Temperature Sensing of Stepped-Metal Coated Optical Fiber Bragg Grating with the Restructured Dual-Peak Resonance

Abstract

This paper demonstrates a method for the development of stepped-metal coating on optical fiber Bragg grating. The paper also analyzes the dual-peak resonance restructured by the nickel/copper stepped-metal coating. According to the coefficients of linear thermal expansion of the coatings, the modeling and experimental analysis is categorized into three types: Type A, Type B, and Type C. We denote the temperature sensitivity difference between the two peaks as ΔK_T for Type A, ΔK′_T for Type B, and ΔK″_T for Type C. The experimental results show that ΔK_T, ΔK′_T, and ΔK″_T are 2.1 pm/°C, 6.5 pm/°C, and 0.8 pm/°C, respectively. The model analysis and the experimental results all show the Type B stepped-metal coating causes the most obvious temperature sensitivity difference between the two resonance peaks. The stepped-metal coating on the same one Bragg grating can restructure the single resonance into dual-peak resonance with different temperature sensing, and Type B can be used to develop a dual-parameter optical fiber Bragg grating sensor at one location which can measure two physical parameters simultaneously.

1. Introduction

Optical fiber Bragg grating (FBG) sensing technology has become one of the most attractive sensing technologies in a variety of fields, such as the optical fiber smart structures [1,2,3,4]. FBG offers many advantages, such as wavelength encoded nature, wavelength-division multiplexing, immunity to electric–magnetic interference, and small size, etc. FBG is fragile, thus, is required to be protected before its practical use. Previous studies have demonstrated the protective packages can function as parameter compensations [5,6,7,8]. During the FBGs actual use period, the birefringence is induced when FBGs are bent, clamped or twisted [9,10,11,12]. As a result, the corresponding two Bragg spectra are shown in the reflection spectrum. This might reduce the accuracy of measuring the principal strain and, therefore, be considered as a noise signal. But on the other hand, the dual-peak resonance will provide an opportunity to develop the sensor with the capability of measuring both strain and temperature simultaneously using one optical fiber Bragg grating. Other studies of simultaneous measurement of strain and temperature using birefringence FBGs have been conducted [13,14,15].

Metal coatings can protect FBG and also enhance their temperature sensitivity and have attracted considerable interest [16,17,18]. However, there have been few reports about the metallized FBGs’ dual-peak resonance restructured by thermal strains induced by stepped-metal coating on the same Bragg length.

This paper describes the experimental evaluation of the temperature sensing of the single-mode FBG with the Ni/Cu stepped-metal coating by electroless-plating and electroplating. The simulation models analyze the dual-peak resonance restructured by thermal strains and demonstrate the influence of the coating parameters on the two peaks. This kind of optical fiber Bragg grating can be used for a dual-parameter sensor at one location which can measure two physical parameters simultaneously.

2. Experimental Set-Up and Results

In the experiments, three FBGs were inscribed in the single mode fibers SMF-128 by UV phase mask with a nominal resonance wavelength of 1541.325 nm,1539.502 nm, and 1547.835 nm at 25 °C. The length of the Bragg gratings was 10 mm. The stepped-metal coated FBG is hereby expressed as SMC-FBG. We employed a temperature oven (DK-500, Shanghai, China) to control the electroless-plating temperature. Its temperature range is from room temperature to 100 °C, and its temperature resolution is 0.5 °C. And the optical spectrum analyzer (MS9740A, Anritsu, Japan) was used to record the FBGs’ data.

2.1. First Layer of Inner Metal Coating by Electroless-Plating

Before being electroless-plated, three FBGs were pretreated in sensitizing solution (SnCl₂·2H₂O, 10 g/L; HCl, 40 mL/L) for about ten minutes and then in nucleating solution (PdCl₂, 0.5 g/L; HCl, 5 mL/L) for about fifteen minutes. After the pretreatment, the first layer metal coating was deposited on the FBGs by electroless-plating as shown in Figure 1. We chose copper as the first layer of inner metal coating for one FBG and nickel for the other two FBGs. These first layer metal coatings cover the entire length of Bragg grating. The electroless copper plating solution is mainly listed as the following: CuSO₄·5H₂O, 10 g/L; NaKC₄H₄O₆·4H₂O, 40 g/L; NaOH, 8 g/L; Na₂CO₃, 2 g/L; NiCl₂·6H₂O, 1 g/L; and HCHO (37%), 20 mL/L. The electroless nickel plating solution is mainly listed as the following: NiSO₄·6H₂O, 25 g/L; NaH₂PO₂·H₂O, 20 g/L; H₃BO₃, 20 g/L; and C₃H₆O₂, 20 mL/L.

