2. Capillary-like fiber designs for sensing applications

Figure 1 shows the fiber designs we present here. In Figure 1a, a diagram of the embedded-core fiber is shown [7, 8]. This structure consists of a silica capillary endowed with a germanium-doped core, which is placed inside the wall of the capillary. The embedded-core fiber can be employed for pressure or temperature sensing measurements. Specifically, when the embedded-core fiber acts as a temperature sensor, the capillary hollow part must be filled with metal (Figure 1b). The principle of operation of these sensors is centered on the capillary wall displacements that occur when the hollow embedded-core fiber is pressurized or when the metal-filled embedded-core fiber experiences temperature variations. These wall displacements within the capillary wall entail asymmetric stress distributions in the

Figure 1. (a) Embedded-core fiber, (b) metal-filled embedded-core fiber, (c) surface-core fiber and (d) capillary fiber.

Minimalist Approach for the Design of Microstructured Optical Fiber Sensors DOI: http://dx.doi.org/10.5772/intechopen.81265

fiber structures, which generate, by virtue of the photoelastic effect, birefringence variations in the fiber core.

Figure 1c shows a diagram of the so-called surface-core fiber [9]. In this structure, the fiber core is placed on the fiber external surface. As here the core directly interfaces the external medium, the evanescent field of the guided optical mode permeates the external environment. Surface-core fibers are, then, a suitable platform for refractive index sensing. A possible approach is to imprint fiber Bragg gratings (FBGs) in the fiber core and measure the sensor spectral response as the external refractive index is altered [9]. A second approach is to perform plasmonic sensing by metal-coating the surface-core fiber with a nanometric metallic layer [10]. Additionally, the off-center position of the fiber core permits the surface-core fibers to act as directional curvature sensors. In this case, the curvature-induced strain levels within the core can be probed by a FBG [9].

Figure 1d presents a forth structure, which is simply a capillary fiber [12]. Here, we study the guidance of light in the hollow part of the capillary and investigate how the optical response of the fiber is changed when it experiences temperature variations. It is worth saying that, in this investigation, we employed polymethyl methacrylate (PMMA) capillaries. This choice was due to the higher thermal expansion and thermo-optic coefficients of PMMA when compared to silica.

In the next sections, we specifically describe the principle of operation of each configuration. Moreover, we present theoretical and experimental results and compare them with the ones available in the literature.

### 3. Embedded-core capillary fibers for pressure sensing

The application of pressure to capillary fibers generates displacements on their walls. This, in turn, induces an asymmetric stress distribution within the capillary structure which, due to the stress-optic effect, entails birefringence variations in it. As described in [7], an analytical model can be used to account for the material birefringence variations (ΔBmat) in pressurized capillaries. To do that, we can employ Eq. (1), where C1 and C2 are the elasto-optic coefficients (C1 <sup>=</sup> �0.69 � <sup>10</sup>�<sup>12</sup> and C2 <sup>=</sup> �4.19 � <sup>10</sup>�<sup>12</sup> Pa�<sup>1</sup> for silica), and <sup>σ</sup><sup>x</sup> and <sup>σ</sup><sup>y</sup> are the pressure-induced stresses on the horizontal and vertical directions, respectively [13, 14].

$$
\Delta B\_{\rm mat} = (\mathbf{C}\_2 - \mathbf{C}\_1) \left( \sigma\_\mathbf{x} - \sigma\_\mathbf{y} \right) \tag{1}
$$

The stresses σ<sup>x</sup> and σ<sup>y</sup> can be obtained from Lamé solution inside thick-walled tubes subjected to pressure [15]. The resulting expression for the material birefringence at a position x on the horizontal axis is shown in Eq. (2), where rin and rout are the inner and outer radius of the capillary, and pgauge = pout – pin (pin and pout are the inner and outer pressure levels) [7].

$$
\Delta B\_{mat} = \mathcal{Z}(C\_2 - C\_1) p\_{gauge} \left[ 1 - \left(\frac{r\_{in}}{r\_{out}}\right)^2 \right]^{-1} \frac{r\_{in}^2}{\varkappa^2} \tag{2}
$$

By observing Eq. (2), we see that, when maintaining rin constant, |ΔBmat| will be greater for higher rin/rout ratios. It means that the analytical model predicts that the change in the birefringence is increased for thin-walled capillaries. Moreover, we see that, for fixed rin and rout values, the change in the birefringence is higher for positions (x) which are closer to the inner wall of the capillary [7].

