The paper describes the implementation of fiber Bragg gratings inscribed by femtosecond laser pulses with a wavelength of 400 nm. The use of a Talbot interferometer for the inscription process makes multiplexing practicable. We demonstrate the functionality of a three-grating multiplexing sensor and the temperature stability up to 1200 °C for a single first-order Bragg grating.
© 2013 OSA
Fiber Bragg gratings (FBGs) are sensor elements often used in harsh environments such as extreme temperatures, strong electromagnetic fields or chemically aggressive conditions, because they are not influenced by electromagnetic radiation, have limited cross talk from many environmental influences and are very flexible. Due to their small size, they can easily be embedded in compound materials. Typical applications are temperature and strain sensing. There are limitations, however, for the use of such gratings in silica fibers for temperatures beyond 300 °C or 1000 °C. Fiber gratings based on color center effects bleach out at temperatures higher than 200 °C – 300 °C. With additional heat treatment known as thermal regeneration it is possible to stabilize the gratings and, thus, expand the temperature range up to 1000 °C [1,2] or, for short-term measurements, even up to 1200 °C  near the glass transition point of fused silica. The softening of the silica glass then defines the ultimate temperature for which such sensors can be applied. There is, however, great interest to use such sensors for even higher temperatures, e.g. for temperature sensing and material monitoring in gas turbines or melting furnaces. Fibers made of single crystalline sapphire are a good option to overcome the temperature limit of fused silica, because the material melting point is at temperatures beyond 2040 °C [4–6]. Single Bragg gratings in sapphire fibers have been reported for sensing applications up to 1745 °C [4–7]. Thin film temperature sensors on a sapphire fiber tip have also been described . Femtosecond (fs)-laser pulses were used for inscription of the FBGs, since they provide high peak intensities and multi-photon processes to provide a permanent change of the refractive index.
FBGs are formed by a spatial periodic change of the refractive index achieved by special illumination techniques . The most common techniques are point-by-point fabrication  and phase mask exposure . For the point-by-point method, the inscription laser is focused into the fiber to change the refractive index locally and then the grating is built up by scanning the fiber. The phase mask technique uses the interference pattern directly located behind a phase mask, which is designed so that the interference pattern forms the whole grating structure. Another technique uses a phase mask as a beam-splitting element. The spatially separated beams are then superimposed to form an interference pattern with great geometrical flexibility. Such an interferometer of the Talbot type is used in our experiments .
Although the potential applicability of FBGs in sapphire fibers for high temperature sensing has been experimentally shown, the realization of the gratings still suffers from limitations. Until now, only the phase mask method has been applied successfully for the inscription of fiber Bragg gratings in sapphire fibers. The use of an interferometric inscription concept could simplify considerably the implementation of wavelength-multiplexed arrays of gratings.
A second limitation in the inscription process is the wavelength used. From the simplified Bragg condition (Eq. (1)) for perpendicular incidence4–7] were inscribed e.g. for a doubled reflection wavelength (3100 nm) but used in second diffraction order for 1550 nm. In this case the reflection efficiency might be reduced especially in case of non-perfect grating structures.
In the following we describe the implementation of multiplexed fiber Bragg gratings inscribed by an interferometric setup. We show that, by use of the second harmonic wave from a Titanium:Sapphire laser, we can inscribe fiber Bragg gratings also in first-order. This method is then easily applied to realize multiplexed arrays of gratings.
2. Inscription and characterization of the Bragg gratings
For the inscription of FBGs we used a femtosecond laser system. This system provides pulses with a wavelength of 800 nm, a pulse duration of 135 fs and an averaged power of 3 W with a repetition rate of 1 kHz. These pulses pass a nonlinear crystal to generate the second harmonic of the pump wave. The transformed pulses with a wavelength of 400 nm have an averaged power of 1 W. Femtosecond laser pulses were used for inscription of the FBGs, since they provide high peak intensities and multi-photon processes for a permanent change of the refractive index. We also tested the third harmonic with a resulting wavelength of 266 nm, but there was no power regime found that enabled a permanent change of the sapphires' refractive index without destroying the fiber.
