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Superstructure Fiber Bragg Grating Sensors for Multiparameter Sensing

Hamid Alemohammad AOMS Technologies Inc., Toronto, ON, Canada

Abstract

This chapter is focused on the modeling, design, and fabrication of superstructure fiber Bragg gratings (SFBGs) for the simultaneous measurement of temperature and strain. The methodology for the development of a structural model, along with the opto-mechanical model of SFBGs, is presented. The chapter concludes with experimental results consisting of the optical response of SFBGs exposed to structural loading and temperature variations, and also, the simultaneous measurement of strain and temperature.

Keywords

On-fiber film; Opto-mechanical modeling; Periodic coating; Superstructure fiber Bragg grating; Strain; Temperature

2.1. Superstructure Fiber Bragg Gratings With Periodic On-Fiber Films

Superstructure fiber Bragg gratings (SFBGs) are secondary modulations of the index of refraction along the FBG axis with a longer period (typically larger than 100 μm) compared to the Bragg gratings. The long-period variations in the index of refraction cause the formation of equally spaced sidebands in the reflection spectrum of FBGs, as described in Chapter 1.

The concept of SFBGs can also be realized by the deposition of periodic coatings (i.e., metal films) on FBGs, as shown in Fig. 2.1. In an SFBG with periodically deposited on-fiber films, a periodic distribution of strain is induced along the grating when the fiber is exposed to axial force (F) or thermal heating/cooling (ΔT). This is due to the differences in the geometries and the thermal expansions of the coating material and the optical fiber. The periodic distribution of the strain components along the grating causes the periodic variations in the average index of refraction (

\bar{Δ n}

$\bar{Δ n}$

) due to photoelastic effects. In addition to the index of refraction, the grating pitch (Λ) varies periodically along the fiber axis. The sideband spacing in the reflection spectrum of the SFBG, coated with coatings with a period of Γ, is derived from the phase matching condition as described in Chapter 1:

Δ λ = \frac{λ_{B}^{2}}{2 n_{e f f} Γ}

$Δ λ = \frac{λ_{B}^{2}}{2 n_{e f f} Γ}$

(2.1)

The periodically spaced sidebands in the reflection spectrum of SFBGs have a broad range of applications in fiber lasers and tunable filters [3]. In contrast to the SFBGs fabricated by UV exposure, the reflectivity of the sidebands in SFBGs with on-fiber films can be tuned by changing temperature and force applied on the fiber. The concept of tunable SFBGs via the fabrication of metal films on optical fibers has been elaborated on in Ref. [2] by proposing tunable SFBGs for wavelength-division multiplexing, optical sensing, and fiber lasers. In their work, thin films of gold with periodic variable diameters were deposited on a predeposited on-fiber titanium thin film by using electron beam evaporation. They showed that joule heating causes the periodic distribution of temperature along the fiber axis, which creates sidebands whose reflectivities can be tuned by electric current.

Figure 2.1 Periodic coatings on a fiber Bragg grating and their effects on the average index of refraction ( $\bar{Δ n}$ $\bar{Δ n}$ ) when the optical fiber is exposed to axial tensile force and/or temperature variations [2]. Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

From the sensing point of view, SFBGs with periodic coatings can be used for multiparameter measurements, which eliminates the inherent limitations of FBGs in thermal and structural sensing. The intensity of the sidebands generated in SFBGs is regulated by the applied temperature and force on the optical fiber. The intensity of the sidebands combined with the Bragg wavelength shift can be used to decouple the effects of temperature and strain [1,4,5].

2.2. Opto-Mechanical Modeling

To design SFBGs with multiparameter sensing capabilities, an opto-mechanical model can be developed. The model consists of two components: (1) a structural model of SFBGs to obtain the state of stress and strain in optical fibers and (2) an opto-mechanical model consisting of the photoelastic and thermooptic effects to obtain the reflection spectrum of SFBGs.