2.2. Second Layer of Outer Stepped-Metal Coating by Electroplating

Figure 2 shows the schematic of the stepped-metal electroplating equipment. Regulating the screw column can control the length of the stepped-metal coating. Different electroplating solutions can develop different packages for this sensor. The SMC-FBGs are divided into three types shown in Figure 3 Type A: a copper layer by electroless-plating and then a stepped-nickel layer by electroplating, Type B: a nickel layer by electroless-plating and then a stepped-copper layer by electroplating and Type C: a nickel layer by electroless-plating and then a stepped-nickel layer by electroplating. The subscript i (i = 1, 2, 3) means FBG, the first layer metal coating and the outer stepped-metal coating, respectively. L_i refers to the length and d_i to the diameter. Due to the different deposition rate between the copper layer and nickel layer, deposition time was adjusted to get the same thickness of coatings. For Type A, it took about three hours to get the inner copper layer and thirteen hours to get the stepped-nickel layer. For Type B, it took about two hours to get the inner nickel layer and fourteen hours to get the stepped-copper layer. For Type C, it took about two hours to get the inner nickel layer and twelve hours to get the stepped-nickel layer. These three types SMC-FBGs are of d₁ = 125 μm, d₂ = 130 μm and d₃ = 400 μm, respectively. Let h₁ be the thickness of inner uniform metal layer and h₂ be the thickness of outer stepped-metal layer, h₁ = (d₂ − d₁)/2, h₂ = (d₃ − d₂)/2, h₁ = 2.5 μm, h₂ = 135 μm.

2.3. Temperature Sensing of the SMC-FBG (Stepped-Metal Coated Fiber Bragg Grating)

Three SMC-FBGs were tested by the controllable temperature oven with a precision of 1 °C, and their temperature sensing characteristics are shown in Figure 4, Figure 5 and Figure 6. The spectra of these three SMC-FBGs all split into two resonance peaks with two different temperature sensitivities. We describe the temperature sensitivity difference between the two peaks as ΔK_T for Type A, ΔK′_T for Type B and ΔK″_T for Type C. ΔK_T, ΔK′_T and ΔK″_T are 2.1 pm/°C, 6.5 pm/°C and 0.8 pm/°C, respectively.

3. Analysis of the Dual-Peak Resonance Restructured by Thermal Strains

In this article, α_i is used for thermal expansion coefficient, E_i for Young’s modulus and μ_i for Poisson ratio. The model is based on the following assumptions: (1) Thermal expansion coefficients of FBG and the metal coating and thermo-optic coefficient of FBG are constants, independent of temperature changes; (2) The inner metal coating is made on the FBG tightly and; (3) The outer stepped-metal coating and the inner metal coating are attached tightly and there is no relative displacement between them. Three distinct models were developed corresponding to the type of SMC-FBG.

Under strain and temperature, the SMC-FBG’s Bragg wavelength shifts by Δλ_B can be expressed as [19]:

$$\Delta {\lambda }_B=2\mathrm{n}\mathsf{\Lambda }\left(\left\{1-\left(\frac{{\mathrm{n}}^2}{2}\right)[p_{12}-\mu (p_{11}+p_{12})]\right\}\epsilon +[\alpha +\frac{\left(\frac{dn}{dT}\right)}{n}]\Delta T\right)$$

(1a)

where n is the effective index of the fiber core, Λ is the grating pitch, α the coefficient of linear thermal expansion of the fiber, p_i,j are the Pockel’s coefficient of the stress-optic tensor, μ is the Poisson’s ration, and ΔT is the temperature change, ε is the applied axial strain. The factor 2nΛ is the resonance condition of a Bragg grating and expressed as λ_B, the Bragg wavelength. The factor {(n²/2)[p − μ (p₁₁ + p₁₂)]} is usually expressed as p_e, the Pockels constant. The factor [(dn/dT)/n] is usually expressed as ξ, the thermo-optic coefficients. Equation (1a) can be given simply by Equation (1b).

$$\Delta {\lambda }_B={\lambda }_B(\alpha +\xi )\Delta T+{\lambda }_B(1{-\mathrm{p}}_{\mathrm{e}})\epsilon$$

(1b)

For an SMC-FBG sensor, the Bragg grating is divided into two sections: double-layer metal coating and single-layer metal coating. Each layer tends to expand or contract when the temperature fluctuates. However, the expansions and contractions generally cannot occur freely due to the boundary limits. Because the restrictions lead to two different thermal strains of the fiber Bragg grating sensor, the dual-peak resonance is induced.

