5. Surface-core fibers for refractive index sensing

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.

ΔBmat ¼ �2δΔT Cð Þ <sup>2</sup> � C<sup>1</sup>

<sup>δ</sup> <sup>¼</sup> ð Þ <sup>1</sup> <sup>þ</sup> <sup>ν</sup><sup>2</sup> <sup>α</sup><sup>2</sup> � ð Þ <sup>1</sup> <sup>þ</sup> <sup>ν</sup><sup>1</sup> <sup>α</sup><sup>1</sup>

2 <sup>þ</sup> ð Þ <sup>1</sup>þν<sup>2</sup>

Thus, indium was chosen to be the filling metal due to its high thermal expan-

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

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

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.

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

ð Þ 1þν<sup>1</sup> <sup>E</sup><sup>1</sup> <sup>ν</sup><sup>1</sup> � <sup>1</sup>

°C�<sup>1</sup>

pressure is applied to push it into the hollow region.

to adequately alter the fiber temperature.

sion coefficient (32.1 � <sup>10</sup>�<sup>6</sup>

Applications of Optical Fibers for Sensing

Figure 4.

12

different temperature conditions.

r2 out

> <sup>2</sup> � <sup>r</sup><sup>2</sup> out r2 in

) and reasonably low melting point (156°C) [3].

<sup>E</sup><sup>2</sup> <sup>ν</sup><sup>2</sup> � <sup>1</sup>

<sup>x</sup><sup>2</sup> (4)

(5)

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 surfacecore fiber.

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

$$
\lambda\_{\mathbb{B}} = 2n\_{\text{eff}}\Lambda \tag{6}
$$

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

### Figure 5.

(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.

field and the external medium and improve the sensitivity. The results measured for tapers with 80 and 20 μm diameter are also shown in Figure 5b. The Bragg peaks for the untapered surface-core and for the 80 and 20 μm tapers are shown in Figure 5c–e—the gratings were imprinted via phase-mask technique by employing phase masks with pitches 1075.34 nm (for the 80 μm taper) and 1071.2 nm (for the untapered fiber and for the 20 μm taper). Around 1.42 RIU (refractive index unit), the measured sensitivities were 8 and 40 nm/RIU for the 80 and 20 μm tapers, respectively. These sensitivity values compare well with other results for FBG-based refractive index sensors. In [22], it is reported a sensitivity of 15 nm/RIU for a Bragg grating inscribed in a 6–μm-thick taper (measured around 1.326 and 1.378 RIU) and, in [23], a sensitivity of 30 nm/RIU was measured for a 8.5-μm taper (in the same refractive index range). It is worth observing that the results for surface-core fibers were attained for thicker tapers, which implies in sensor robustness improvement.

University (Finland) [10] by immersing the sensor into glycerol-water solutions at different concentrations. Figure 6c shows the transmittance spectra as a function of the external refractive index. By following the spectral position of the spectral dip, we could measure a sensitivity of 1380 nm/RIU. This sensitivity value is comparable to the ones reported for other plasmonic sensors, which employ fragile fiber tapers and more sophisticated microstructured optical fibers [24, 25]. Thus, we can visualize that the plasmonic sensor based on a gold-coated surface-core fiber is a powerful platform for the realization of highly sensitive refractive index sensing. Moreover, the setup presents the advantages of increased robustness when compared to fragile fiber tapers and simpler preparation than the sensors, which

Besides refractive index sensing using Bragg gratings or surface plasmon resonance, surface-core fibers also offer the possibility of the realization of directional curvature sensing. This is possible because the off-center position of the fiber core allows it to experience compression or expansion depending on the curvature direction. In this context, a FBG can be inscribed in the core of the surface-core fiber for probing the bend-induced strain levels inside the core and determine the

Compression and expansion of the core introduces strain levels in it. The induced strain in a bent fiber, ε, is proportional to the curvature, C (�1/curvature radius). If the core is at a distance y from the fiber neutral axis, the induced strain level can be calculated from Eq. (7) [26]. Since the existence of a strain level in a fiber entails variations in its refractive index (by virtue of the strain optic effect) and length, the spectral response of a FBG in this fiber is expected to shift when it is subjected to strain increments. Eq. (8) describes the dependence of the Bragg peak shift as a function of the curvature. In Eq. (8), P<sup>ε</sup> is the photoelastic coefficient of

