a high-density of measurements in the temperature domain to make sure discontinuities, which were observed in a previous report , are not missed.
We use a spectral method to interrogate the FBG’s Bragg wavelength, which provides accurate interrogation over a broad wavelength range, in a simple fashion. While there are methods which provide higher resolutions, they lack the flexibility required in our exploratory research. With data post-processing sub-picometer resolution of the sensor’s Bragg wavelength is achieved. Our experiments confirm some other results which reported a decrease in the FBG temperature sensitivity with decreasing temperature. It has been suggested that the nonlinearity of the FBG’s temperature response can be explained by the nonlinearity of the thermo-optic coefficient . While this can be true at high temperatures, this effect alone does not suffice to explain the nonlinearity observed at low temperatures.
Our results verify for the first time that the nonlinear FBG sensitivity is quantitatively predictable, using a functional form of the sensor’s thermal expansion combined with the nonlinear thermo-optic coefficient. Although using fibers of different compositions, we show that their thermal behavior are essentially the same, indicating that the divergences found in the literature come mainly from the different coating materials and measurement techniques. It is shown that standard FBGs can be used for sensing down to 77 K with a resolution better than 0.3 K with a spectral interrogator set to a resolution of 0.5 nm.
The Bragg wavelength λB of a fiber Bragg grating of spatial period Λ and effective refractive index neff is given by 1, 17]. However, as the temperature decreases, ξ and ΨT also decrease, which becomes more important at temperatures below the ice point. The consequences are that one cannot use a single value of ΨT for the recovery of temperature and by keeping the Bragg wavelength interrogator unchanged, one should expect a lower temperature sensitivity of the sensor. This nonlinearity has been studied in previous works, in the range and conditions summarized in the Table 1.
Although most previous works shown in Table 1 have observed nonlinear behavior of the Bragg wavelength shift, the resulting data is divergent. Quantitative comparison is not always possible since most works give more comprehensive data on the experiments with embedded FBGs. For instance, a comparable total Bragg wavelength shift in the works [7, 14, 15] was observed, but the exact temperature dependence was not clear for the bare FBG [7, 15], and in some cases the nonlinearity was simply not observed . The FBGs studied in  show inflection points and discontinuity in the range LNT – RT, which were not observed elsewhere, and a discontinuity just below LNT, which could be justified by the difficulties of working with liquid helium . mentions a dn/dT at LNT to be half of the value at RT. This value comes from the fact that the authors assumed the expansion coefficient to be constant, thus the derived expression for the refractive index derivative, although useful to describe their sensor, is not representative for the material. From these divergences, it becomes clear that more studies must be performed in order to fully understand the thermal behavior of FBGs at cryogenic temperatures.
3. FGB fabrication
The 3 mm long FBGs were produced using a Q-switched 100 mW Xiton Photonics laser source operating at a wavelength of 213 nm, as described in . The laser produces pulses of 7 ns duration with an energy of 10 μJ. The gratings are imprinted using the scanning phase-mask interferometer technique . A mirror on a linear translation stage was used to scan the fiber, and a cylindrical lens of 20 cm focal length is used to focus the light on the fiber, which is held at the intersection of the beams, using a PhotoNova Inc. BraggTune® Interferometer. The details of the three FBGs are summarized in the Table 2.
Although GerFBG and PurFBG are not intrinsically photosensitive, all the FBGs were written in non-hydrogenated fibers, using ns-long 213 nm radiation pulses, rather than the femtosecond lasers typically used for these fibers. The reflection peak of the PurFBG is weak compared to the other FBGs, thus its spectrum could not be measured in transmission. The reflection spectrum of the PurFBG and the transmission spectra of the others are shown in Fig. 1.
Since the operating wavelength of the PurFBG is on the unflatened, low power, left tail of the broadband erbium-doped fiber probing source (BBS), its reflection spectra shown in Fig. 1 is the reflection data normalized by the spectral profile of the BBS. All the fibers had their coating stripped-off at the FBG section. Since the fibers have no coating and are not embedded in a substrate, we refer to them as “bare fibers”, avoiding the ambiguous definition of “non-embedded”, which can include coated fibers as well as uncoated ones.