3.1. Analysis of Type A SMC-FBG

Let ΔT > 0. Taking Type A as an example, the parameters of coating satisfy α₁ <α₃ < α₂. Figure 7 shows the diagram of the thermal strains. ε₁L₁ is the total thermal strain of FBG, which is caused by the double-layer coating on the half-length of FBG and the single-layer coating on the other half-length of FBG. The letters ΔL₁, ΔL₂, and ΔL₃, are the free axial elongations of FBG, inner coating and outer coating, respectively, and they can be expressed as Equations (2a)–(2c).

$$\Delta L_1={\alpha }_1\ast \Delta T\ast L_1$$

(2a)

$$\Delta L_2={\alpha }_2\ast \Delta T\ast L_2$$

(2b)

$$\Delta L_3={\alpha }_3\ast \Delta T\ast L_3$$

(2c)

where, L₁ = L₂ = 2L₃.

3.1.1. Wavelength Shift Δλ_dT Caused by the Double-Layer Coating

Because of α₁ < α₃ < α₂ and no relative displacement exists between the inner coating and FBG, the factual elongation of the inner coating will be smaller than ∆L₂, the factual elongation of FBG will be greater than ∆L₁, and the factual elongation of the outer coating will be greater than ∆L₃. At the same time, the thermal stress is satisfied by Equation (3a). The factual elongations of the outer coating, inner coating and FBG are satisfied by Equations (3b) and (3c).

$${\sigma }_{d2z}{A}_2={\sigma }_{d1z}{A}_1+{\sigma }_{d3z}{A}_3$$

(3a)

$${\alpha }_1\Delta T\frac{L_1}{2}+\frac{{\sigma }_{d1z}}{E_1}\frac{L_1}{2}={\alpha }_2\Delta T\frac{L_2}{2}-\frac{{\sigma }_{d2z}}{E_2}\frac{L_2}{2}$$

(3b)

$${\alpha }_2\Delta T\frac{L_2}{2}-\frac{{\sigma }_{d2z}}{E_2}\frac{L_2}{2}={\alpha }_3\Delta T{L}_3+\frac{{\sigma }_{d3z}}{E_3}{L}_3$$

(3c)

where σ_diz (i = 1, 2, 3) represents the thermal stress of No. i layer of coating induced by the double-layer coating. A_i (i = 1, 2, 3) is the cross section of No. i layer. Let ε_d1z represent the axial thermal strain of the FBG induced by the double-layer coating. From the Equations (3a)–(3c), ε_d1z can be expressed by Equation (4),

$${\epsilon }_{d1z}=\frac{{\sigma }_{d1z}}{E_1}=\frac{(E_2{A}_2+E_3{A}_3)({\alpha }_2-{\alpha }_1)\Delta T-E_3{A}_3({\alpha }_2-{\alpha }_3)\Delta T}{E_1{A}_1+E_2{A}_2+E_3{A}_3}$$

(4)

From Equation (1b), the corresponding wavelength shift Δλ_dT is expressed using Equation (5)

$$\begin{array}{l}\Delta {\lambda }_{dT}={\lambda }_B(\alpha +\xi )\Delta T+{\lambda }_B(1-p_{\mathrm{e}}){\epsilon }_{d1z}\\ ={\lambda }_B\ast \Delta T\left[(\alpha +\xi )+(1-p_{\mathrm{e}})\ast \frac{(E_2{A}_2+E_3{A}_3)({\alpha }_2-{\alpha }_1)-E_3{A}_3({\alpha }_2-{\alpha }_3)}{E_1{A}_1+E_2{A}_2+E_3{A}_3}\right]\\ =K_{dT}\ast \Delta T\end{array}$$

(5)

where K_dT is the temperature sensitivity of the SMC-FBG with the double-layer coating.

$$K_{dT}={\lambda }_B\ast \left[(\alpha +\xi )+(1-p_e)\ast \frac{(E_2{A}_2+E_3{A}_3)({\alpha }_2-{\alpha }_1)-E_3{A}_3({\alpha }_2-{\alpha }_3)}{E_1{A}_1+E_2{A}_2+E_3{A}_3}\right]$$

(6)