structure and changes its birefringence via the photoelastic effect. Additionally, metal-filled side-hole PCFs have been demonstrated to act as high-sensitivity temperature sensors [3, 4]. In this approach, the metal expansion inside the fiber structure induces an asymmetric stress distribution within the same (due to the different thermal expansion coefficients of silica and of the metal). It entails changes in the fiber birefringence which can be optically probed and related to the

Microstructured optical fibers can also be used as refractive index sensors. Among those ones, plasmonic sensors acquire great importance due to the high sensitivities they can achieve. In these platforms, selected regions of the fiber structure are coated with a nanometric-thick metallic layer to provide coupling between the optical mode and a plasmonic mode. Possible approaches are to coat the inner holes of microstructured fibers [5] or to open up a channel in the fiber structure to expose the fiber core for metallic nanospheres immobilization [6]. However, the microstructured optical fibers usually employed in the sensing schemes described above are sophisticated, which demand great technical efforts for their fabrication. Here, alternatively, we present sensors which are endowed with ultra-simplified microstructures based on capillary-like fibers (embedded-core fibers [7, 8], surface-core fibers [9, 10], and capillary fibers [11]). As it will be shown in the following, even though these configurations are very simple, the attained sensitivities are high when compared to other fiber sensors based on more complex structures. Thus, we can identify the use of capillary-like fibers as a new avenue for obtaining highly sensitive fiber sensors with simplified fabrication

temperature variation through a suitable calibration.

Applications of Optical Fibers for Sensing

2. Capillary-like fiber designs for sensing applications

Figure 1 shows the fiber designs we present here. In Figure 1a, a diagram of the

embedded-core fiber is shown [7, 8]. This structure consists of a silica capillary endowed with a germanium-doped core, which is placed inside the wall of the capillary. The embedded-core fiber can be employed for pressure or temperature sensing measurements. Specifically, when the embedded-core fiber acts as a temperature sensor, the capillary hollow part must be filled with metal (Figure 1b). The principle of operation of these sensors is centered on the capillary wall displacements that occur when the hollow embedded-core fiber is pressurized or when the metal-filled embedded-core fiber experiences temperature variations. These wall displacements within the capillary wall entail asymmetric stress distributions in the

(a) Embedded-core fiber, (b) metal-filled embedded-core fiber, (c) surface-core fiber and (d) capillary fiber.

process.

Figure 1.

8

Although the analytical model for the material birefringence can provide important information on the most important geometrical parameters that affects the sensitivity of the sensor, it is necessary to account for the modal birefringence dependence on the applied pressure for a broader understanding of the sensor characteristics. To do this, a numerical simulation of the embedded-core fiber structure was carried on. Figure 2 presents the results for dBmodal/dP (derivative of the modal birefringence as a function of the pressure) as a function of the core position within the capillary. In the simulations, rin = 40 μm and rout = 67.5 μm. The core dimensions were considered to be 5.7 and 11.4 μm.

The results presented in Figure 2 show, as could be expected from the analytical model, that dBmodal/dP values are higher for core positions which are closer to the inner wall of the capillary. However, we note that, very interestingly, the trend that is expected from the analytical model is verified only when the whole core is within the capillary wall. When the core has part of its area outside of the capillary wall, a strong decrease in dBmodal/dP is observed (core region is represented as dark blue ellipses in Figure 2). This allows observing that, for maximizing dBmodal/dP in embedded-core fibers, it is crucial that the whole core is inside the capillary wall.

In order to obtain an experimental demonstration of the proposed design acting as a pressure sensor, we performed the fabrication of the embedded-core fiber. The fabrication process is simple and with few steps. Initially, a germanium-doped silica rod is merged to a silica tube. In sequence, the resulting preform is inserted in another silica tube, which acts as a jacket. The preform is then drawn in a fiber tower facility [7]. Figure 3a shows the cross-section of the embedded-core fiber.

of the modal phase birefringence derivative with respect to the pressure, <sup>∂</sup>Bmodal

(a) Embedded-core fiber. (b) Experimental setup for pressure sensing measurements. BLS: broadband light source. P1 and P2: polarizers. L1 and L2: objective lenses. PC: pressure chamber. (c) Spectral response of the