4. Temperature control
In order to characterize the FBGs we used a passive temperature sweeping system, consisting of a minichamber which is allowed to exchange heat slowly with two temperature baths, laboratory air and liquid nitrogen (LN2). A diagram of the experimental setup is shown in the Fig. 2. The mini-chamber is an aluminum circular rod of 25 mm height and 25 mm diameter, with two ports around its center, one with a pt-100 platinum resistor (RTD) and a steel needle of 780 μm outer diameter as the fiber receptacle. Both the RTD and the needle are placed in holes filled with thermal grease. The fiber is cut after the FBG, inserted into and attached to the upper side of the receptacle, thus it is free to move longitudinally with negligible friction. The small diameter of the needle allows little or no temperature gradients inside it, and together with the high thermal emissivity of silica, provide good thermal coupling between the aluminum rod and the FBG. A small volume of 0.25(10) L of LN2 is placed in a 1.0 L glass dewar, where the mini-chamber is subsequently immersed without touching the bottom of the dewar, and the top of the dewar is closed with aluminum foil to prevent turbulence from room air. This allows overnight evaporation of all LN2 while keeping the mini-chamber temperature steady enough to allow thermalization between the sensors.
Due to the large range of temperatures involved, the electrical resistance variation of the RTD wires must be compensated, which is done by a 4-wire resistance interrogation scheme using an Agilent 34401A benchtop multimeter. The measured resistance is converted to temperature using a 6th order polynomial which we fit to the inverse of the combination of both 2nd order (T > 273.15 K) and 3rd order (T < 273.15 K) Callendar-Van Dusen’s resistance equation from , so that a single equation can be used for the whole measurement range: where τ0 = 31.336(4) K, τ1 = 2.2002(3) K⋅Ω−1, τ2 = 34.295(62) × 10−4 K⋅Ω−2, τ3 = −18.617(62) × 10−6 K⋅Ω−3, τ4 = 74.33(31) × 10−9 K⋅Ω−4, τ5 = −14.521(7) × 10−11 K⋅Ω−5 and τ6 = 11.551(70) × 10−14 K⋅Ω−6 are the fitted coefficients of T(R), which provide a root-mean-square deviation of 13 mK in the range 65 – 350 K.
5. FBG interrogation
The reflection spectra of the FBG is measured by an ANDO AQ6317B optical spectrum analyzer (OSA) connected to the third port of an optical circulator (Fig. 3), whose first port is fed by a C-band broadband source (BBS) model BBS 1560 + 2FA00 from JDS Uniphase. The optical circulator transmits the power from the first to the second port, where the FBG is connected. The reflected power from the FBG enters the second port and is directed to the third port.
The FBG reflection spectra is then measured by the OSA with a 500 pm resolution, and has its center wavelength λTHR determined with 1 pm resolution using the 5 dB envelope threshold function (THR) of the OSA. A personal computer then extracts both the spectra and λTHR information from the OSA. The Bragg wavelength resolution can be further increased with digital processing of the spectra. A six-order Fourier (F6 method) series presented a good fit to the reflection spectra of all the FBGs, thus it was used to calculate the Bragg wavelength shift ΔλB,F6(T) = λB(T) - λB(RT) with a resolution 2σ < 0.2 pm for the BorFBG and GerFBG, and 2σ < 0.5 pm for the PurFBG.
Assuming that the FBGs are at the same temperature as the RTD, one can plot the Bragg wavelength shift as a function of the RTD temperature, as shown in Fig. 4. One can easily see some anomalous data for the BorFBG at ~85 K when using the THR method during the cooling process. Using exactly the same raw spectrum, but analysed with the F6 method, the previously anomalous points lie on a smooth curve. During the slow minichamber thermalization, or heating, the data from both methods overlap. We also concentrate on the data during the heating process, since it is slower than the cooling, as more time is allowed for the FBG and the RTD to thermalize. No hysteresis was observed in any of the FBGs, as expected for both Germania and boron-doped silica, but so far unknown for F-SiO2, whose CTE presents hysteresis at high temperatures . Due to the poorer resolution of the THR method, and possible misreading, we consider only the data from the F6 method, which is shown in the Fig. 4 for all the FBGs.