2.2.1. Structural Modeling of Superstructure Fiber Bragg Gratings Exposed to Force and Temperature Variations

For the structural modeling, it is assumed that the optical fiber is uniformly heated by ΔT and is exposed to an axial tensile force of F. The approach is similar to the modeling of thick-walled cylinders under structural loading and temperature variations [6]. Fig. 2.2 demonstrates the coated segment of the optical fiber in cylindrical coordinates (r,θ,z). It is assumed that the optical fiber with a diameter of r_f is coated with a layer with a thickness of t = r_c − r_f.

The displacement component in the θ direction (v) is neglected, because of the symmetry, and the dependency of the radial and axial displacements (u, w) on z is considered to be small at the points far from the ends. At these points, the shear components are also zero because of symmetry. The strain-displacement relations are written as in Ref. [3],

Figure 2.2 Coated segment of an optical fiber in cylindrical coordinates [2]. Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

\begin{matrix} e_{r r} = \frac{d u}{d r} \\ e_{θ θ} = \frac{u}{r} \end{matrix}

$\begin{matrix} e_{r r} = \frac{d u}{d r} \\ e_{θ θ} = \frac{u}{r} \end{matrix}$

(2.2)

where e_rr and e_θθ are the radial and tangential strain components and are related as

\frac{d}{d r} (r e_{θ θ}) = e_{r r}

$\frac{d}{d r} (r e_{θ θ}) = e_{r r}$

(2.3)

From the equilibrium conditions, the radial and tangential stress components, σ_rr and σ_θθ, are related as

r \frac{d σ_{r r}}{d r} = σ_{θ θ} - σ_{r r}

$r \frac{d σ_{r r}}{d r} = σ_{θ θ} - σ_{r r}$

(2.4)

which yields

\frac{d}{d r} (r σ_{r r}) = σ_{θ θ}

$\frac{d}{d r} (r σ_{r r}) = σ_{θ θ}$

(2.5)

The stress–strain–temperature relations are written as

[\begin{matrix} e_{r r} \\ e_{θ θ} \\ e_{z z} \end{matrix}] = \frac{1}{E} [\begin{matrix} 1 & - ν & - ν \\ - ν & 1 & - ν \\ - ν & - ν & 1 \end{matrix}] [\begin{matrix} σ_{r r} \\ σ_{θ θ} \\ σ_{z z} \end{matrix}] + α Δ T

$[\begin{matrix} e_{r r} \\ e_{θ θ} \\ e_{z z} \end{matrix}] = \frac{1}{E} [\begin{matrix} 1 & - ν & - ν \\ - ν & 1 & - ν \\ - ν & - ν & 1 \end{matrix}] [\begin{matrix} σ_{r r} \\ σ_{θ θ} \\ σ_{z z} \end{matrix}] + α Δ T$

(2.6)

where ν is the Poisson ratio, E is the modulus of elasticity, and α is the coefficient of thermal expansion. By integrating Eqs. (2.3) and (2.5) and using Eq. (2.6), the stress components in the optical fiber and the coating are obtained as follows:

\begin{matrix} σ_{r r}^{f} = \frac{- α_{f} E_{f}}{2 (1 - ν_{f})} Δ T + C_{1}^{f} \\ σ_{θ θ}^{f} = \frac{- α_{f} E_{f}}{2 (1 - ν_{f})} Δ T + C_{1}^{f} \\ σ_{r r}^{c} = \frac{- α_{c} E_{c}}{2 (1 - ν_{c})} Δ T + C_{1}^{c} (1 - \frac{r_{f}^{2}}{r^{2}}) + \frac{C_{2}^{c}}{r^{2}} \\ σ_{θ θ}^{c} = \frac{- α_{c} E_{c}}{2 (1 - ν_{c})} Δ T - C_{1}^{c} (1 - \frac{r_{f}^{2}}{r^{2}}) - \frac{C_{2}^{c}}{r^{2}} \end{matrix}