To experimentally test the response of the proposed sensor, a FBG was imprinted in the surface-core fiber (by using a phase mask with 1071.2 nm pitch) and the fiber was subjected to curvature increments. The results of the curvature sensing measurements are exposed in Figure 7. It is seen that when the fiber experiences expansion, the Bragg peak spectral position redshifts (positive spectral shift). Otherwise, when the fiber is compressed by the bending, the Bragg peak blueshifts (negative spectral shift). The measured sensitivities were (188 � 5) and (202 � 5) pm/m�<sup>1</sup> for the expansion and compression conditions, respectively. The achieved sensitivity values are high when compared to other FBG-based sensors whose performance is reported in the literature (sensitivities from 50 to

ε ¼ y C (7)

Δλ<sup>B</sup> ¼ ð Þ 1 � P<sup>ε</sup> λBε ¼ ½ � ð Þ 1 � P<sup>ε</sup> λBy C (8)

) [28–30]. Additionally, the sensitivity for the surface-core fiber sensor

is greater than the one obtained for FBGs sensors in eccentric core polymer optical fibers [31]. It is worth saying, however, that greater sensitivity values can be attained in other configurations. For example, we find in the literature that fibers with two or three cores can provide sensitivities of hundreds of nanometers per inverse meter [32, 33]. Nevertheless, the spectral features whose spectral shifts are considered in [32, 33] are much broader than the Bragg peak in the surface-core fiber we measured. This has an important impact on the sensor resolution. For the

demand metal coating of the inner holes of microstructured fibers.

Minimalist Approach for the Design of Microstructured Optical Fiber Sensors

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

6. Surface-core fibers for directional curvature sensing

direction of the curvature.

silica (P<sup>ε</sup> = 0.22) [27].

100 pm/m�<sup>1</sup>

15

Another possibility for exploring the sensitivity of surface-core fibers to variations in the refractive index of the external medium is to functionalize the core with a metallic nanolayer and make the fiber to act as a plasmonic sensor. In this approach, the core mode can be resonantly coupled to a plasmonic mode when phase-matching occurs between them (surface plasmon resonance—SPR). The coupling between these modes is seen as a spectral dip at the wavelength where the phase matching condition is achieved. As the fiber core directly interfaces the external medium, the spectral position of the plasmonic resonance will be dependent on the refractive index of the external environment. The sensitivity of the configuration is, therefore, accounted from the spectral shift of the plasmonic resonance as a function of the external refractive index variation.

Figure 6a presents a simulation on the transmittance of the surface-core fiber plasmonic sensor for different refractive index values. In the simulations, the fiber core is assumed to have a 10 μm diameter and to be coated with a gold layer of 50 nm thick. It is seen that the plasmonic resonance is shifted toward longer wavelengths as the external refractive index increases. The sensitivity accounted from the simulations is 1290 nm/RIU. In addition, in Figure 6b, the core mode intensity profiles are shown when it is not phase-matched (off-resonance) and when it is phase-matched (in resonance) with the plasmonic mode. We can observe that, when the modes are in resonance, they hybridize. The intensity profiles in Figure 6b were calculated for an external refractive index of 1.39. The phasematched intensity profile was accounted at 600 nm and the one for the offresonance condition was accounted at 720 nm.

To experimentally test the proposed sensor, the fiber core was coated with a gold layer of 50 nm thick, and sensing measurements were performed at the Aalto

### Figure 6.

(a) Simulated transmittance for different external refractive indexes (next). (b) Intensity profiles of the core mode when off-resonance and when in resonance with the plasmonic mode. (c) Experimental transmittance for different external refractive indices.

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

University (Finland) [10] by immersing the sensor into glycerol-water solutions at different concentrations. Figure 6c shows the transmittance spectra as a function of the external refractive index. By following the spectral position of the spectral dip, we could measure a sensitivity of 1380 nm/RIU. This sensitivity value is comparable to the ones reported for other plasmonic sensors, which employ fragile fiber tapers and more sophisticated microstructured optical fibers [24, 25]. Thus, we can visualize that the plasmonic sensor based on a gold-coated surface-core fiber is a powerful platform for the realization of highly sensitive refractive index sensing. Moreover, the setup presents the advantages of increased robustness when compared to fragile fiber tapers and simpler preparation than the sensors, which demand metal coating of the inner holes of microstructured fibers.

## 6. Surface-core fibers for directional curvature sensing

Besides refractive index sensing using Bragg gratings or surface plasmon resonance, surface-core fibers also offer the possibility of the realization of directional curvature sensing. This is possible because the off-center position of the fiber core allows it to experience compression or expansion depending on the curvature direction. In this context, a FBG can be inscribed in the core of the surface-core fiber for probing the bend-induced strain levels inside the core and determine the direction of the curvature.