By simply taking the first derivative of the polynomial form of λB(T), it is straightforward to calculate ΨT(T) and thus ξ(T) from the values shown in Table 3, using the expressions:Fig. 5(a). In order to better quantify the fiber material properties, it is convenient to express the Bragg wavelength thermal coefficient ξ(T), shown in Fig. 5(b), rather than the Bragg wavelength sensitivity ΨT.
The Bragg wavelength thermal sensitivity ΨT of the PurFBG at RT is smaller than for the other two FBGs. This can be explained due to the lower thermal expansion coefficient of the fluorine-doped cladding compared to the pure-silica cladding of the doped fibers. Since the PurFBG was fabricated with a shorter Bragg wavelength than the others, one should expect a smaller absolute thermal sensitivity by a fraction equal to the ratio of its Bragg wavelength to the one of the other fibers. Here it is clear that the PurFBG has indeed a thermal coefficient ξ(RT) smaller than the other two FBGs, which have essentially the same ξ(RT). At LNT the effect is inverted and the PurFBG has the largest value of ξ. The origins of the difference for PurFBG are discussed in the next section.
One can clearly observe the nonlinearity of the FBG from the results shown in Fig. 4 and Fig. 5, as observed before by [7, 14]. Here we used a high density of points (~50/K), and contrary to the quantitative values observed in some previous works [6, 14], a continuous nonlinear curve is obtained, with no anomalous effects or inflexion points in the temperature range from 77 K to 295 K. Surprisingly, the FBGs with considerably different composition, strength and center wavelength show essentially the same behavior at low temperatures. The use of the pure-silica-core FBG ruled out dopant concentration in the core as the main factor contributing for the observed nonlinearity. Coating effects were also eliminated as the bare FBGs are completely free to move inside their receptacle.
Previous works which modeled the behavior of the FBG at low temperatures did not compare their prediction with the measured values for bare fiber, since their focus was on coated fibers. Most works neglect the fact that the thermal expansion coefficient αL is dependent on the temperature. Others, e.g , overestimate ΨT at 77 K, mostly due to an overestimation of αL, for instance their value is always positive, while it is well known that silica has a negative expansion coefficient at cryogenic temperatures . Here we use two approaches to derive the individual contributions of the CTE and the thermo-optic coefficient ζ. For the BorFBG and GerFBG we found that the fibers have an effective coefficient of thermal expansion (eCTE) of the same value as pure fused silica, and calculate their thermo-optic coefficient. For the PurFBG, we assume that the waveguide has the same refractive index as pure fused silica, and calculate the fiber eCTE.
The local CTE of a silica binary mixture can be calculated as αSiO2-d = (1 - Cmol)αSiO2 + Cmolαd, where Cmol, αSiO2 and αd are respectively the molar concentration of the dopant, the CTEs of silica and of the dopant oxide . The CTE of silica can be obtained by the expression αSiO2 (T) × 106 K = a(b/T)cexp(b/T)(exp(b/T) + 1)−2 + d(e/T)2exp(e/T)(exp(e/T) - 1)−2, where a = −4.22, b = 35.5 K−1, c = 0.335, d = 1.253 and e = 535 K−1 . Boron-doped silica fibers can have concentrations up to 10 mol%, for which one can calculate a CTE of αB2O3-SiO2 ~15 × 10−7 K−1. The core of the GerFBG has a fractional refractive index increase of Δ/1 = deff (n – n0)/n0 = 36 × 10−4, where n0 is the refractive index of the undoped silica. Using the data from  one can relate the fractional refractive index change due to the GeO2 concentration CGeO2,mole% as Δ/1 = −1.27(14) + 9.44(1) × CGeO2,mole%. This implies a GeO2 concentration of 3.95 Mole%, which is in line with the values reported in the literature of 3-5 Mole% . One can estimate the mixture CTE to be αGeO2-SiO2 ~8 × 10−7 K−1, which is also consistent with the measurements from . To calculate all the stresses locally in the fiber, one must have access to all the thermal history of the fiber, including fabrication parameters such as the drawing conditions, the latter changing the refractive indexes significantly . Alternatively, the three fibers used can be modeled as composite cylinders, and their eCTE can be calculated following the procedure shown in . We consider the materials to have the same Young’s modulus E and Poisson’s ratio ν as fused silica ESiO2 = 76 GPa and νSiO2 = 0.164 [29, 30], and use the calculated local CTEs, which lead to the estimate of a fractional eCTE increase of only 0.35% and 1% for the GerFBG and BorFBG, respectively. Meanwhile, the same dopant concentrations are expected to change the thermo-optic coefficient by ~1% . Since the thermo-optic coefficient contributes to the sensitivity by ~10 times the contribution from the CTE, in addition to the fact that the CTE data is scarce and pure silica refractive index has been extensively investigated, the assumption we made is not only justifiable but may be considered accurate. For the PurFBG, the assumption about its refractive index is straightforward, since the core, where most of the mode is confined, is made of pure silica, and the cladding, which is responsible for most of the eCTE is doped with fluorine.
