Temperature-insensitive refractive index sensor based on tilted moir&#x00E9; FBG with high resolution

Tao Wang; Kun Liu; Junfeng Jiang; Meng Xue; Pengxiang Chang; Tiegen Liu

doi:10.1364/OE.25.014900

1. Introduction

At present, the refractive index sensing based on optical fiber sensors is an extraordinarily important subject in the chemical-biochemical sensing area. It attracts considerable research interests due to its excellent characteristics such as compact size, immunity to electromagnetic interference, real-time sensing and so on. Various fiber-based RI sensors including optical ring resonator [1–3], tapered optical fiber [4], fiber-optic coupler [5], hetero-core structured optical fiber [6,7] and Mach-Zehnder interferometer [8–10] have been reported. These devices, though a relatively high sensitivity has been obtained, are relatively fragile and difficult to use for a long time. Tilted fiber Bragg gratings (TFBG) [11–13] are widely used in the refractive index sensing for that their cladding mode can be easily interacted with the external environmental media. Papers about basic theory [11], polarization characteristics [14, 15] and demodulation methods [16, 17] for TFBG refractive sensors have been reported extensively. TFBG assisted surface plasmon resonance (SPR) [18–20] sensors get high sensitivity and resolution, TFBG-SPR sensor measures refractive changes of order of 10⁻⁸ for acoustic wave detection [20]. However, the refractive index resolution of the TFBG refractive sensors has no advantage over other types of refractive index sensors.

The moiré FBG [21, 22] is a kind of fiber grating whose grating section is exposed twice by UV light with two phase masks. The parameter of the moiré FBG, such as FWHM [23], can be adjusted by changing the parameters of the two phase masks. In this paper, we proposed and fabricated a tilted moiré FBG (TMFBG) to carry on refractive index sensing experiment. Different from the TMFBG reported in paper [24], our TMFBG is fabricated by scribing two consecutive TFBGs in the same region of the fiber. We conducted the refractive index measuring experiment with such a fiber grating, and the refractive index resolution is an order of magnitude higher than that of the single TFBG, which can reach the quantity level of about 10⁻⁷.

2. Principle

TFBGs are governed by phase matching conditions which give the wavelength position of the resonance bands corresponding to the couplings between two modes. The resonance wavelength $λ_{B r a g g}$ and the wavelength at which the discrete coupling to particular $i^{t h}$ cladding mode occurs $λ_{c l a d, i}$ are given by [17]

λ_{B r a g g} = 2 n_{e f f, c o r e} \frac{Λ}{\cos θ}

λ_{c l a d, i} = (n_{e f f, c o r e} + n_{e f f, c l a d, i}) \frac{Λ}{\cos θ}

where

n_{e f f, c o r e}

and

n_{e f f, c l a d, i}

are the effective refractive indices of the core mode and the cladding mode, respectively. represents the grating period while

θ

denotes the tilt angle between the grating plane and the vertical line of the fiber axis.

For the weakly tilted fiber Bragg gratings (tilt angle is between 0°-10°), we consider the change of the Bragg wavelength $λ_{B r a g g}$ and the $i^{t h}$ cladding mode wavelength $λ_{c l a d, i}$ varied with the temperature change as below:

\begin{matrix} Δ λ_{B r a g g} = λ_{B r a g g} (\frac{1}{n_{e f f, c o r e}} \frac{d n_{e f f, c o r e}}{d T} + \frac{1}{Λ} \frac{d Λ}{d T}) Δ T \\ = λ_{B r a g g} (α + β) Δ T \end{matrix}

\begin{matrix} Δ λ_{c l a d, i} = [\frac{Λ}{\cos θ} \frac{d (n_{e f f, c o r e} + n_{e f f, c l a d, i})}{d T} + \frac{n_{e f f, c o r e} + n_{e f f, c l a d, i}}{\cos θ} \frac{d Λ}{d T}] Δ T \\ = λ_{c l a d, i} (A_{i} + β) Δ T \end{matrix}

where

Δ T

is the change of the temperature,

α = (1 / n_{e f f, c o r e}) (d n_{n e f f, c o r e} / d T)

is the thermo-optic coefficient of the fiber core material (about 8.16 × 10⁻⁶ K⁻¹ for silica fiber [25]);

