3. Results and discussion

As a first step, we analyze the power conversion along the fiber between the pump and signal radiations for the different taper schemes described in 0. In

addition, we consider the following absorption and emission cross-sections for the Yb-doped fiber amplifier at 20° C: σ p abs <sup>¼</sup> <sup>1</sup>:488x10�24m2, <sup>σ</sup> p em <sup>¼</sup> <sup>1</sup>:829x10�24m2, σs abs <sup>¼</sup> <sup>6</sup>x10�27m2, and <sup>σ</sup><sup>s</sup> em <sup>¼</sup> <sup>3</sup>:58x10�25m2, where the wavelengths 976 and 1064 nm correspond to the pump and signal radiation, respectively. In the numerical simulation, we have fixed the numerical aperture of 0.18 along the tapered fiber, and we change the temperature from 20 to 120°C. In both taper structures named Taper 1 (Figure 1a) and Taper 2 (Figure 1b,) we employ a pump power of

#### Figure 2.

Modeling of a tapered Yb-doped amplifier. Evolution of the pump and signal radiations at two different temperature;, (a), (b) and (c) for the scheme named taper 1 at 1 W of pump power for different tapered core shapes; (d), (e), and (f) for the scheme named taper 2 at 1 W of pump power for different tapered core shapes.

Temperature Sensing Characteristics of Tapered Doped Fiber Amplifiers DOI: http://dx.doi.org/10.5772/intechopen.89894

1 W, and the corresponding numerical results are shown in Figure 2 for each tapered structure. In this figure it is relevant to observe the behavior of the crosspoint where the signal and pump conversion occurs, due to the fact that this crosspoint shifts to different lengths according to temperature variations. Then, this shift is an indicative of which tapered structure is affected principally by temperature, modifying in this way the Yb-doped fiber amplifier performance. To visualize this temperature response in a better way, we proceed to analyze the amplified signal power at the end of the tapered fiber at 20°C with respect to the signal generated at different temperatures T using the following normalized expression:

$$\left[P\_s \text{(20}^\circ\text{C)} - P\_s(T)\right] / P\_s \text{(20}^\circ\text{C)}.\tag{25}$$

We evaluate this equation for each tapered structure given in Figure 1. In the calculations we employ a fiber length = 3 m, and a pump power = 1 W. The results are shown in Figure 3. According to Figure 3, all tapered fiber structures show a high temperature sensitivity for large values of temperature. In addition, we can observe that the tapered fiber structure named Taper 2 is more sensitive to temperature for different tapered shapes. Especially, for the Taper 2 with a parabolic-1 shape, we obtain an improvement of the temperature sensitivity in the fiber amplifier.

Figure 3. Efficiency signal conversion for different temperatures at the end of the tapered fiber.

#### Figure 4.

Temperature behavior of the generated signal for different temperatures T = 30 and 120°C at different pump powers: 0:1 � 0:5W.

Temperature response at different pump powers is shown in Figure 4, where temperatures of 30 and 120°C are used. The signal is calculated at the end of the tapered fiber (3 m) according to the scheme of Figure 1.

According to Figure 4, the temperature sensitivity of the signal radiation for both tapered fiber schemes shown in Figure 1 is higher as the temperature is increased, and it can be improved if we employ lower pump powers than 1 W, respectively. In particular, this increment on sensitivity highly depends on the taper

Figure 5.

Modeling of a tapered Tm-doped amplifier. Evolution of the pump and signal radiations at two different temperatures,; (a), (b), and (c) for the scheme named taper 1 at 1 W of pump power for different tapered core shapes; (d), (e), and (f) for the scheme named taper 2 at 1 W of pump power for different tapered core shapes.

### Temperature Sensing Characteristics of Tapered Doped Fiber Amplifiers DOI: http://dx.doi.org/10.5772/intechopen.89894

shape and the pump scheme employed in the amplifier design. Additionally, this temperature sensitivity can change according to the tapered fiber length. In our calculations, the tapered length was 3 m, but other temperature sensitivities can be obtained if we consider tapered fiber length between 2 and 2.5 m, where the crosspoint of the signal and pump radiations is located (See Figure 2). In this sense, further analysis needs to be performed to optimize the temperature sensitivity using different taper ratios and different taper lengths and modifying the longitudinal shape of the tapered doped fiber amplifier. Similarly, in the case of Th, we analyze the radiation conversion along the fiber between the pump and signal radiations of the different schemes described in Figure 1. The numerical aperture NA ¼ 0:18 is considered constant along the taper, and the temperature is changed from 17–117°C. For both schemes shown in Figure 1, the co-propagating pump and signal power were set at 1 W and 20 mW, respectively; the corresponding results of the signal conversion for three different temperatures are shown in Figure 5 for each longitudinal tapered core shape.

According to Figure 6, all tapered doped fiber amplifiers show an increasing temperature sensitivity for values starting even at 27°C and up to the maximum temperature of 117°C. The curves for "Taper 2" scheme (all in blue color) showed a saturation at around 87°C, indicating less sensitivity to temperature with respect to "Taper 1" scheme (in black color). However, this behavior could vary if we use other fiber lengths. In this context, the curves shown in Figure 5 represent a design map that could allow us to choose the taper shape and its corresponding taper length, given by the cross-point in order to improve the temperature sensitivity of the tapered doped fiber amplifier around a specific temperature value.

On the other hand, Figure 7 shows the temperature response at different pump powers for the two tapered core shapes analyzed in this work, where temperatures of 27 and 117°C are used. The signal is calculated at the end of the tapered fiber (3 m) according to the scheme of Figure 1.

According to Figure 7, the temperature sensitivity of the tapered doped fiber amplifier grows as the temperature is increased, and it is higher for low values of the pump power. This is an important result to consider for the design of fiber lasers and temperature fiber sensors. Therefore, we can consider that the temperature sensitivity of the signal radiation is higher for low pump powers, and this sensitivity is different for each pump scheme and depends on the taper used. This sensitivity can vary according to the length of the fiber used. For example, these calculations were made at 3 m; however, more sensitivity changes can be obtained at shorter length, as it is shown in Figure 2. Additionally, further analysis needs to be

Figure 6. Normalized amplified signal for different temperatures at the end of the tapered fiber with L ¼ 3m.

#### Figure 7.

Temperature behavior of the generated signal for temperatures T <sup>¼</sup> 300 and 390<sup>∘</sup> K at different pump powers (0.2–1 W): (a) taper 1, parabolic 1 and 2, (b) taper 2, parabolic 1 and 2.


#### Table 1.

Comparison of the performance of rare-earth-doped fibers and materials as temperature-sensing elements.

performed to optimize the temperature sensitivity using different taper ratios and the longitudinal shape of the tapered doped fiber.

Similar results were obtained as in the case of using an Yb-doped fiber amplifier for temperature sensing. However, although the response follows a similar behavior, the results are different, the evolution of the pump and signal radiation is shifted to shorter lengths along the fiber, the efficiency signal conversion is larger, and the temperature behavior of the generated signal for different temperatures as a function of the pump power shows an increased response for the Tm-doped fiber amplifier. The sensitivity of both tapers can be compared with other kinds of sensor of temperatures using similar techniques as shown in Table 1. Table 1 compares the parameters of the authors' tapered ytterbium- and thulium-doped fiber temperature sensors with existing ones. It can be seen that the sensitivity of the sensors is close to early work on doped silica fibers for intrinsic fiber-optic temperature sensors.