$\begin{matrix} σ_{r r}^{f} = \frac{- α_{f} E_{f}}{2 (1 - ν_{f})} Δ T + C_{1}^{f} \\ σ_{θ θ}^{f} = \frac{- α_{f} E_{f}}{2 (1 - ν_{f})} Δ T + C_{1}^{f} \\ σ_{r r}^{c} = \frac{- α_{c} E_{c}}{2 (1 - ν_{c})} Δ T + C_{1}^{c} (1 - \frac{r_{f}^{2}}{r^{2}}) + \frac{C_{2}^{c}}{r^{2}} \\ σ_{θ θ}^{c} = \frac{- α_{c} E_{c}}{2 (1 - ν_{c})} Δ T - C_{1}^{c} (1 - \frac{r_{f}^{2}}{r^{2}}) - \frac{C_{2}^{c}}{r^{2}} \end{matrix}$

(2.7)

where

C_{1}^{c}

$C_{1}^{c}$

C_{1}^{f}

$C_{1}^{f}$

, and

C_{2}^{c}

$C_{2}^{c}$

are integration constants and the superscripts f and c are associated with the optical fiber and the coating, respectively. Considering the following boundary conditions,

\begin{matrix} e_{z z}^{f} = e_{z z}^{c} \\ σ_{z z}^{f} A_{f} + σ_{z z}^{c} A_{c} = F \\ σ_{r r}^{c} (r_{c}) = 0 \\ e_{θ θ}^{f} (r_{f}) = e_{θ θ}^{c} (r_{f}) \\ \int_{r_{f}}^{r_{c}} σ_{θ θ}^{c} d r = \int_{0}^{r_{l}} σ_{θ θ}^{f} d r \end{matrix}

$\begin{matrix} e_{z z}^{f} = e_{z z}^{c} \\ σ_{z z}^{f} A_{f} + σ_{z z}^{c} A_{c} = F \\ σ_{r r}^{c} (r_{c}) = 0 \\ e_{θ θ}^{f} (r_{f}) = e_{θ θ}^{c} (r_{f}) \\ \int_{r_{f}}^{r_{c}} σ_{θ θ}^{c} d r = \int_{0}^{r_{l}} σ_{θ θ}^{f} d r \end{matrix}$

(2.8)

σ_{z z}^{f}

$σ_{z z}^{f}$

σ_{z z}^{c}

$σ_{z z}^{c}$

C_{1}^{c}

$C_{1}^{c}$

C_{1}^{f}

$C_{1}^{f}$

, and

C_{2}^{c}

$C_{2}^{c}$

are obtained, which are substituted in Eqs. (2.6) and (2.7) to obtain the strain components.

2.2.2. Opto-Mechanical Modeling of Superstructure Fiber Bragg Gratings With Periodic On-Fiber Films

The results of the structural modeling are used in the opto-mechanical model to find the anisotropic index of refraction and the modified effective mode index of refraction in the coated and uncoated segments of the optical fiber. The anisotropic index of refraction and modified effective mode index of refraction are used along with the coupled mode equations to obtain the spectral response of SFBGs. According to Chapter 1, the coupled-mode theory for FBGs can be written as

\begin{matrix} \frac{d R (z)}{d z} = - i (\frac{2 π n_{e f f}}{λ} - \frac{π}{Λ} - \frac{1}{2} \frac{d Φ}{d z} + K_{d c}) R (z) - i K_{A C} S (z) \\ \frac{d S (z)}{d z} = i (\frac{2 π n_{e f f}}{λ} - \frac{π}{Λ} - \frac{1}{2} \frac{d Φ}{d z} + K_{d c}) S (z) + i K_{A C} R (z) \end{matrix}

$\begin{matrix} \frac{d R (z)}{d z} = - i (\frac{2 π n_{e f f}}{λ} - \frac{π}{Λ} - \frac{1}{2} \frac{d Φ}{d z} + K_{d c}) R (z) - i K_{A C} S (z) \\ \frac{d S (z)}{d z} = i (\frac{2 π n_{e f f}}{λ} - \frac{π}{Λ} - \frac{1}{2} \frac{d Φ}{d z} + K_{d c}) S (z) + i K_{A C} R (z) \end{matrix}$