Using the thermal sensitivity data of Fig. 5, and the assumption that αGerFBG = αBorFBG = αSiO2, and Eq. (3), one can obtain the graph of Fig. 6(a). As a reference, also shown is the thermo-optic coefficient of pure silica ζ(T, λB(T)) at the Bragg wavelength of the GerFBG and the BorFBG at the temperature T, and the difference of thermo-optic coefficients is highlighted in the Fig. 6(b).
ζ is higher in GerFBG than in FS7980. This is expected due to the effect of GeO2 doping on the refractive index and its temperature-derivative  and secondly due to the increase in the Bragg wavelength of ~0.0007%, but the latter is already compensated for in the graph, since the ζFS shown in Fig. 6(a) is calculated at the Bragg wavelength of both GerFBG and BorFBG at the same temperature. As expected, the thermo-optic coefficient changes by ~1% due to the dopant between ice and room temperatures. At cryogenic temperatures the effect is amplified and the thermo-optic coefficient can be modified by up to 7% increase for the GerFBG and a 5% decrease for the BorFBG. While the thermo-optic coefficient for the GerFBG is close to that reported in the literature, the analysis of previous theoretical results show that it is easy to overestimate the effect of boron-doping in the fiber. For instance, using the data from , one should expect a Δζ/ζ = - 0.059 for a typical 14-18 mol % B2O3 – 10% GeO2 fiber, while in the experiment we measured Δζ/ζ = - 0.008, which is much smaller.
Since the fluorine-doped cladding and pure-silica core fiber PurFBG has a numerical aperture of 0.12, one can expect a refractive index difference between the depressed cladding and the core to be (nclad - ncore)/ncore = - 0.35%, assuming the pure-silica core to have the same refractive index as the FS7980. On the basis of the measurements by , we relate the refractive index changes to the fluorine concentration as CF,at% = −4.02(2) Δn%, which for our fiber corresponds to a concentration of CF = 1.4 at. %. The thermal expansion coefficient can have a discontinuous, non-monotonic dependence with the fluorine concentration , as well as with temperature , but it is expected that the CTE of silica with a fluorine doping concentration of 1.4 at.% at room temperature can decrease by as much as (α0% - α)/α0% = 17% . Unlike for the BorFBG and GerFBG, this cladding CTE is not negligible, however since the core of the PurFBG is pure-silica one can start the modeling from the well-known thermo-optic properties of this material.
Here, we approximate the thermo-optic coefficient ζ using the temperature-dependent Sellmeier equation for the refractive index nFS7980(T), of Corning 7980 fused silica, from . Assuming nPurFBG(T) = nFS7980(T), and using our measured data (Fig. 5) and Eq. (3), one can find the red curve shown in Fig. 7. As a comparison, other data from the literature is shown in the graph as well.
The CTE of F:SiO2 shown in Fig. 7 is that of 1.4 at. % fluorine concentration, as it is our pure-silica-core fiber, PurFBG. For an estimate of the CTE of an arbitrary concentration and temperature one can use the expression32], in the temperature range from 123 K to 473 K and fluorine concentration from 0 ppm to 13500 ppm.