3.1.2. Wavelength Shift Δλ_sT Caused by the Single-Layer Coating

The factual elongations of inner layer and FBG are satisfied by the restrictive conditions of Equations (7a) and (7b)

$${\sigma }_{s1z}{A}_1={\sigma }_{s2z}{A}_2$$

(7a)

$${\alpha }_1\Delta T\frac{L_1}{2}+\frac{{\sigma }_{s1z}}{E_1}\frac{L_1}{2}={\alpha }_2\Delta T\frac{L_2}{2}-\frac{{\sigma }_{s2z}}{E_2}\frac{L_2}{2}$$

(7b)

where, σ_siz (i = 1, 2) represents the thermal stress of No. i layer of coating induced by the single-layer coating. Then, the thermal strain ε_s1z is obtained by Equation (8).

$${\epsilon }_{s1z}=\frac{{\sigma }_{s1z}}{E_1}=\frac{E_2{A}_2({\alpha }_2-{\alpha }_1)}{E_1{A}_1+E_2{A}_2}\Delta T$$

(8)

The corresponding wavelength shift Δλ_sT is expressed using Equation (9).

$$\begin{array}{l}\Delta {\lambda }_{sT}={\lambda }_B(\alpha +\xi )\Delta T+{\lambda }_B(1-p_{\mathrm{e}}){\epsilon }_{s1z}\\ ={\lambda }_B\ast \Delta T\left[(\alpha +\xi )+(1-p_{\mathrm{e}})\ast \frac{E_2{A}_2({\alpha }_2-{\alpha }_1)}{E_1{A}_1+E_2{A}_2}\right]\\ =K_{sT}\ast \Delta T\end{array}$$

(9)

where K_sT is the temperature sensitivity of SMC-FBG with the single-layer coating.

$$K_{sT}={\lambda }_B\ast \left[(\alpha +\xi )+(1-p_{\mathrm{e}})\ast \frac{E_2{A}_2({\alpha }_2-{\alpha }_1)}{E_1{A}_1+E_2{A}_2}\right]$$

(10)

3.2. Analysis of Type B SMC-FBG

In this case, the parameters of coating satisfy α₁ < α₂ < α₃. Figure 8 shows the diagram of the thermal strains. Similarly, ε₁L₁ is caused by the double-layer coating on the half-length of FBG and the single-layer coating on the other half-length of FBG. Let σ′_diz and σ′_siz (i = 1, 2, 3) represent the thermal stresses of No. i layer of coating induced by the double-layer coating and the single-layer coating, respectively. σ′_diz (i = 1, 2, 3) can be expressed using Equations (11a)–(11c), and σ′_siz (i = 1, 2) can be expressed using Equations (12a) and (12b).

$${\sigma }_{d1z}^{\prime }{A}_1={\sigma }_{d2z}^{\prime }{A}_1+{\sigma }_{d3z}^{\prime }{A}_3$$

(11a)

$${\alpha }_1\Delta T\frac{L_1}{2}+\frac{{\sigma }_{d1z}^{\prime }}{E_1}\frac{L_1}{2}={\alpha }_2\Delta T\frac{L_2}{2}-\frac{{\sigma }_{d2z}^{\prime }}{E_2}\frac{L_2}{2}$$

(11b)

$${\alpha }_2\Delta T\frac{L_2}{2}-\frac{{\sigma }_{d2z}^{\prime }}{E_2}\frac{L_2}{2}={\alpha }_3\Delta T{L}_3-\frac{{\sigma }_{d3z}^{\prime }}{E_3}{L}_3$$

(11c)

$${\sigma }_{s1z}^{\prime }{A}_1={\sigma }_{s2z}^{\prime }{A}_2$$

(12a)

$${\alpha }_1\Delta T\frac{L_1}{2}+\frac{{\sigma }_{s1z}^{\prime }}{E_1}\frac{L_1}{2}={\alpha }_2\Delta T\frac{L_2}{2}-\frac{{\sigma }_{s2z}^{\prime }}{E_2}\frac{L_2}{2}$$

(12b)

Then, K′_dT and K′_sT can be expressed as Equations (13) and (14)

$$K_{dT}^{\prime }={\lambda }_B\ast \left[(\alpha +\xi )+(1-p_{\mathrm{e}})\ast \frac{E_2{A}_2({\alpha }_2-{\alpha }_1)+E_3{A}_3({\alpha }_3-{\alpha }_1)}{E_1{A}_1+E_2{A}_2+E_3{A}_3}\right]$$