(2.9)

By defining

ρ (z) = \frac{S (z)}{R (z)}

$ρ (z) = \frac{S (z)}{R (z)}$

(2.10)

and taking the derivative of Eq. (2.10),

\frac{d ρ (z)}{d z} = \frac{1}{R (z)} \frac{d S (z)}{d z} - \frac{ρ (z)}{R (z)} \frac{d R (z)}{d z}

$\frac{d ρ (z)}{d z} = \frac{1}{R (z)} \frac{d S (z)}{d z} - \frac{ρ (z)}{R (z)} \frac{d R (z)}{d z}$

(2.11)

The substitution of R(z) and S(z) from Eq. (2.9) in Eq. (2.11) results in a new form of the coupled mode equations, as follows:

\frac{d ρ (z)}{d z} = i K_{A C} ρ^{2} + 2 i (\frac{2 π n_{e f f}}{λ} - \frac{π}{Λ} - \frac{1}{2} \frac{d Φ}{d z} + K_{d c}) ρ + i K_{A C}

$\frac{d ρ (z)}{d z} = i K_{A C} ρ^{2} + 2 i (\frac{2 π n_{e f f}}{λ} - \frac{π}{Λ} - \frac{1}{2} \frac{d Φ}{d z} + K_{d c}) ρ + i K_{A C}$

(2.12)

which is in the form of the Riccati ordinary differential equation (ODE). Accordingly,

r (λ) = {| \frac{S (- L / 2)}{R (- L / 2)} |}^{2}

$r (λ) = {| \frac{S (- L / 2)}{R (- L / 2)} |}^{2}$

is written as

r (λ) = {| ρ (- L / 2) |}^{2}

$r (λ) = {| ρ (- L / 2) |}^{2}$

(2.13)

The boundary condition is

ρ (L / 2) = 0

$ρ (L / 2) = 0$

(2.14)

The Riccati ODE Eq. (2.12) can be solved by direct integration.

2.3. Simulation Results

In this section, the simulation results are presented to study the effects of different parameters on the optical response of the SFBGs. The optical constants for the simulations are listed in Table 2.1.

The coefficient

\hat{K} = 2 π n_{e f f} / λ - π / Λ - d Φ / 2 d z + K_{d c}

$\hat{K} = 2 π n_{e f f} / λ - π / Λ - d Φ / 2 d z + K_{d c}$

in Eq. (2.12) is plotted along an FBG at different force and temperature levels at the wavelength of 1550 nm in Figs. 2.3 and 2.4. It is assumed that the original grating is Gaussian apodized. The graphs are obtained for a 14-mm Bragg grating with periodically spaced on-fiber silver coatings with a thickness of 9 μm and a period of 2 mm (Fig. 2.5).

Table 2.1

Modeling Constants
Parameter	Value
E_f	73 GPa
E_c	83 GPa
n_eff (initial)	1.44405
p₁₁	0.113
p₁₂	0.252
$\bar{Δ n}$ $\bar{Δ n}$	1 × 10⁻⁵
ν_f	25
Λ (nm)	537
∂n/∂T	1.2 × 10⁻⁵
L (mm)	14

Figure 2.3 $\hat{K}$ $\hat{K}$ at the wavelength of 1550 nm along a superstructure fiber Bragg grating with a Bragg grating length of 14 mm at different tensile forces and ΔT = 0 [2].

Figure 2.4 $\hat{K}$ $\hat{K}$ at the wavelength of 1550 nm along a superstructure fiber Bragg grating with a grating length of 14 mm at different temperatures and F = 0 [2].

Figure 2.5 Geometrical dimensions of periodic silver films deposited on a fiber Bragg grating [2].

As shown in Figs. 2.3 and 2.4,

\hat{K}

$\hat{K}$

changes with the same period as the thin films, and its amplitude increases as force and temperature increase.