As it was expected from the results shown in Fig. 5, fluorine-doped silica presents a smaller absolute value of the CTE than the one for pure fused silica, which is evident from Fig. 7 when comparing the data for PurFBG and SRM 739, respectivelly. Thus, not only should the CTE be considered not constant, but its functional form should be different from that of pure silica. The same behavior for the CTE was previously observed in bulk fluorine-doped silica [21, 32]. However, as it is also shown in the Fig. 7, all the silica samples analysed have a very different CTE than that expected from the expression given in , which diverges from the well known CTE of silica at LNT . Our derived value for the CTE of the PurFBG is (αPurFBG - αSRM739)/αSRM739 = 16% at room temperature, which is in good agreement with the expected CTE fractional difference 17% for a 1.4 at. % F:SiO2 with respect to undoped SiO2 . As for the functional dependence with the temperature, the calculated CTE – from our own experimental data – behaves in the same way as previously reported in the literature , although the data diverge slightly as temperature is lowered. The CTE of the PurFBG is within the CTE estimated for F:SiO2 by less than 0.8 × 10−7 K−1 in the whole temperature range, much smaller than the 2 × 10−7 K−1 difference of the CTE of undoped silica by  and of SRM 739 by , and comparable to the divergence of ~0.5 × 10−7 K−1 found in different previous works between pure fused silica . In addition to the good agreement in the overlapping range, our measurements extend the fluorine-doped silica CTE data to cryogenic temperatures for the first time to our knowledge.
It was also shown that for accurate modeling of FBGs one should know the CTE and thermo-optic coefficient of the employed materials. For pure-silica-core fibers, the different concentrations of dopant in the cladding will affect the Bragg wavelength thermal coefficient ξ mostly through the CTE of the structure, while for doped-core fiber, the dopant concentration will affect ξ mostly through the thermo-optic coefficient. Generally speaking, fluorine doping in the cladding increases the total sensitivity at low temperatures by increasing the fiber CTE. The sensitivity at low temperatures is also increased by the increase in boron concentration or decrease in the germanium concentration in the core, this time by increasing the thermo-optic coefficient.
From the material parameters and the model presented above, one can recover the temperature of the sensor by integrating Eq. (4). The results of the integration for all the FBGs are shown in Fig. 8(a). To emphasize the impact of the choice of parameters in the recovery of the temperature, we calculate the difference between the modeled predicted temperature and the sensor’s temperature for the PurFBG in Fig. 8(b).
The temperature recovery for the three FBGs can be done by simply inverting the axes in Fig. 4, which is similar to Fig. 8(a), where the calculated values for the SRM 739 and fluorine-doped silica are also plotted. In the absence of these calibration curves, one can refer to a model for the sensor’s thermo-optic and thermo-elastic properties. For the later, careful modeling and choice of parameter must be made, as shown in Fig. 8(b), where one can observe a systematic error up to 10 K in the temperature recovery at LNT. The pure-silica model (SRM 739) presented an overall smaller error in the temperature recovery of the PurFBG compared to the fluorine-doped silica model. This is coincidental, as can be seen in Fig. 7, the SRM 739 thermal expansion has a crossing point with the CTE of the PurFBG, leading to an integrated value of the error which cancels itself at some extent.
Our data are in line with the literature, albeit here αL was estimated under the influence of cross-sensitivity, in a completely different, indirect fashion. Using the temperature dependence of the thermal expansion coefficient, or the temperature dependence of the thermo-optic coefficient in Eq. (3), one can predict the fiber Bragg gratings’ properties, or conversely calculate the temperature of the sensor head from the Bragg wavelength shift as shown in Fig. 8(a).
We have fabricated three FBGs in different fibers, and interrogated their Bragg wavelength shift from liquid nitrogen to room temperatures. A quasi-continuous, accurate temperature sweeping was performed using a simple setup. The FBGs’ relative nonlinear sensitivities were shown to differ slightly, mainly due to different compositions. It was also shown that the nonlinearity can be accurately modeled using a temperature-dependent thermal expansion coefficient in conjunction with a nonlinear thermo-optic coefficient. We could obtain resolutions down to 0.5 K using a weak pure-silica-cladding FBG and 0.25 K with boron-doped and germanium-doped silica fibers at liquid nitrogen temperature. Previous works have focused on increasing the sensor’s sensitivity by embedding the FBG in a substrate, allowing the use of poor-resolution interrogators. That approach, when applied to bare FBGs, gives inaccurate results which can compromise the modeling of the sensor. We have presented accurate measurement and modeling of FBGs, which resolve and explain the origin of the divergences or anomalous behavior found in previous works. We have also presented a new set of cryogenic data for the thermo-optic coefficient of B2O3 and GeO2 doped silica, as well as the temperature dependence of the thermal expansion coefficient of F-doped silica. The present work shows that bare FBGs have a predictable performance, and are suitable for accurate thermometry in cryogenic to room temperature environments.