(13)

$$K_{sT}^{\prime }={\lambda }_B\ast \left[(\alpha +\xi )+(1-p_{\mathrm{e}})\ast \frac{E_2{A}_2({\alpha }_2-{\alpha }_1)}{E_1{A}_1+E_2{A}_2}\right]$$

(14)

3.3. Analysis of Type C SMC-FBG

In this case, the parameters of coating satisfy α₁ < α₂ = α₃ and E₂ = E₃, and the coating on the same one Bragg grating is divided into two sections with the same material but the different thickness. We use E₂ for coating’s Young’s modulus and α₂ for coating’s thermal expansion coefficient. Figure 9 shows the diagram of the thermal strains. ε₁L₁ is caused by the thinner coating on the half-length of FBG and the thicker coating on the other half-length of FBG. Let A_N2(N=d,s) represent A_d2 and A_s2, which means the cross-section of the thicker coating and the thinner coating. And let σ″_Niz(N=d,s) represent σ″_diz and σ″_siz, which means the thermal stress of the thicker coating and the thinner coating. σ″_diz and σ″_siz can be induced by Equations (15a) and (15b). Then the temperature sensitivity K″_dT and K″_sT can be expressed using Equations (16) and (17).

$${\sigma }_{N1z}^{″}{A}_1={\sigma }_{N2z}^{″}{A}_{N2}$$

(15a)

$${\alpha }_1\Delta T\frac{L_1}{2}+\frac{{\sigma }_{N1z}^{″}}{E_1}\frac{L_1}{2}={\alpha }_2\Delta T\frac{L_1}{2}-\frac{{\sigma }_{N1z}^{\prime }}{E_2}\frac{L_1}{2}$$

(15b)

$$K_{dT}^{″}={\lambda }_B\left[(\alpha +\xi )+(1-p_e)\ast \frac{({\alpha }_2-{\alpha }_1)A_{d2}{E}_2}{E_2{A}_{d2}+E_1{A}_1}\right]$$

(16)

$$K_{sT}^{″}={\lambda }_B\left[(\alpha +\xi )+(1-p_e)\ast \frac{({\alpha }_2-{\alpha }_1)A_{s2}{E}_2}{E_2{A}_{s2}+E_1{A}_1}\right]$$

(17)

In three cases, two different strains make the original single reflectance spectrum split into two peaks. Comparing $K_{sT},K_{sT}^{\prime } and K_{sT}^{″}$, we can find that they are of the same expression with different parameters. We use $\Delta K_T=K_{dT}-K_{sT}$ to describe the temperature sensing difference between the two peaks for Type A SMC-FBG, $\Delta K_T^{\prime }=K_{dT}^{\prime }-K_{sT}^{\prime }$ for Type B SMC-FBG, and $\Delta K_T^{″}=K_{dT}^{″}-K_{sT}^{″}$ for Type C SMC-FBG. Considering h₁ and h₂, ΔK_T and ΔK′_T can be expressed as Equations (18) and (19), whereas, the values of α₂, α₃, E₂ and E₃ are different. Then ΔK″_T can be expressed as Equation (20).

$$\Delta K_T={\lambda }_B(1-p_e)\ast \left\{\frac{\left[E_2{h}_1(h_1+d_1)+E_3{h}_2(2h_1+d_1+h_2)\right]({\alpha }_2-{\alpha }_1)-E_3{h}_2(2h_1+d_1+h_2)({\alpha }_2-{\alpha }_3)}{E_3{h}_2(2h_1+d_1+h_2)+E_2{h}_1(h_1+d_1)+E_1{d}^2{}_1}-\frac{E_2{h}_1(h_1+d_1)({\alpha }_2-{\alpha }_1)}{E_2{h}_1(h_1+d_1)+E_1{d^2}_1}\right\}$$

(18)

$$\Delta K_T^{\prime }={\lambda }_B(1-p_e)\ast \left\{\frac{E_2{h}_1(h_1+d_1)({\alpha }_2-{\alpha }_1)+E_3{h}_2(2h_1+d_1+h_2)({\alpha }_3-{\alpha }_1)}{E_3{h}_2(2h_1+d_1+h_2)+E_2{h}_1(h_1+d_1)+E_1{d^2}_1}-\frac{E_2{h}_1(h_1+d_1)({\alpha }_2-{\alpha }_1)}{E_2{h}_1(h_1+d_1)+E_1{d^2}_1}\right\}$$

(19)

$$\Delta K_T^{″}={\lambda }_B(1-p_e)\ast ({\alpha }_2-{\alpha }_1)\ast E_2\left\{\frac{{(h_1+h_2)}^2+d_1(h_1+h_2)}{E_2[{(h_1+h_2)}^2+d_1(h_1+h_2)]+E_1{d^2}_1}-\frac{h_1(h_1+d_1)}{E_2{h}_1(h_1+d_1)+E_1{d^2}_1}\right\}$$

(20)

4. Parametric Analysis

The parameters of the SMC-FBGs are shown in

Table 1. Parameters of the stepped-metal coated-fiber Bragg grating (SMC-FBGs).

