**4. Experimental results and discussion**

#### **4.1 Mechanical tuning**

The tuning test, based on the scheme in **Figure 1**, is applied to a Bragg network with 1.5 cm long, half-height bandwidth 0.1 nm, center wavelength at 1556.94 nm, and rejection range of 10 dB. The length of the fiber containing the FBG is 18 cm, corresponding to the initial distance between the clamping presses.

According to studies carried out by several authors [18, 19], the maximum relative elongation that can be exerted on a silica optical fiber is 1%. To preserve the elasticity characteristics of the fiber, a more conservative value, around 0.5%, is considered the maximum limit. Regarding the fiber length used, it corresponds approximately to 0.9 mm. In the computerized tuning process, described in [25], this limit is considered to prevent the optical fiber from breaking.

**Figure 5** shows the reflection spectrum of the stretched Bragg grating. The maximum deviation from the central wavelength is 4.9 nm and corresponds to an offset of 0.98 mm. According to **Eq. (3)**, the relative elongation was 0.4%, remaining within the preestablished limit.

**Figure 6** shows the evolution of the bandwidth at 1, 3, and 10 dB, during the stretching process of the Bragg grating. Specifically, the bandwidth at 1 dB exhibits a variation within the range � 0.01 nm, for the bandwidth of 3 dB there is an increase of 0.01 nm, and at 10 dB there is an increase of 0.05 nm in the bandwidth. Changes in maximum reflectivity are less than 1.1 dB.

The relationship between the variation of the central wavelength and the relative elongation is shown in **Figure 7**. The deviation from the central wavelength grows linearly as a function of relative elongation, at a rate of 0.85 pm/με and with a correlation coefficient of 0.9951. The expected value for the growth rate, using expression **(3)**, would be 1.2 pm/με.

To verify whether this discrepancy is caused by imperfections in the motorized system, the influence of positioning errors on central wavelength tuning is calculated:

$$|d(\Delta \lambda\_B)| \le \left| \frac{\partial(\Delta \lambda\_B)}{\partial(\Delta z)} \right| |d(\Delta z)| = \frac{0.78 \lambda\_B}{L} |d(\Delta z)|,\tag{10}$$

where j j *d*ð Þ Δ*z* is the tuning system accuracy (15 μm), *L* is the fiber length (18 cm) and *λ<sup>B</sup>* is the Bragg wavelength of the Bragg grating at rest (1556.94 nm). With these

**Figure 5.** *Reflection profile of a Bragg grating under the effect of mechanical strain.*

**Figure 6.** *Bandwidth evolution over the entire tuning range.*

**Figure 7.** *Bragg wavelength variation as a function of relative elongation.*

values, the variation of the tuning value j j *d*ð Þ Δ*λ<sup>B</sup>* is always less than or equal to 101 pm. If the error j j *d*ð Þ Δ*λ<sup>B</sup>* is included in the set of measurements performed for the central wavelength, the resulting growth rate is in the range [0.84228, 0.85467] pm/ με. Therefore, imperfections in the motorized system are not the main cause of the differences.

A second tuning test had the scheme described in Section 2.2 as its working principle. In the first stage, the fiber is not embedded in an elastic material but fixed directly to the surface of a flexible sheet. The blade used is 15.2 cm long, 2 cm wide, and 1.5 mm thick, and is made of acrylic. A "v" shaped groove is created along the blade, 9 mm deep, to accommodate the fiber, so that it does not suffer transverse deviations. Consequently, *d* = 6 mm (see **Eq. (7)**). The assembly is then glued to increase its strength and to properly fix the FBG inside the groove. Finally, the support is placed between the moving and fixed blocks of the tuning system to start the tests.

It was said earlier that the fiber can be stretched up to 1% without suffering irreversible damage. In compression mode, this value can reach 23% [19], which allows much larger tuning ranges than in elongation. Substituting **Eq. (7)** in **(6)**, the resulting equation allows calculating a priori the maximum displacement allowed without damaging the fiber. Using more conservative values of 0.5% for compression and 11% for relative elongation, the calculated limits are, respectively, 9.96 mm and 14.13 cm.

The Bragg grating used is 2 cm long, it has a 3 dB bandwidth equal to 0.48 nm and a central wavelength of 1550.4 nm. During the tests, the amplitude of the reflection spectrum was recorded by an optical spectral analyzer, at several tuning points, as shown in **Figure 8**.

The results show that the variation achieved in the central wavelength, using compression, and stretching forces reaches practically 19 nm. It is visible in **Figure 8** that there is a gap in the initial phase of the stretching tuning process. This failure occurred simply because the spectral measurement process was started with the Bragg grating already under the effect of a sufficiently strong mechanical stress that the central wavelength was shifted from its initial value of 1550.4 nm.