The averaged power for inscription with the second harmonic was reduced from the maximum of 1 W to 550 mW, and an external dynamic iris diaphragm was used to reduce the mean repetition rate in order to avoid a material ablation of the fiber due to local heating. We did not observe any erasing effect of the gratings due to the heating of the fiber during the inscription process itself . The iris diaphragm was opened for 0.01 s with 0.5 Hz, so that on average a number of 20 pulses per second reached the fiber. Due to the shorter inscription wavelength, the averaged laser power was nearly halved, and a destruction of the fiber became less likely compared to an inscription wavelength of 800 nm.
The FBG was fabricated using the interference pattern of a Talbot interferometer (see Fig. 1 ) . Inside the interferometer the beam is divided by a phase mask. This phase mask has a period of 888 nm and was optimized for an inscription wavelength of λinscription = 400 nm to suppress the zero order (which was additionally blocked). The two diffracted beams were reflected by the mirrors and then interfered under the angle ϑ. The fiber was placed exactly perpendicular to the interference pattern in the field of superposition. Additionally, a cylindrical lens (focal length of 221 mm) was used in front of the interferometer to increase the local intensity at the place of the fiber. Since the sapphire fibers were used as air-clad fibers with a large core diameter of 100 µm, the cylindrical lens was moved to scan through the full diameter with a velocity of 0.1 µm/s. Because of the very short pulses in the fs-regime, all beam paths have to be aligned with a tolerance of less than 50 microns.
For multiplexing of gratings the mirrors were turned symmetrically. This leads to a change in the angle ϑ. Considering the Bragg condition with respect to the interferometric inscription, the design wavelength can be calculated from the following Eq. (2):
Commercial single crystalline sapphire fibers (MicroMaterials Inc.) fabricated by laser-heated pedestal growth to lengths up to one meter were used [13,14]. Attenuation data for Sapphire fibers vary from 0.5 to 4 dB/m at 1550 nm, dependent on fiber diameter, preparation, or annealing procedures [13, 14]. Sapphire fibers guide the light in a large multimode core with an index difference of 0.74 relative to air. Because of this fact, several hundred modes can propagate through the fiber, which results in a very broad reflection spectrum of the FBG of about more than 8 nm. To always measure the same form of the spectrum, the light of a superluminescent diode (SLD) was mode-mixed in a 50 µm graded index fiber and coupled via a commercial APC connector to the sapphire fiber (see Fig. 2 ). To suppress strong back reflection from the coupling, the sapphire fiber end was polished to an angle of 8° to match the APC fused silica fiber. We expected some losses especially for the coupling from 100µm sapphire to the 50µm supply fiber, but this setup achieved a well measurable signal output. The reflected light coming from the grating was then analyzed in a commercial Ibsen Photonics interrogator . With this setup a spectral range from 1510 nm up to 1596 nm could be evaluated.
3. Experimental results
At first a fiber with a single grating was evaluated. Figure 3 shows the reflection spectrum at 100 °C. A strong signal background is observed, belonging to the reflected light at the fiber end having the spectrum of the light source itself.
The real reflection peak was discernible as an offset coming from the grating. The background was subtracted to obtain the reflection spectrum of the grating itself. As the sapphire fiber is a multimode fiber, the reflected modes result in a wider peak compared to single mode fiber. The Bragg wavelength λBragg was derived as the center of a fitted Gaussian function. For the Bragg grating of Fig. 3, a reflection wavelength of λBragg = (1530.310 ± 0.072) nm was found to have a full width at half maximum (FWHM) of 9.44 nm. This would correspond to a numerical aperture of NA = 0.18 in accordance with observations in other experiments . The reflectivity could not be estimated, because it was not possible to measure a reference intensity due to the connection losses of the sapphire fiber. However, the reflectivity is high enough for sensor applications, so that all of the inscribed gratings could be used in the heating experiments. The length of the grating itself is limited by the diameter of the inscription laser beam, which was 8 mm for a 1/e limit.
Due to the multimodal reflection characteristic of the FBGs, an asymmetric Gaussian-like function  would describe the reflection spectrum better (red dash-dotted line in Fig. 3) than a Gaussian function. We heated up a grating to various temperatures between room temperature and 1200°C, stabilizing the temperature for at least 5 min before the spectra were measured. It turned out that the form of the grating spectrum is unaffected by a change of temperature. Therefore the temperature dependency of the Bragg wavelength showed almost the same parameters for the fitting using the Gaussian function, (25.7 ± 0.2) pm/K, and the asymmetric Gaussian function, (25.9 ± 0.2) pm/K. Since the resulting temperature dependencies were almost identical, we therefore used the Gaussian function for further experiments to evaluate the spectra, because of the simpler calculation procedure.