β = (1 / Λ) (d Λ / d T)

is the coefficient of the thermal expansion of the fiber core material (about 5.5 × 10⁻⁷ K⁻¹ for silica fiber [26]);

A_{i} = \frac{1}{n_{e f f, c o r e} + n_{e f f, c l a d, i}} \frac{d (n_{e f f, c o r e} + n_{e f f, c l a d, i})}{d T}

is the thermo-optic coefficient of the

i^{t h}

cladding mode, so

A_{i}

and

α

are the same order of magnitude and approximately equal to each other. The following is the difference between the

i^{t h}

cladding mode wavelength and the Bragg wavelength varies with the temperature.

\begin{matrix} \frac{Δ λ_{B r a g g} - Δ λ_{c l a d, i}}{Δ T} = (λ_{B r a g g} - λ_{c l a d, i}) β + (λ_{B r a g g} α - λ_{c l a d, i} A_{i}) \\ \approx (λ_{B r a g g} - λ_{c l a d, i}) (β + α) \end{matrix}

For the weakly TFBGs, the spectral range of the cladding mode comb is less than 100 nm, so the difference between the $i^{t h}$ cladding mode wavelength and the Bragg wavelength is less than 100nm. The formula (5) can be rewritten as:

\frac{Δ λ_{B r a g g} - Δ λ_{c l a d, i}}{Δ T} < 100 n m * (β + α) = 0.87 p m \cdot K^{- 1}

The formula (6) shows that the difference between the $i^{t h}$ cladding mode wavelength and the Bragg wavelength is insensitive to the temperature, and the sensitivity is only less than one twentieth of common FBG sensor. Thus when $λ_{c l a d, i} - λ_{B r a g g}$ was used as a parameter to measure refractive index, the result is temperature-insensitive.

The distinct feature of the tilted moiré FBGs is that the grating periods and the tilted angles of the two TFBG are different. Figure 1 shows the diagram of a tilted moiré FBG, which contains two TFBGs in the same region of a fiber. The grating periods and the tilt angles of both TFBGs are different. $Λ_{1}$ and $Λ_{2}$ are respectively the grating periods of the TFBG1 and the TFBG2, $θ_{1}$ and $θ_{2}$ are respectively the tilt angles of the TFBG1 and the TFBG2. By adjusting the grating periods and the tilt angles of the two TFBGs, the cladding mode comb of the two TFBGs can be non-overlapped. Thus such a tilt moiré FBG can be used for high performance refractive index sensing with the property of temperature-insensitivity.

Fig. 1 The structure diagram of a tilted moiré FBG

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3. Experiments and Analysis

3.1 Fabrication

The tilted moiré FBG was fabricated by using direct phased mask with two-stage UV exposure method, and the fabrication procedure is depicted schematically in Fig. 2. A KrF excimer laser (Coherent BraggStar) operating at 248 nm was used as the UV source. A phase mask was mounted on a displacement stage whose inclination angle can be adjusted. A cylindrical lens was used to focus the UV beam. The fibers were hydrogen-loaded in a sealed chamber with a pressure of 13.4 MPa at 98 °C for 14 days. When scribing the tilted moiré FBG, the fiber whose coating was stripped was hold behind the phase mask. In the first exposure, a tilted grating with tilt angle $θ_{1}$ was written in the fiber with the phase mask 1. In the second exposure, the other tilted grating was written in the same region of the fiber by replacing the phase mask 1 by the phase mask 2 and adjusting the tilt angle to angle $θ_{2}$ . After the tilted moiré FBG was fabricated, it was annealed in a thermostat at the temperature of 85 °C for 24 hours.

Fig. 2 Fabrication procedure for the tilted moiré FBG

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In order to make the two cladding mode combs non-overlapped, the Bragg wavelengths and the tilt angles of two TFBGs are respectively chosen as 1569.8 nm, 3.8° and 1535.3 nm and 7.4°. The parameters are selected based on the simulation results from OptiGrating and limited by our laboratory experimental condition, because the tilt angles of the fabricated TFBG can’t be exactly the same as the simulated angles. The transmission spectrum of the fabricated TMFBG in the air are shown as Fig. 3. In the following, the left comb is called TFBG1, the right comb is called TFBG2.