When an FBG is under tensile force F,

\hat{K}

$\hat{K}$

in the coated segments of the optical fiber is less than that in the uncoated segments owing to the larger strain in the uncoated segments. As a result of the temperature increase,

\hat{K}

$\hat{K}$

in the coated segments is larger than that in the uncoated segments. This is attributed to larger strain components in the coated segments of the fiber due to the differences in the coefficients of thermal expansions.

Fig. 2.6 shows the reflection spectra of the SFBG as a function of applied axial loads for 5-, 7-, and 9-μm silver film thicknesses. The simulations were run for the SFBG design shown in Fig. 2.5. The silver films are 1.5 mm long with a period of 2 mm. Figs. 2.7 and 2.8 show the reflectivity of the first upper sideband and the Bragg wavelength of the SFBG as functions of the applied axial force at different film thicknesses. Table 2.2 contains the Bragg wavelength sensitivity to axial load for different film thicknesses. As seen, the sensitivity of the Bragg wavelength to the applied axial load decreases with increasing film thickness. At the film thickness of 1 μm the sensitivity is 1.32 nm/N and is reduced to 1.05 nm/N at the thickness of 15 μm. Increasing the film thickness results in the reduction of the average strain along the grating, which leads to the reduction of the sensitivity of the Bragg wavelength. The sensitivity of the sideband reflectivity increases with thicker films; however, the trend of the variations in reflectivity with axial force is not linear. The effect of the film thickness is dominant on the amplitude of the periodic variation in strain along the grating.

Figure 2.6 Reflection spectra as a function of applied tensile force for a superstructure fiber Bragg grating with silver film thicknesses of 5, 7, and 9 μm [2].

Figure 2.7 Reflectivity of the first upper sideband as a function of applied tensile force on a superstructure fiber Bragg grating with different film thicknesses [2].

Figure 2.8 Bragg wavelength shift superstructure fiber Bragg grating with different film thicknesses [2].

Table 2.2

Bragg Wavelength Sensitivity to Axial Force for Different Film Thicknesses
Film Thickness (μm)	Bragg Wavelength Sensitivity (nm/N)
1	1.32
5	1.23
7	1.17
9	1.10
15	1.05

The reflection spectra at various temperatures are plotted in Fig. 2.9. The Bragg wavelength versus temperature and reflectivity versus temperature graphs are plotted in Figs. 2.10 and 2.11. Table 2.3 summarizes the Bragg wavelength sensitivity to temperature for different film thicknesses. The thermal sensitivity of the Bragg wavelength to temperature increases from 14.2 pm/°C at the film thickness of 1 μm–18.8 pm/°C at the film thickness of 15 μm. In addition, the sensitivity of the sideband reflectivity to temperature increases in thicker films.

Figure 2.9 Reflection spectra as a function of temperature for a superstructure fiber Bragg grating with silver film thicknesses of 5, 7, and 9 μm [2].

Figure 2.10 Reflectivity of the first upper sideband as a function of temperature for a superstructure fiber Bragg grating with different film thicknesses [2].

Figure 2.11 Bragg wavelength shift as a function of temperature for a superstructure fiber Bragg grating with different film thicknesses [2].

Table 2.3

Bragg Wavelength Sensitivity to Temperature for Different Film Thicknesses
Film Thickness (μm)	Bragg Wavelength Sensitivity (pm/°C)
1	14.3
5	16.0
7	16.8
9	18.2
15	18.8

It is evident that the tensile force and temperature can change the reflectivity of the sidebands as well as the Bragg wavelength. The sensitivity of the reflectivity of the sidebands to temperature and axial force is determined by the geometrical features of the coatings. Thicker coatings lead to higher sensitivities by increasing the amplitude of the periodic variations in the index of refraction along the fiber when the fiber is exposed to axial loading or temperature.

2.4. Geometrical Features of Fabricated Superstructure Fiber Bragg Gratings With On-Fiber Films

An SFBG was fabricated by depositing silver coatings on the outer surface of regular FBGs [1,2,4]. The FBG has a grating length of 14 mm, on which seven silver films with a duty cycle of 3/4 were fabricated with the geometrical features depicted in Fig. 2.5.