> dP <sup>¼</sup> <sup>λ</sup> G

magnitude order of the ones found for much more sophisticated microstructured fibers [1]. Therefore, we see that the embedded-core fiber structure allows achiev-

recognizing embedded-core fiber as a promising platform for the realization of

Embedded-core fibers can also act as highly sensitive temperature sensors if a metal is inserted into the hollow part of the capillary (Figure 1b). In analogy to the embedded-core fiber pressure sensor, the principle of operation is based on the induction of stresses inside the capillary and on the consequent variation of the fiber

In this configuration, the metal expansion inside the capillary causes its volume elements to displace and to compress the silica capillary structure. This, in turn,

pressure sensing using optical fibers and a novel route for the design of

4. Embedded-core capillary fibers for temperature sensing

Figure 3c presents the measured optical response of the embedded-core fiber for different pressurization conditions. It is seen that when the pressure level increases, the fringes blueshift. After performing an appropriate correction on the fiber pressurized and nonpressurized lengths [2, 16], we can estimate a sensitivity value of (1.04 � 0.01) nm/bar [7]. This value is high when compared to other results measured in polarimetric measurements reported in the literature. For example, in [17], a sensitivity of 0.342 nm/bar was measured for a commercial photonic-crystal fiber. Additionally, in [18, 19], the sensitivities of 0.30 and 0.52 nm/bar were

∂Bmodal

<sup>∂</sup><sup>P</sup> value for the embedded-core fiber can be estimated from

<sup>∂</sup><sup>P</sup> even with a nonoptimized fiber. It also allows

CS � <sup>d</sup>λIF

Minimalist Approach for the Design of Microstructured Optical Fiber Sensors

reported for specially designed microstructured fibers.

Eq. (3). The resulting value is (2.33 � 0.02) � <sup>10</sup>�<sup>7</sup> bar�<sup>1</sup>

Moreover, the <sup>∂</sup>Bmodal

birefringence [8].

11

ing high sensitivity (Cs) and <sup>∂</sup>Bmodal

embedded-core fiber for different pressure levels.

DOI: http://dx.doi.org/10.5772/intechopen.81265

microstructured optical fiber pressure sensors.

Eq. (3) [2].

Figure 3.

<sup>∂</sup><sup>P</sup> —

<sup>∂</sup><sup>P</sup> (3)

, which is in the same

Figure 3b exposes a diagram of the experimental setup used for pressure measurements. Light from a broadband source (BLS) is launched in the fiber and detected with an optical spectrum analyzer (OSA). Polarizers (P1 and P2) are used to excite the orthogonal modes of the fiber and to recombine them after traveling along the fiber. A pressure chamber is used to subject the fiber to different pressure levels.

By using the configuration of Figure 3b, an interference spectrum is measured in the OSA. Since the embedded-core fiber is sensitive to pressure variations, the spectral position of the interferometric fringes is shifted when the external pressure level is altered. A sensitivity coefficient, CS, is defined to account for the spectral shift of the fringes as a function of the pressure variation, <sup>d</sup>λIF dP . The CS value can also be written as a function of the wavelength, λ, the fiber group birefringence, G, and

### Figure 2.

Modal birefringence derivative as a function of pressure for different core positions inside the capillary wall. Light blue region represents the capillary wall, and dark blue ellipses represent the core region. Insets illustrate the core position within the capillary.

Minimalist Approach for the Design of Microstructured Optical Fiber Sensors DOI: http://dx.doi.org/10.5772/intechopen.81265

Figure 3.

Although the analytical model for the material birefringence can provide important information on the most important geometrical parameters that affects the sensitivity of the sensor, it is necessary to account for the modal birefringence dependence on the applied pressure for a broader understanding of the sensor characteristics. To do this, a numerical simulation of the embedded-core fiber structure was carried on. Figure 2 presents the results for dBmodal/dP (derivative of the modal birefringence as a function of the pressure) as a function of the core position within the capillary. In the simulations, rin = 40 μm and rout = 67.5 μm. The

The results presented in Figure 2 show, as could be expected from the analytical model, that dBmodal/dP values are higher for core positions which are closer to the inner wall of the capillary. However, we note that, very interestingly, the trend that is expected from the analytical model is verified only when the whole core is within the capillary wall. When the core has part of its area outside of the capillary wall, a strong decrease in dBmodal/dP is observed (core region is represented as dark blue ellipses in Figure 2). This allows observing that, for maximizing dBmodal/dP in embedded-core fibers, it is crucial that the whole core is inside the capillary wall. In order to obtain an experimental demonstration of the proposed design acting as a pressure sensor, we performed the fabrication of the embedded-core fiber. The fabrication process is simple and with few steps. Initially, a germanium-doped silica rod is merged to a silica tube. In sequence, the resulting preform is inserted in another silica tube, which acts as a jacket. The preform is then drawn in a fiber tower facility [7]. Figure 3a shows the cross-section of the embedded-core fiber. Figure 3b exposes a diagram of the experimental setup used for pressure mea-