Compression and expansion of the core introduces strain levels in it. The induced strain in a bent fiber, ε, is proportional to the curvature, C (�1/curvature radius). If the core is at a distance y from the fiber neutral axis, the induced strain level can be calculated from Eq. (7) [26]. Since the existence of a strain level in a fiber entails variations in its refractive index (by virtue of the strain optic effect) and length, the spectral response of a FBG in this fiber is expected to shift when it is subjected to strain increments. Eq. (8) describes the dependence of the Bragg peak shift as a function of the curvature. In Eq. (8), P<sup>ε</sup> is the photoelastic coefficient of silica (P<sup>ε</sup> = 0.22) [27].

$$
\varepsilon = \mathcal{Y} \cdot \mathbf{C} \tag{7}
$$

$$
\Delta\lambda\_B = (\mathbf{1} - P\_e)\lambda\_B e = [(\mathbf{1} - P\_e)\lambda\_B y]\mathbf{C} \tag{8}
$$

To experimentally test the response of the proposed sensor, a FBG was imprinted in the surface-core fiber (by using a phase mask with 1071.2 nm pitch) and the fiber was subjected to curvature increments. The results of the curvature sensing measurements are exposed in Figure 7. It is seen that when the fiber experiences expansion, the Bragg peak spectral position redshifts (positive spectral shift). Otherwise, when the fiber is compressed by the bending, the Bragg peak blueshifts (negative spectral shift). The measured sensitivities were (188 � 5) and (202 � 5) pm/m�<sup>1</sup> for the expansion and compression conditions, respectively.

The achieved sensitivity values are high when compared to other FBG-based sensors whose performance is reported in the literature (sensitivities from 50 to 100 pm/m�<sup>1</sup> ) [28–30]. Additionally, the sensitivity for the surface-core fiber sensor is greater than the one obtained for FBGs sensors in eccentric core polymer optical fibers [31]. It is worth saying, however, that greater sensitivity values can be attained in other configurations. For example, we find in the literature that fibers with two or three cores can provide sensitivities of hundreds of nanometers per inverse meter [32, 33]. Nevertheless, the spectral features whose spectral shifts are considered in [32, 33] are much broader than the Bragg peak in the surface-core fiber we measured. This has an important impact on the sensor resolution. For the

field and the external medium and improve the sensitivity. The results measured for tapers with 80 and 20 μm diameter are also shown in Figure 5b. The Bragg peaks for the untapered surface-core and for the 80 and 20 μm tapers are shown in Figure 5c–e—the gratings were imprinted via phase-mask technique by employing phase masks with pitches 1075.34 nm (for the 80 μm taper) and 1071.2 nm (for the untapered fiber and for the 20 μm taper). Around 1.42 RIU (refractive index unit), the measured sensitivities were 8 and 40 nm/RIU for the 80 and 20 μm tapers, respectively. These sensitivity values compare well with other results for FBG-based refractive index sensors. In [22], it is reported a sensitivity of 15 nm/RIU for a Bragg grating inscribed in a 6–μm-thick taper (measured around 1.326 and 1.378 RIU) and, in [23], a sensitivity of 30 nm/RIU was measured for a 8.5-μm taper (in the same refractive index range). It is worth observing that the results for surface-core

fibers were attained for thicker tapers, which implies in sensor robustness

a metallic nanolayer and make the fiber to act as a plasmonic sensor. In this approach, the core mode can be resonantly coupled to a plasmonic mode when phase-matching occurs between them (surface plasmon resonance—SPR). The coupling between these modes is seen as a spectral dip at the wavelength where the phase matching condition is achieved. As the fiber core directly interfaces the external medium, the spectral position of the plasmonic resonance will be dependent on the refractive index of the external environment. The sensitivity of the configuration is, therefore, accounted from the spectral shift of the plasmonic

resonance as a function of the external refractive index variation.

resonance condition was accounted at 720 nm.