**Figure 8.** *Tuning the central wavelength of the Bragg grating at 18.9 nm.*

It is possible to obtain better results, especially in compression mode, as the mobile platform moved only 6.8 cm to obtain a variation of 15.9 nm. However, the mechanical characteristics of the acrylic sheet did not allow to compress the fiber further. On the other hand, the 3 nm spectral variation in stretching mode was achieved by moving the system 4.3 mm and could theoretically reach 4.2 nm with a displacement equal to 9.96 mm.

**Figure 9** shows the relationship between tuning range Δ*λ* and normalized length Δ*z=L*.

The results show a good agreement between the theoretical curve, calculated by **Eq. (8)**, and most of the measurements performed.

The main differences are located at the ends of the graph, which correspond to situations of greater mechanical stress. They are somehow correlated with the progressive decrease in the maximum reflectivity amplitude, visible in **Figure 8**. These changes can be caused by undetected problems in the tuning system. In particular, the glue used can lose its fixing qualities when subjected to large deformations, resulting in bends on the fiber [18].

The evolution of the bandwidth at 1, 3, and 10 dB is represented in **Figure 10**. Starting from the initial position, the axial mechanical forces applied on the FBG do not cause great changes in the width at 3 dB, which oscillates between 0.1 and 0.04 nm. The bandwidth at 1 dB also remains practically constant, with a maximum deviation of 12.5% from the initial value. However, the bandwidth at 10 dB undergoes a gradual increase that reaches 0.4 nm in compression and 0.56 nm in stretching, in addition to showing an irregular behavior.

The increase in bandwidth at 10 dB is clearly visible in **Figure 11**, where the reflection spectrum is not symmetrical, especially when the FBG is subjected to strong

#### **Figure 9.**

*Wavelength variation as a function of normalized horizontal displacement. (Dashed line: theoretical value, points: measured values).*

*Bragg Grating Tuning Techniques for Interferometry Applications DOI: http://dx.doi.org/10.5772/intechopen.106735*

**Figure 10.** *Bandwidth evolution over the entire tuning range.*

**Figure 11.** *Spectral response of a Bragg grating at rest (solid line) and under compression (dashed line).*

compressions. Under these conditions, the pressure exerted along the grating is not uniform, which causes a variation in the grating period Λ and consequently a chirped spectrum. Consequently, the coupling between the propagation modes within the

FBG is no longer tuned to just one wavelength, thus decreasing the maximum reflectivity amplitude, and increasing the width at the base of the reflection spectrum.

On the other hand, the irregularities observed are largely due to the noise level being very close to 10 dB, causing sudden and profound variations in the reflectivity value.

According to **Eq. (7)**, the tension exerted on a Bragg grating, fixed at a distance *d* from the flexible blade, makes it possible to increase the tuning range without changing the length *L*. Theoretically, it is possible to move the reflection spectrum by 50 nm, even for small Δ*z* deviations [7].

Another tuning test was performed with a Bragg grating with a reflectivity peak at 1546.3 nm, 3 dB spectral width equal to 0.46 nm and length 1.5 cm. The FBG was inserted into silicone, 6 mm away from the surface of a flexible acrylic base 16 cm long.

**Figure 12** shows the relationship between the tuning range and the normalized travel distance. The measured tuning points do not follow the theoretical curve for *d* = 6 mm. The main cause for this deviation is a cause of the elastic properties of silicone. The curvature of the acrylic base is not followed by the silicone surface where the Bragg grating is inserted. Thus, the resulting tuning is much smaller than expected.

This problem is accompanied by a progressive decrease in the maximum reflectivity amplitude and in the broadening of the reflection spectrum, visible in **Figure 13**. The FBG reflectivity decreases by 3 dB over approximately 8 nm of tuning. The spectral widths at 1, 3, and 10 dB increase by 0.07, 0.29, and 1.33 nm, respectively.

#### **4.2 Temperature tuning**

To verify the dependence of the central reflection wavelength of the Bragg grating on temperature, the reflectivity spectrum of a grating centered initially at 1548.11 nm,

*Wavelength variation as a function of normalized horizontal displacement. (Dashed line: theoretical values, points: measured values).*

*Bragg Grating Tuning Techniques for Interferometry Applications DOI: http://dx.doi.org/10.5772/intechopen.106735*

**Figure 13.** *Bragg grating tuning at 7.9 nm.*

**Figure 14.**

*Bragg wavelength variation as a function of FBG temperature (dashed line: theoretical value, points: measured values).*

at a temperature of 14.3°C, was measured. The tuning method is based on the procedure described in Section 2.3. **Figure 14** shows the tuning results achieved at the expense of temperature variation in the Bragg grating. The tuning range accomplished was 0.4 nm, for a temperature variation of 40°C, and follows a linear relation between temperature and central wavelength variations.