The spectra of different gratings inscribed with the same parameters are reproducible with high accuracy. However, the amplitude and therefore the reflectivity strength may vary. This could be explained by the shape of the fiber itself, because single crystalline sapphire has a rounded hexagonal cross section. The orientation of the fiber was not adjusted in the experimental setup.
For high temperature investigations, fibers were also heated up to 1200 °C. The Fig. 4 shows the temperature dependency of the Bragg wavelength. The reflected intensity was constant during the whole heating process. This demonstrates that, with 400 nm fs-pulses, the material modifications induced in sapphire cause the gratings to be stable also at temperatures beyond 1000 °C and that way to be applicable for measurements in high temperature regimes. The average temperature sensitivity for the fiber of Fig. 4 was (27.2 ± 0.4) pm/K. In Fig. 4, a slight deviation from a linear slope can be observed. The slope, and therefore the sensitivity, slightly increases monotonously with increasing temperature. Over the whole temperature range of 1200 K variation of +/−2.9 pm/K can be found for the local slope of a linear fit. This behavior is already known and especially reported for sapphire fibers in reference .
To demonstrate the possibility of multiplexing and, hence, the main advantage of using a Talbot interferometer, three gratings with different wavelengths were inscribed one after another separated by ca. 1 cm. The wavelengths (1527 nm, 1549 nm and 1574 nm) were chosen in such a way that the three gratings had no spectral overlap during the subsequently heating in the furnace from 100 °C up to 1000 °C in 50 K steps. Figure 5 shows the grating signals at 100 °C and 400 °C. Due to the wavelength-dependent intensity of the SLD, the grating spectra were normalized to the SLD spectrum. The Bragg wavelength was determined by the center of the fitted Gaussian peak. The result is shown in Fig. 6 .All three gratings showed a mostly linear dependency between temperature and Bragg wavelength with a slope of (28.7+/−0.9) pm/K. The temperature dependence of the fiber Bragg wavelength is ∆λBragg / ∆T = λBragg (αΛ + αT) with αΛ being the thermo-optic coefficient, which is αΛ = 12.6x10−6 /K  for 633 nm, and αT being the thermal expansion coefficient with αT = 7.15x10−6 /K . The temperature dependence calculated from these numbers is 30.1 pm/K, so that there is a good agreement between the theoretical and the experimental value. For the fibers with the single grating we had observed a dependence of 25.7 ± 0.2) pm/K and of (27.2 ± 0.4) pm/K, using the same experimental setup under identical conditions. The differences may be related to structural changes from one fiber to the other. An imperfect crystallization process or crystal defects are possible reasons for these variations. Also for higher order gratings inscribed with 800 nm the temperature dependency varied between 25 pm/K and  and 28 pm/K  or even more  depending on the environmental temperature.
The grating with the highest reflection wavelength was only observable up to 500 °C, because of the maximally possible evaluable wavelength determined by the light source and interrogator used. In general, the wide wavelength shift in case of extreme temperature variations results in some limitation for the number of possible multiplexed gratings within a certain spectral range. Within a temperature range of 1000 °C, the Bragg wavelength shifts by nearly 30 nm. If the spectral separations of the gratings are about 10 nm (no cross talk between two different gratings), three gratings could be used within a spectral range of about 100 nm. The multiplexing capacity could be increased in case of a more restricted temperature measurement range. Further optimization concerning the number of multiplexed sensors would be possible by selective generation of only the fundamental fiber mode  or by a sapphire fiber structure with a smaller number of allowed propagating modes.
We have demonstrated the applicability of femtosecond pulses with a wavelength of 400 nm to inscribe first-order FBGs in sapphire fibers. An external, additional, dynamic iris diaphragm was used to avoid heating up or destroying the fiber during the inscription process. Single gratings as well as three multiplexed gratings were fabricated using the Talbot interferometer. The gratings showed a nearly linear wavelength dependency of the maximum of reflection. Sapphire fibers are stable up to temperatures of 2000 °C. The high temperature stability of the reported gratings has been experimentally tested for temperatures up to 1200 °C.
Funding by the German Federal Ministry of Economics and Technology under contract 13INE036, and the Thuringian Ministry of Education, Science and Culture (EFRE program) is gratefully acknowledged.
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