Another possibility for exploring the sensitivity of surface-core fibers to variations in the refractive index of the external medium is to functionalize the core with

Figure 6a presents a simulation on the transmittance of the surface-core fiber plasmonic sensor for different refractive index values. In the simulations, the fiber core is assumed to have a 10 μm diameter and to be coated with a gold layer of 50 nm thick. It is seen that the plasmonic resonance is shifted toward longer wavelengths as the external refractive index increases. The sensitivity accounted from the simulations is 1290 nm/RIU. In addition, in Figure 6b, the core mode intensity profiles are shown when it is not phase-matched (off-resonance) and when it is phase-matched (in resonance) with the plasmonic mode. We can observe that, when the modes are in resonance, they hybridize. The intensity profiles in Figure 6b were calculated for an external refractive index of 1.39. The phasematched intensity profile was accounted at 600 nm and the one for the off-

To experimentally test the proposed sensor, the fiber core was coated with a gold

layer of 50 nm thick, and sensing measurements were performed at the Aalto

(a) Simulated transmittance for different external refractive indexes (next). (b) Intensity profiles of the core mode when off-resonance and when in resonance with the plasmonic mode. (c) Experimental transmittance for

improvement.

Applications of Optical Fibers for Sensing

Figure 6.

14

different external refractive indices.

Figure 7. Wavelength shift as a function of the curvature, representation of the curvature direction and spectral response of the directional curvature sensor based on a FBG inscribed in a surface-core fiber.

sensor reported in [32], for example, one can estimate a resolution limit of 0.01 m�<sup>1</sup> , which is similar to the one we can find in our results (0.02 m�<sup>1</sup> ).

### 7. Polymer capillary fibers for temperature sensing

A simpler structure, which can be employed in sensing measurements , is capillary fibers [12]. In our approach, we investigated the sensitivity of polymer capillary fibers to temperature variations by studying the spectral characteristics of the light that is transmitted through its hollow part.

The typical transmission spectra through the hollow part of capillaries have wavelengths of high loss, λmin. These wavelengths encounter high leakage during propagation because they are resonant with the capillary wall. At these wavelengths, which are given by Eq. (9), transmission minima are observed. In Eq. (9), n1 is the refractive index of the hollow core, n2 is the refractive index of the capillary material, d is the thickness of the capillary wall, and m is the order of the minimum. Eq. (9) tells that if the thickness and the refractive index of the capillary are altered, the minima spectral locations are expected to shift. As temperature variations are able to change both these parameters, capillary fibers can act as temperature sensors.

$$
\lambda\_{\min} = \frac{2n\_1 d}{m} \sqrt{\left(\frac{n\_2}{n\_1}\right)^2 - 1} \tag{9}
$$

where Din is inner diameter of the capillary and uμυ is a root of the equation

(a) Simulated transmittance of a capillary fiber 2 cm long and with 160 μm inner diameter and 240 μm outer diameter. (b) Experimental transmitted spectrum for a 13 cm long PMMA capillary fiber. Insets stands for the experimental setup (BLS: broadband light source; MMF: multimode fiber; OSA: optical spectrum analyzer)

� �ln 1 � <sup>1</sup> � <sup>Γ</sup><sup>2</sup> � �<sup>2</sup>

n1

n1

To experimentally test the proposed sensor, a PMMA capillary fiber was fabricated (with inner diameter 160 μm and outer diameter 240 μm) and its performance as a temperature sensor was measured. In the experimental setup, light from a broadband light source was coupled to the capillary fiber (13 cm length) and collected from it by using silica multimode fibers, as shown in the inset of

Figure 8b. A typical transmission spectrum is shown in Figure 8b, and the wavelength shift (Δλ) as a function of the temperature variation (ΔT) is shown in the inset in Figure 8b. A sensitivity of (�140 � 6) pm/°C was measured. This sensitivity is around 14 times higher than conventional Bragg gratings-based temperature

In this chapter, we presented the recent research yields of our group in the State

University of Campinas (Unicamp, Brazil) regarding ultra-simplified

Figure 8a presents the simulation for a transmission minimum of a PMMA capillary with 2 cm length, inner diameter 160 μm, and outer diameter 240 μm for different temperature conditions. In the simulation, both thermal expansion and thermo-optic effects are considered. It is seen that, when the temperature increases, the transmission dip is expected to blueshift. It is worth saying that, for the consid-

r

<sup>1</sup> � <sup>Γ</sup><sup>2</sup> � �<sup>2</sup> <sup>þ</sup> <sup>4</sup>Γ<sup>2</sup> sin <sup>2</sup> <sup>2</sup>πn2<sup>d</sup>

<sup>1</sup> � <sup>n</sup><sup>1</sup> n2 � �<sup>2</sup>

<sup>1</sup> � <sup>n</sup><sup>1</sup> n2 � �<sup>2</sup> λ

sin <sup>2</sup>θ<sup>1</sup>

sin <sup>2</sup>θ<sup>1</sup>

<sup>r</sup> (11)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

sin <sup>2</sup>θ<sup>1</sup>

9 >>>>=

>>>>;

(10)

<sup>1</sup> � <sup>n</sup><sup>1</sup> n2 � �<sup>2</sup>

! r

Jυ-1(uμυ) = 0, where J is the Bessel function [34, 35].

and for the wavelength shift (Δλ) as a function of the temperature variation (ΔT).