surements. Light from a broadband source (BLS) is launched in the fiber and detected with an optical spectrum analyzer (OSA). Polarizers (P1 and P2) are used to excite the orthogonal modes of the fiber and to recombine them after traveling along the fiber. A pressure chamber is used to subject the fiber to different pressure

shift of the fringes as a function of the pressure variation, <sup>d</sup>λIF

By using the configuration of Figure 3b, an interference spectrum is measured in the OSA. Since the embedded-core fiber is sensitive to pressure variations, the spectral position of the interferometric fringes is shifted when the external pressure level is altered. A sensitivity coefficient, CS, is defined to account for the spectral

be written as a function of the wavelength, λ, the fiber group birefringence, G, and

Modal birefringence derivative as a function of pressure for different core positions inside the capillary wall. Light blue region represents the capillary wall, and dark blue ellipses represent the core region. Insets illustrate

dP . The CS value can also

core dimensions were considered to be 5.7 and 11.4 μm.

Applications of Optical Fibers for Sensing

levels.

Figure 2.

10

the core position within the capillary.

(a) Embedded-core fiber. (b) Experimental setup for pressure sensing measurements. BLS: broadband light source. P1 and P2: polarizers. L1 and L2: objective lenses. PC: pressure chamber. (c) Spectral response of the embedded-core fiber for different pressure levels.

of the modal phase birefringence derivative with respect to the pressure, <sup>∂</sup>Bmodal <sup>∂</sup><sup>P</sup> — Eq. (3) [2].

$$\mathbf{C}\_{S} \equiv \frac{d\lambda\_{IF}}{dP} = \frac{\lambda}{G} \frac{\partial B\_{model}}{\partial P} \tag{3}$$

Figure 3c presents the measured optical response of the embedded-core fiber for different pressurization conditions. It is seen that when the pressure level increases, the fringes blueshift. After performing an appropriate correction on the fiber pressurized and nonpressurized lengths [2, 16], we can estimate a sensitivity value of (1.04 � 0.01) nm/bar [7]. This value is high when compared to other results measured in polarimetric measurements reported in the literature. For example, in [17], a sensitivity of 0.342 nm/bar was measured for a commercial photonic-crystal fiber. Additionally, in [18, 19], the sensitivities of 0.30 and 0.52 nm/bar were reported for specially designed microstructured fibers.

Moreover, the <sup>∂</sup>Bmodal <sup>∂</sup><sup>P</sup> value for the embedded-core fiber can be estimated from Eq. (3). The resulting value is (2.33 � 0.02) � <sup>10</sup>�<sup>7</sup> bar�<sup>1</sup> , which is in the same magnitude order of the ones found for much more sophisticated microstructured fibers [1]. Therefore, we see that the embedded-core fiber structure allows achieving high sensitivity (Cs) and <sup>∂</sup>Bmodal <sup>∂</sup><sup>P</sup> even with a nonoptimized fiber. It also allows recognizing embedded-core fiber as a promising platform for the realization of pressure sensing using optical fibers and a novel route for the design of microstructured optical fiber pressure sensors.

### 4. Embedded-core capillary fibers for temperature sensing

Embedded-core fibers can also act as highly sensitive temperature sensors if a metal is inserted into the hollow part of the capillary (Figure 1b). In analogy to the embedded-core fiber pressure sensor, the principle of operation is based on the induction of stresses inside the capillary and on the consequent variation of the fiber birefringence [8].

In this configuration, the metal expansion inside the capillary causes its volume elements to displace and to compress the silica capillary structure. This, in turn,

entails an asymmetric stress distribution within the capillary wall and induces birefringence variations. An analytical model can be used to predict the most relevant parameters that contribute to the sensor response. This analytical model provides Eq. (4), which accounts for the variation in the material birefringence of the capillary, ΔBmat, for a given temperature variation, ΔT (rin and rout are the capillary inner and outer radii, and C1 and C2 are the silica elasto-optic coefficients). The parameter δ in Eq. (4) is given by Eq. (5), where υ is the Poisson ratio, E is the Young modulus, and α is the thermal expansion coefficient. In Eq. (5), index 1 refers to the filling metal and index 2 refers to silica [8]. By observing Eq. (4) and Eq. (5), it is possible to realize that |ΔBmat| will be greater for positions closer to the inner radius and when the filling metal has a larger thermal expansion coefficient.

$$
\Delta B\_{mat} = -2\delta \Delta T (C\_2 - C\_1) \frac{r\_{out}^2}{\varkappa^2} \tag{4}
$$

5. Surface-core fibers for refractive index sensing

DOI: http://dx.doi.org/10.5772/intechopen.81265

Minimalist Approach for the Design of Microstructured Optical Fiber Sensors

core fiber.