RK acknowledges support from the Natural Sciences and Engineering and Research Council (NSERC) of Canada’s Strategic grants program, NSERC’s Discovery Grants program, Canada Council for the Arts’ Killam Research Fellowships program, and the Government of Canada’s Canada Research Chairs program.
References and links
1. G. Adamovsky, S. F. Lyuksyutov, J. R. Mackey, B. M. Floyd, U. Abeywickrema, I. Fedin, and M. Rackaitis, “Peculiarities of thermo-optic coefficient under different temperature regimes in optical fibers containing fiber Bragg gratings,” Opt. Commun. 285(5), 766–773 (2012). [CrossRef]
2. M. Ahlawat, B. Saoudi, E. Soares de Lima Filho, M. Wertheimer, and R. Kashyap, “Use of an FBG sensor for in-situ temperature measurements of gas dielectric barrier discharges,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, OSA Technical Digest (online) (Optical Society of America, 2012), BTu2E.4.
3. G. M. H. Flockhart, R. R. J. Maier, J. S. Barton, W. N. MacPherson, J. D. C. Jones, K. E. Chisholm, L. Zhang, I. Bennion, I. Read, and P. D. Foote, “Quadratic behavior of fiber Bragg grating temperature coefficients,” Appl. Opt. 43(13), 2744–2751 (2004). [CrossRef] [PubMed]
4. R. Mahakud, J. Kumar, O. Prakash, and S. K. Dixit, “Study of the nonuniform behavior of temperature sensitivity in bare and embedded fiber Bragg gratings: experimental results and analysis,” Appl. Opt. 52(31), 7570–7579 (2013). [CrossRef] [PubMed]
5. S. Pal, T. Sun, K. T. V. Grattan, S. A. Wade, S. F. Collins, G. W. Baxter, B. Dussardier, and G. Monnom, “Non-linear temperature dependence of Bragg gratings written in different fibres, optimised for sensor applications over a wide range of temperatures,” Sensor. Actuat. A-Phys. 112(2–3), 211–219 (2004).
6. M. B. Reid and M. Ozcan, “Temperature dependence of fiber optic Bragg gratings at low temperatures,” Opt. Eng. 37(1), 237–240 (1998). [CrossRef]
7. M. Toru, T. Hiroaki, and K. Hideo, “High-sensitivity cryogenic fibre-Bragg-grating temperature sensors using teflon substrates,” Meas. Sci. Technol. 12(7), 914 (2001).
8. H. Yamada, Y. Tanaka, M. Ogata, K. Mizuno, K. Nagashima, S. Okumura, and Y. Terada, “Measurement and improvement of characteristics using optical fiber temperature sensors at cryogenic temperatures,” Physica C 471(21–22), 1570–1575 (2011). [CrossRef]
9. E. Soares de Lima Filho, G. Nemova, S. Loranger, and R. Kashyap, “Laser-induced cooling of a Yb:YAG crystal in air at atmospheric pressure,” Opt. Express 21(21), 24711–24720 (2013). [CrossRef] [PubMed]
10. E. Soares de Lima Filho, G. Nemova, S. Loranger, and R. Kashyap, “Direct measurement of laser cooling of Yb:YAG crystal at atmospheric pressure using a fiber Bragg grating,” Proc. SPIE 9000, 90000I (2014). [CrossRef]
11. E. Soares de Lima Filho, M. Gagne, G. Nemova, R. Kashyap, M. Saad, and S. Bowman, “Sensing of laser cooling with optical fibres,” in 7th Workshop on Fibre and Optical Passive Components (IEEE,2011), 1–5. [CrossRef]
12. Y. Dai, M. Yang, G. Xu, and Y. Yuan, “Magnetic field sensor based on fiber Bragg grating with a spiral microgroove ablated by femtosecond laser,” Opt. Express 21(14), 17386–17391 (2013). [CrossRef] [PubMed]
13. A. J. Wyk, L. S. Pieter, and A. C. Anatoli, “Fibre Bragg grating gas temperature sensor with fast response,” Meas. Sci. Technol. 17(5), 1113–1117 (2006). [CrossRef]
14. M.-C. Wu, R. H. Pater, and S. L. DeHaven, “Effects of coating and diametric load on fiber Bragg gratings as cryogenic temperature sensors,” Proc. SPIE 6933, 693303 (2008). [CrossRef]
15. S. Parne, R. Sai Prasad, S. G. Dipankar, M. Sai Shankar, and S. Kamineni, “Polymer‐coated fiber Bragg grating sensor for cryogenic temperature measurements,” Microw. Opt. Technol. Lett. 53(5), 1154–1157 (2011). [CrossRef]