Minimalist Approach for the Design of Microstructured Optical Fiber Sensors

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

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � sin <sup>2</sup>θ<sup>1</sup> <sup>p</sup> � <sup>n</sup><sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � sin <sup>2</sup>θ<sup>1</sup> <sup>p</sup> <sup>þ</sup> <sup>n</sup><sup>2</sup>

ered capillary fiber, the thermo-optic effect is the dominant effect.

L Din tan θ<sup>1</sup>

Γ ¼

8 >>>><

>>>>:

Pout ¼ Pin exp

Figure 8.

sensors [36].

17

8. Conclusions

Taking this into account, polymethyl methacrylate (PMMA) capillaries were chosen to be used in this investigation. This decision was due to the high thermal expansion coefficient of PMMA (2.2 � <sup>10</sup>�<sup>4</sup> °C�<sup>1</sup> ) and its high thermo-optic coefficient (�1.3 � <sup>10</sup>�<sup>4</sup> °C�<sup>1</sup> ).

An analytical model can be used to investigate the influences of the thermal expansion and of the thermo-optic effect in the sensor [11, 34]. Eq. (10) presents an expression for calculating the output power (Pout) as a function of the wavelength (λ). In Eq. (10), Pin is the input power, L is the fiber length, d is the capillary wall thickness, n1 and n2 are refractive indexes of the hollow core and of the capillary material, and the parameter Γ is given by Eq. (11). In Eq. (10) and Eq. (11), θ<sup>1</sup> is the angle of incidence of the light rays on the capillary wall for a specific leaky mode—given by <sup>θ</sup><sup>1</sup> <sup>¼</sup> sin �<sup>1</sup> neff n1 � �. In the expression for <sup>θ</sup>1, the effective refractive index of the leaky mode guided in the core, neff, can be found by neff <sup>¼</sup> <sup>1</sup> � <sup>1</sup> 2 uμνλ <sup>π</sup>Din � �<sup>2</sup> , Minimalist Approach for the Design of Microstructured Optical Fiber Sensors DOI: http://dx.doi.org/10.5772/intechopen.81265

Figure 8.

,

(9)

2 uμνλ πDin � �<sup>2</sup> ,

) and its high thermo-optic coeffi-

).

sensor reported in [32], for example, one can estimate a resolution limit of 0.01 m�<sup>1</sup>

Wavelength shift as a function of the curvature, representation of the curvature direction and spectral response

A simpler structure, which can be employed in sensing measurements , is capillary fibers [12]. In our approach, we investigated the sensitivity of polymer capillary fibers to temperature variations by studying the spectral characteristics of the light

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2 n1 � �<sup>2</sup>

°C�<sup>1</sup>

s

Taking this into account, polymethyl methacrylate (PMMA) capillaries were chosen to be used in this investigation. This decision was due to the high thermal

An analytical model can be used to investigate the influences of the thermal expansion and of the thermo-optic effect in the sensor [11, 34]. Eq. (10) presents an expression for calculating the output power (Pout) as a function of the wavelength (λ). In Eq. (10), Pin is the input power, L is the fiber length, d is the capillary wall thickness, n1 and n2 are refractive indexes of the hollow core and of the capillary material, and the parameter Γ is given by Eq. (11). In Eq. (10) and Eq. (11), θ<sup>1</sup> is the angle of incidence of the light rays on the capillary wall for a specific leaky

� 1

. In the expression for θ1, the effective refractive

The typical transmission spectra through the hollow part of capillaries have wavelengths of high loss, λmin. These wavelengths encounter high leakage during propagation because they are resonant with the capillary wall. At these wavelengths, which are given by Eq. (9), transmission minima are observed. In Eq. (9), n1 is the refractive index of the hollow core, n2 is the refractive index of the capillary material, d is the thickness of the capillary wall, and m is the order of the minimum. Eq. (9) tells that if the thickness and the refractive index of the capillary are altered, the minima spectral locations are expected to shift. As temperature variations are able to change both these parameters, capillary fibers can act as temperature sensors.