2.5. Measurement Test Rig

The SFBG was loaded axially at different temperatures to study the effects of force and temperature simultaneously. The test rig is shown in Fig. 2.12. The grating section was placed in the proximity of a thermoelectric module in a chamber to control its temperature. The reflection spectra of the FBG were taken by an sm125 FBG interrogation system (Micron Optics, Inc., Atlanta, GA, USA).

Figure 2.12 Test setup for axial loading of a superstructure fiber Bragg grating (FBG) at different temperatures. Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

2.6. Optical Response Analysis

The reflection spectra of the SFBG before and after the fabrication of the silver films are shown in Fig. 2.13. A comparison of the two graphs indicates the presence of sidebands in the reflectivity after the deposition of the silver films. This is attributed to the formation of residual stresses as a result of the fiber coating process [1,3,4]. In Fig. 2.13, the wavelength spacing of the reflectivity peaks is ∼400 pm, which is consistent with the results obtained from Eq. (2.1) with Γ = 2 mm. The Bragg wavelength shift to lower wavelengths is the result of compressive stress in the coated segments of the fiber. The spectrum graph obtained from opto-mechanical modeling is also plotted in the figure, showing that the modeling and experimental results are in good agreement.

2.6.1. Superstructure Fiber Bragg Grating Under Temperature Variations

Fig. 2.14 shows the reflectivity of the upper sideband as a function of the Bragg wavelength in a thermal cycle ranging from 45°C to 85°C. At temperatures higher than 45°C, the reflectivity reduces monotonically from 20% to 3% as temperature rises.

Fig. 2.15 shows the Bragg wavelength shift as a linear function of temperature with a sensitivity of 17.3 pm/°C. In addition, the results obtained from modeling are plotted in Figs. 2.14 and 2.15, showing agreement between the modeling and the experimental results. The variations in the reflectivity with temperature are the results of changes in the amplitude of the strain components along the fiber. As mentioned before, the deposition of silver films causes the formation of residual stress in the coated segments of the optical fiber. This leads to the periodic distribution of strain and, as a result, periodic variations in n_eff and Λ along the optical fiber. Upon heating, the state of stress in the silver films changes from tensile to compressive, whereas the opposite occurs in the optical fiber. In the uncoated segments of the optical fiber, the strain components are generated purely because of thermal expansion that is equal to α_silicaΔT. The strain components in the coated and uncoated segments of the FBG are schematically plotted in Fig. 2.16. As shown, the difference between the strain components reduces with temperature, which causes the reduction of the amplitude of n_eff and Λ and as a result the coefficient

\hat{K}

$\hat{K}$

Figure 2.13 Reflection spectra of a fiber Bragg grating before and after the deposition of the on-fiber silver films showing the effects of residual stress. Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

Figure 2.14 Reflectivity of the first upper sideband as a function of the Bragg wavelength in a thermal cycle [2].

Figure 2.15 Bragg wavelength as a function of temperature [2].

2.6.2. Structural Loading

The structural parameter that can be measured by SFBGs is strain. To induce strain, an axial load is applied on the optical fiber. For axial loading, the SFBG was installed on the test rig and tensile loads of 0–0.9 N were applied to the fiber. Fig. 2.17 shows the reflectivity of the first upper sideband as a function of the Bragg wavelength at 45°C during the tensile loading. According to this figure, the reflectivity increases to 32% by applying a tensile load of 0.9 N. Owing to the existence of periodic films, tensile forces acting on the optical fiber produce the periodic strain distribution along the grating. The tensile force increases the amplitude of the strain distribution and that of n_eff and Λ, which amplifies the sideband reflectivity.

Figure 2.16 Strain components in the coated and uncoated segments of the optical fiber. Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

Figure 2.17 Reflectivity of the first upper sideband as a function of the Bragg wavelength in tensile loading. Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

Fig. 2.18 shows the corresponding Bragg wavelength shift as a function of the axial force. The shift of the Bragg wavelength has a sensitivity of 1.2 nm/N.