Figure 5.

13

A third sensing opportunity under the approach of simplified optical fiber sensors is the employment of surface-core fibers [9]. In this kind of fibers, the core is placed on the outer surface of the same (Figure 1c). The proximity of the core to the external environment makes surface-core fibers suitable to be used as refractive index sensors, and the off-center position of the core allows these fibers to operate as directional curvature sensors. Figure 5a presents the cross-section of the surface-

In order to explore the refractive index sensitivity of surface core fibers, fiber Bragg gratings (FBGs) can be inscribed in the fiber core [9]. FBGs consist of a refractive index modulation in the core of the fiber able to couple the propagating core mode to a contra-propagating one. The coupling between the modes is

achieved at a specific wavelength, λB, which can be accounted by Eq. (6), where neff is the effective refractive index of the core mode and Λ is the pitch of the grating.

As the optical mode guided in the core directly interfaces the external medium, the effective refractive index of the core mode will be dependent on the external refractive index variations. Thus, if the refractive index of the external environment is altered, a shift in the spectral position of the Bragg peak is expected.

Figure 5b presents the measured wavelength shift of the Bragg peak as a function of the external refractive index. As can be seen in Figure 5b, the results for the surface-core fiber showed low sensitivity. To improve the sensor response, tapers from the surface-core fiber were prepared prior to grating inscription. By doing this, it is possible to enhance the interaction between the guided mode evanescent

(a) Surface-core fiber. (b) Wavelength shift of the Bragg peak as a function of the external refractive index. Reflected Bragg peaks in the (c) untapered surface-core fiber and in the (d) 80 μm and (e) 20 μm tapers.

λ<sup>B</sup> ¼ 2neffΛ (6)

Experimentally, the response of FBGs is seen as a reflection peak at λB.

$$\delta = \frac{(\mathbf{1} + \nu\_2)a\_2 - (\mathbf{1} + \nu\_1)a\_1}{\frac{(\mathbf{1} + \nu\_1)}{E\_1} \left(\nu\_1 - \frac{1}{2}\right) + \frac{(\mathbf{1} + \nu\_2)}{E\_2} \left(\nu\_2 - \frac{1}{2} - \frac{r\_{out}^2}{r\_{in}^2}\right)} \tag{5}$$

Thus, indium was chosen to be the filling metal due to its high thermal expansion coefficient (32.1 � <sup>10</sup>�<sup>6</sup> °C�<sup>1</sup> ) and reasonably low melting point (156°C) [3]. The low melting point is an important property since it simplifies the metal filling process. To insert the metal inside the embedded-core fiber, the metal is molten and pressure is applied to push it into the hollow region.

Figure 4a shows the indium-filled embedded-core fiber. To measure its temperature sensitivity, the same experimental setup as represented in Figure 3b was used. The unique difference is that, for the temperature sensing measurements, the pressure chamber was substituted by a water reservoir placed on a hot plate in order to adequately alter the fiber temperature.

Figure 4b shows the spectra measured for different temperature conditions. We see that there is a spectral shift toward longer wavelengths as the temperature is increased. After performing a suitable correction on the heated and unheated fiber lengths, the sensitivity was calculated to be (8.40 � 0.06) nm/°C [8]. This sensitivity value compares well to the highest temperature sensitivity values reported in the literature such as 9.0[4], 6.6 [20], and 16.49 nm/°C [21], which were measured for photonic-crystal fibers filled with indium, ethanol, and index matching liquid, respectively. This once again demonstrates that embedded-core fibers are a very promising platform for the realization of high-sensitivity optical sensing.

### Figure 4.

(a) Indium-filled embedded-core fiber. (b) Spectral response of the indium-filled embedded-core fiber for different temperature conditions.

Minimalist Approach for the Design of Microstructured Optical Fiber Sensors DOI: http://dx.doi.org/10.5772/intechopen.81265