> <sup>λ</sup>min <sup>¼</sup> <sup>2</sup>n1<sup>d</sup> m

n1 � �

index of the leaky mode guided in the core, neff, can be found by neff <sup>¼</sup> <sup>1</sup> � <sup>1</sup>

which is similar to the one we can find in our results (0.02 m�<sup>1</sup>

of the directional curvature sensor based on a FBG inscribed in a surface-core fiber.

7. Polymer capillary fibers for temperature sensing

that is transmitted through its hollow part.

Applications of Optical Fibers for Sensing

expansion coefficient of PMMA (2.2 � <sup>10</sup>�<sup>4</sup>

°C�<sup>1</sup> ).

mode—given by <sup>θ</sup><sup>1</sup> <sup>¼</sup> sin �<sup>1</sup> neff

cient (�1.3 � <sup>10</sup>�<sup>4</sup>

16

Figure 7.

(a) Simulated transmittance of a capillary fiber 2 cm long and with 160 μm inner diameter and 240 μm outer diameter. (b) Experimental transmitted spectrum for a 13 cm long PMMA capillary fiber. Insets stands for the experimental setup (BLS: broadband light source; MMF: multimode fiber; OSA: optical spectrum analyzer) and for the wavelength shift (Δλ) as a function of the temperature variation (ΔT).

where Din is inner diameter of the capillary and uμυ is a root of the equation Jυ-1(uμυ) = 0, where J is the Bessel function [34, 35].

$$P\_{out} = P\_{in} \exp\left\{ \left(\frac{L}{D\_{in}\tan\theta\_1}\right) \ln \left[1 - \frac{\left(1 - \Gamma^2\right)^2}{\left(1 - \Gamma^2\right)^2 + 4\Gamma^2 \sin^2\left(\frac{2\pi n\_d d}{\lambda} \sqrt{1 - \left(\frac{n\_i}{n\_2}\right)^2 \sin^2\theta\_1}\right)}\right] \right\} \tag{10}$$

$$\Gamma = \frac{\sqrt{\mathbf{1} - \sin^2 \theta\_1} - \frac{\mathbf{n}\_2}{\mathbf{n}\_1} \sqrt{\mathbf{1} - \left(\frac{\mathbf{n}\_1}{\mathbf{n}\_2}\right)^2 \sin^2 \theta\_1}}{\sqrt{\mathbf{1} - \sin^2 \theta\_1} + \frac{\mathbf{n}\_2}{\mathbf{n}\_1} \sqrt{\mathbf{1} - \left(\frac{\mathbf{n}\_1}{\mathbf{n}\_2}\right)^2 \sin^2 \theta\_1}}\tag{11}$$

Figure 8a presents the simulation for a transmission minimum of a PMMA capillary with 2 cm length, inner diameter 160 μm, and outer diameter 240 μm for different temperature conditions. In the simulation, both thermal expansion and thermo-optic effects are considered. It is seen that, when the temperature increases, the transmission dip is expected to blueshift. It is worth saying that, for the considered capillary fiber, the thermo-optic effect is the dominant effect.

To experimentally test the proposed sensor, a PMMA capillary fiber was fabricated (with inner diameter 160 μm and outer diameter 240 μm) and its performance as a temperature sensor was measured. In the experimental setup, light from a broadband light source was coupled to the capillary fiber (13 cm length) and collected from it by using silica multimode fibers, as shown in the inset of Figure 8b. A typical transmission spectrum is shown in Figure 8b, and the wavelength shift (Δλ) as a function of the temperature variation (ΔT) is shown in the inset in Figure 8b. A sensitivity of (�140 � 6) pm/°C was measured. This sensitivity is around 14 times higher than conventional Bragg gratings-based temperature sensors [36].

## 8. Conclusions

In this chapter, we presented the recent research yields of our group in the State University of Campinas (Unicamp, Brazil) regarding ultra-simplified

microstructured optical fibers designs for sensing applications. In this context, we firstly discussed hollow and metal-filled embedded-core fibers as pressure and temperature sensors. We showed that the achieved sensitivities with this structure are high when compared to other sensors which employ much more sophisticated fiber designs. Additionally, we described surface-core fibers as refractive index and directional curvature sensors by employing fiber Bragg gratings and a plasmonic configuration. Finally, polymer capillary fibers were presented as an even simpler structure for temperature sensing.

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The results presented herein demonstrate the great potential of capillary-like fibers to act as sensors for multiple purposes. Hence, it is possible to identify that this minimalist approach for the design of microstructured fiber sensors consists of a novel and very promising avenue for obtaining sensors with simplified structures and optimized performances.