It should be noted that the accuracy of the modeling graphs is dependent on the initial residual stress formed in the coated segments of the optical fiber. In the analyses performed in this research, the model was tuned to fit the experimental data. The tuning was done by finding the initial residual stress for the best fit. Despite this tuning, obtaining accurate values for the residual stress components requires microstructural analysis of the films.

Figure 2.18 Bragg wavelength as a function of tensile force. Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

2.6.3. Simultaneous Measurement of Strain and Temperature

The capabilities of the developed SFBG sensor for the simultaneous measurement of strain and temperature were also investigated. The experimental results are displayed in Figs. 2.19 to 2.21. Fig. 2.19 provides the spectra of the SFBG at different temperatures and tensile forces. It is apparent from the figure that both structural loading and temperature shift the Bragg wavelength. As discussed in the previous sections, structural load, inducing strain on the optical fiber, increases the reflectivity of the sidebands; however, temperature inversely affects the reflectivity. This feature enables the simultaneous measurement of strain and temperature using a single FBG. Fig. 2.20 contains the reflectivity versus Bragg wavelength graphs for the SFBG in multiparameter sensing. The graphs are obtained by measuring the reflectivity and the Bragg wavelength in thermal cycles while the sensor is under tensile force.

Figure 2.19 Reflection spectra of a superstructure fiber Bragg grating exposed to axial tensile force and temperature variations. Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

Figure 2.20 Reflectivity of the first upper sideband as a function of the Bragg wavelength for the superstructure fiber Bragg grating exposed to axial tensile force at four thermal cycles (TC₁ to TC₄). Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

Figure 2.21 Bragg wavelength as a function of temperature for a superstructure fiber Bragg grating exposed to tensile force at four thermal cycles (TC₁ to TC₄). Alemohammad H, Toyserkani E. Simultaneous measurement of temperature and tensile loading using superstructure FBGs developed by laser direct writing of periodic on-fiber metallic films. Smart Materials and Structures 2009;18(9):095048. http://dx.doi.org/10.1088/0964-1726/18/9/095048. IOP Publishing. Reproduced with permission. All rights reserved.

Figure 2.22 Characteristic curves for a superstructure fiber Bragg grating with periodic on-fiber thin films. (A) Reflectivity as a function of Bragg wavelength and (B) Bragg wavelength as a function of temperature [2].

When the sensor is exposed to tensile force and temperature variations, the strain can be directly obtained from Fig. 2.20 by locating the corresponding force graph from the Bragg wavelength and the reflectivity readings. The strain on the optical fiber is related to the applied force. Temperature is obtained by using the Bragg wavelength versus temperature curves in Fig. 2.21.

For each sensor, a set of characteristic curves needs to be obtained to enable multiparameter measurements. The characteristic curves are in the form of reflectivity versus Bragg wavelength and Bragg wavelength versus temperature (Fig. 2.22). The plots consist of a series of constant curves. Strain can be measured by using the reflectivity versus Bragg wavelength graph. To obtain temperature, the corresponding constant strain curve is located in the Bragg wavelength versus temperature graph in Fig. 2.22B.

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Abstract

Keywords

2.1. Superstructure Fiber Bragg Gratings With Periodic On-Fiber Films

2.2. Opto-Mechanical Modeling

2.2.1. Structural Modeling of Superstructure Fiber Bragg Gratings Exposed to Force and Temperature Variations

2.2.2. Opto-Mechanical Modeling of Superstructure Fiber Bragg Gratings With Periodic On-Fiber Films

2.3. Simulation Results

2.4. Geometrical Features of Fabricated Superstructure Fiber Bragg Gratings With On-Fiber Films

2.5. Measurement Test Rig

2.6. Optical Response Analysis

2.6.1. Superstructure Fiber Bragg Grating Under Temperature Variations

2.6.2. Structural Loading

2.6.3. Simultaneous Measurement of Strain and Temperature

Table of Contents for
2. Superstructure Fiber Bragg Grating Sensors for Multiparameter Sensing