Fig. 3 The transmission spectrum of the TMFBG in the air (The modes marked by arrows will be used to study the temperature response in the following experiment.)

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3.2 Temperature response

As we know, the common TFBG has a significant temperature response. But for the sensor fabricated in our work, the wavelength difference between the cladding modes and the core mode is hardly affected by the temperature.

The grating region of the TMFBG is tightly attached to the heating area of the heating belt with the high temperature resistant tape. In the experiments, we adjusted the temperature of the heating belt to heat the grating section and recorded the transmission spectrum when the temperature reached stabilization. The temperature was changed from 25 °C to 80 °C with the interval of 5 °C by adjusting the control panel of the heating belt.

Figure 4 displays the overlapped transmission spectra of the TMFBG recorded at the different temperature. The left inset in Fig. 4 shows the enlarge view of the core mode of the TFBG1 and the right inset in Fig. 4 shows the enlarge view of the ghost mode of the TFBG2. We can see that both the core mode wavelength and the cladding mode wavelength changes with the temperature. Figure 5 shows the wavelength of the core mode of the TFBG1 and TFBG2 varied with temperature. From the linear fitting results, it can be concluded that the wavelength of the core mode has good linearity with the temperature change for both TFBG1 and TFBG2 with similar sensitivity. In addition, we also studied the temperature response of the cladding mode wavelength for both TFBG1 and TFBG2, the results are shown in Table 1. The studied cladding modes are marked in Fig. 3. The Table 1 gives us the temperature sensing sensitivity of the corresponding cladding mode, the r square of the linear fit and the difference with the sensitivity of the respective core modes. We can see that the cladding mode has a similar temperature sensitivity to the corresponding core mode, and the temperature sensitivity difference between the cladding mode and the corresponding core mode is quite small. So the experimental results are in agreement with the theoretical derivation in part 2. The difference of the cladding mode and the core mode temperature sensitivity is less than 0.2 pm/°C, only one fourth of the maximum value of theoretical calculation, this is because an approximate approach is taken in the theoretical calculation. The effect of temperature on the difference between cladding mode wavelength and core mode wavelength can be negligible. It is therefore clear that when we choose the difference of the cladding mode and the core mode wavelength as the parameter to measure refractive index, the result is not affected by the environmental temperature.

Fig. 4 Overlapped transmission spectra of the TMFBG varied with temperature. The left inset shows the zooming of the core mode of the TFBG1 and the right inset shows the zooming of the ghost mode of the TFBG2.

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Fig. 5 The relationship between the wavelength of the core mode and temperature and the linear fitting of the corresponding data for TFBG1 and TFBG2.

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Table 1. The temperature sensing sensitivity of the cladding modes and their differences with the temperature sensing sensitivity of the respective core mode.

View Table

3.3 Refractive index sensing

We carried on refractive index measuring experiments with the fabricated TMFBG at the temperature of 22. °C To keep the strain on the fiber constant during the experiments, the grating region of the TMFBG was attached permanently to a microscope slide and small quantities of liquids with various refractive indices were dispensed with a pipette onto the grating. The grating region and slides were cleaned thoroughly among experiments. The immersion liquids used in this work were glycerin aqueous solution providing a wide range of refractive indices. The nominal refractive index ( $n_{D}$ ) of all solutions was measured by an Abbe refractometer. The transmission spectra were recorded using an 8164B lightwave measurement system (Keysight) with a wavelength resolution of 2 pm. Figure 6 displays the evolution of the TMFBG transmission spectrum with respect to the surrounding refractive index $n_{e x t}$ , where $n_{D}$ indicates that the refractive index of the glycerin aqueous solution was measured at the wavelength of 589.3 nm.

Fig. 6 Evolution of the TMFBG spectrum versus $n_{e x t}$ .