16. R. Kashyap, Fiber Bragg Gratings (Academic, 2009).
17. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). [CrossRef]
18. G. M. Flockhart, R. R. Maier, J. S. Barton, W. N. MacPherson, J. D. Jones, K. E. Chisholm, L. Zhang, I. Bennion, I. Read, and P. D. Foote, “Quadratic behavior of fiber Bragg grating temperature coefficients,” Appl. Opt. 43(13), 2744–2751 (2004). [CrossRef] [PubMed]
19. M. Gagné and R. Kashyap, “New nanosecond q-switched Nd:VO4 laser fifth harmonic for fast hydrogen-free fiber Bragg gratings fabrication,” Opt. Commun. 283(24), 5028–5032 (2010). [CrossRef]
20. T. J. Quinn, Temperature (Academic, 1983).
21. P. K. Bachmann, D. U. Wiechert, and T. P. M. Meeuwsen, “Thermal expansion coefficients of doped and undoped silica prepared by means of PCVD,” J. Mater. Sci. 23(7), 2584–2588 (1988). [CrossRef]
22. W. H. Souder and P. Hidnert, Measurements on the thermal expansion of fused silica (US Government Printing Office, 1926).
23. K. Oh and U.-C. Paek, Silica Optical Fiber Technology for Devices and Components: Design, Fabrication, and International Standards (John Wiley & Sons, 2012), Vol. 240.
24. M. Okaji, N. Yamada, K. Nara, and H. Kato, “Laser interferometric dilatometer at low temperatures: application to fused silica SRM 739,” Cryogenics 35(12), 887–891 (1995). [CrossRef]
25. Y.-G. Han, Y. Chung, and S. B. Lee, “Compositional dependence of the temperature sensitivity in long-period fiber gratings with doping concentration of GeO2 and B2O3 and their applications,” Opt. Eng. 43(5), 1144–1147 (2004). [CrossRef]
26. D. N. Nikogosyan, “Multi-photon high-excitation-energy approach to fibre grating inscription,” Meas. Sci. Technol. 18(1), R1–R29 (2007). [CrossRef]
28. E. Suhir, S. Kang, J. Nicolics, C. Gu, A. Bensoussan, and L. Bechou, “Predicted thermal stresses in a cylindrical tri-material body, with application to optical fibers embedded into silicon,” J. Elec. Cont. Eng. 3(6), 9–16 (2013).
30. W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30(5), 779–788 (1959). [CrossRef]
31. Y.-G. Han, W.-T. Han, B. H. Lee, U.-C. Paek, Y. Chung, and C.-S. Kim, “Temperature sensitivity control and mechanical stress effect of boron-doped long-period fiber gratings,” Fiber Integrated Opt. 20(6), 591–600 (2001). [CrossRef]
32. A. Koike and N. Sugimoto, “1. Temperature dependences of optical path length in inorganic glasses,” Reports Res. Lab. Asahi Glass Co, Ltd 56, 1–6 (2006).
33. D. B. Leviton and B. J. Frey, “Temperature-dependent absolute refractive index measurements of synthetic fused silica,” Proc. SPIE 6273, 62732K (2006). [CrossRef]