	Type	A	B	C
Parameters
λB (nm)		1550	1550	1550
α1 (/°C)		0.55 × 10−6	0.55 × 10−6	0.55 × 10−6
ξ (/°C)		6.3 × 10−6	6.3 × 10−6	6.3 × 10−6
E1 (Pa)		7.4 × 1010	7.4 × 1010	7.4 × 1010
α2 (/°C)		17.2 × 10−6	14.2 × 10−6	14.2 × 10−6
E2 (Pa)		10.8 × 1010	19.6 × 1010	19.6 × 1010
α3 (/°C)		14.2 × 10−6	17.2 × 10−6	14.2 × 10−6
E3 (Pa)		19.6 × 1010	10.8 × 1010	19.6 × 1010

.

4.1. Analysis of the Temperature Sensitivity

Figure 10 shows the temperature sensing of three types of SMC-FBGs. The following observations can be drawn from Figure 10: (1) If the three types of coating are of the same thickness, K″_dT < K_dT < K′_dT. (2) K_dT and K″_dT increases with increasing of h₁ at the beginning of increasing of h₂. Whereas, K′_dT reduces slightly with increasing of h₁ when h₂ > 0.18 mm. (3) When h₂ reaches a certain thickness, K_dT, K′_dT, and K″_dT will all tend to be constants. (4) K′_sT and K″_sT coincide with each other. (5) K_sT, K′_sT, and K″_sT all increase with increasing of h₁. If h₁ is of the same value, K_sT > K′_sT = K″_sT. When h₁ reaches a certain thickness, they all tend to be constants.

4.2. Analysis of the Temperature Sensitivity Difference

The effect of the coating thickness on the temperature sensitivity difference is shown in Figure 11. We can conclude the followings: (1) When h₂ increases to a certain value, they all tend to be constant values. (2) For the same h₂, ΔK_T, ΔK′_T, and ΔK″_T decrease with the increasing of h₁. (3) ΔK′_T is the largest among them. (4) There is a threshold of h₂ between ΔK_T and ΔK″_T for every h₁ ≤ 8 μm and ΔK_T > ΔK″_T when h₂ is smaller than this threshold. For example, for h₁ = 2 μm, the threshold of h₂ is 200 μm.

Figure 12 shows the effects of the coating’s thermal expansion coefficient on ΔK_T, ΔK′_T, and ΔK″_T. Under the certain coating thickness (e.g., h₂ = 200 μm, h₁ = 5 μm) and Young’s modulus, ΔK_T and ΔK′_T increase with the increase of α₃ when α₂ remains unchanged. Whereas, ΔK_T and ΔK′_T decrease slightly with the increase of α₂ when α₃ remains unchanged. ΔK″_T increases with the increasing of α₂.

5. Discussion and Conclusions

The two sections of metal layers coated on the same Bragg grating caused two resonance peaks with different temperature sensitivities.

The experimental results show that ΔK″_T < ΔK_T < ΔK′_T, which is in agreement with the modeling analysis. From the experimental results and the analysis, it can be concluded that Type B SMC-FBG can result in the most obvious difference in the temperature sensitivity between the two resonance peaks among these three type. In Type B, when the outer stepped-metal coating can be successfully plated, with a thinner thickness and a smaller thermal expansion coefficient of the inner coating, and with a larger thermal expansion coefficient of the outer coating, a more obvious difference of the temperature sensitivity is caused. We can choose another metal material for Type B SMC-FBG to restructure the dual-peak resonance with a much bigger difference between the two peaks, e.g., aluminum/nickel and silver/nickel. This kind of SMC-FBG can be used as a dual-parameter sensor which can measure two physical parameters at one location simultaneously.

On the other hand, the spectrum deformation of Type A is much less than Type B and Type C from the experimental results. We consider that the spectrum deformation is related to the stresses caused by the plating process. We will study this problem in future.