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When $n_{e x t}$ reaches the value of $n_{e f f, c l a d, i}$ , the coupling strength of the $i^{t h}$ cladding mode decreases. When $n_{e x t}$ is equal to $n_{e f f, c l a d, i}$ , the $i^{t h}$ cladding mode is no longer guided. The boundary between guided and leaky modes is called the “cut-off mode” (as the blue and green stars marked in Fig. 7). We chose the wavelength difference of the “cut-off mode” and the corresponding core mode to measure the refractive index of the liquid around the TMFBG. We now plot the relative resonance wavelength of the “cut-off mode”(with respect to the respective Bragg wavelength) as a function of $n_{D}$ (Fig. 8). The linear fitting method was used to fit the experimental results and we got a good linearity for the TFBG1 and the TFBG2 with r square of 0.9997 and 0.9991 respectively. The sensitivity of the TFBG1 is 545.918 nm/RIU for the refractive index of $n_{D}$ ranging from 1.39 to 1.445, while the sensitivity of the TFBG2 is 574.229nm/RIU for the refractive index of $n_{D}$ ranging from 1.4005 to 1.445. As the wavelength resolution of 8164b system is 2 pm, combining the two TFBGs we can get the refractive index resolution of the TMFBG as follows:

R_{t o t a l} = R_{L} - R_{R} = \frac{2 p m}{545.818 n m \cdot R I U^{- 1}} - \frac{2 p m}{547.229 n m \cdot R I U^{- 1}} = 2 \times 10^{- 7} R I U

where

R_{t o t a l}

is the refractive index resolution of the TMFBG, while

R_{L}

and

R_{R}

are respectively the refractive index resolution of the TFBG1 and the TFBG2. We can see that the resolution of TMFBG is an order of magnitude higher for refractive index detection than that of a single original TFBG. According to the result of the part 3.2, the wavelength difference of the cladding mode and corresponding core mode is not affected by temperature, so the fabricated TMFBG can measure the refractive index with high resolution and the result is insensitive to temperature.

Fig. 7 The cut-off point of the TMFBG as $n_{e x t} = 1.4224$ (the blue star and the green star marked the cut-off mode)

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Fig. 8 Relative wavelength shifts in the distance of the cut-off mode to the Bragg wavelength as a function of the refractive index of glycerin solution at 598.3 nm:(a) the TFBG1, (b)the TFBG2.

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4. Conclusion

In this paper, we proposed and produced a tilted moiré FBG (TMFBG), which is made by scribing two TFBG with different parameters in the same region of the fiber successively. By adjusting the periods and tilt angles of the two TFBG, the two cladding mode optical combs of the transmission spectrum of the TMFBG are non-overlapped. When the TMFBG is used to sensing the refractive index, the refractive index resolution of the TMFBG is an order of magnitude higher than that of the single TFBG. The refractive index resolution can reach 2 × 10⁻⁷ RIU in the refractive index range of 1.4005-40445 when the spectral resolution is 2 pm. Because the difference of the cut-off cladding mode wavelength and the core mode wavelength is adopted as the parameter to measure refractive index, the measuring results are not affected by temperature when the TMFBG is used to measure refractive index. We believe that by the way of fine design and fabrication, fine refractive index measurement instruments like Vernier caliper can be made by MTFBG.

Funding

This work was supported by National Natural Science Foundation of China under Grant 61108070, 61227011, 61378043, 61475114, National Instrumentation Program under Grant 2013YQ030915.

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	TFBG1				TFBG2
Cladding mode number	L1	L2	L3	L4	R1	R2	R3	R4
Temperature sensitivity(pm/°C)	13.24	13.33	13.256	13.16	13.62	13.5	13.5	13.54
R square of the linear fit	0.99946	0.99946	0.99952	0.99927	0.9995	0.99949	0.99954	0.99964
Sensitivity difference with core mode(pm/°C)	−0.09	0	−0.074	−0.17	−0.03	−0.15	−0.15	−0.11

Temperature-insensitive refractive index sensor based on tilted moiré FBG with high resolution

Abstract

1. Introduction

2. Principle

3. Experiments and Analysis

3.1 Fabrication

3.2 Temperature response

3.3 Refractive index sensing

4. Conclusion

Funding

References and links

Cited By

Figures (8)

Tables (1)

Equations (7)

Optics Express