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Parallel Fabry-Perot interferometers fabricated on multicore-fiber for temperature and strain discriminative sensing

Cong Zhang, Songnian Fu, Ming Tang, and Deming Liu

Open Access Open Access

Abstract

We experimentally demonstrate parallel Fabry-Perot interferometers (FPIs) fabrication in multicore-fiber with individually variable cavity length, for the purpose of discriminative sensing of temperature and strain. First, we theoretically find that, in order to obtain a small condition number of sensitivity matrix, it is necessary to fabricate parallel FPIs with large cavity difference in single multicore fiber. Then, parallel FPIs are inscribed by femtosecond laser selective micro-holes drilling on the seven-core fiber facet, together with fiber fusion splicing process. By the use of image processing algorithm, individual core position is precisely locked, and then parallel FPIs can be obtained on arbitrary two cores of seven-core fiber. With the location of parallel micro-holes and duration time of fiber fusion splicing adjusted, parallel FPIs with different cavity length of 26µm and 61µm can be simultaneously obtained at the central core and surrounding core, respectively. Consequently, each FPI possesses different sensitivity towards environmental temperature and strain. Finally, a proof-of-concept experiment verifies that relative measurement errors of both temperature and strain discriminative sensing are less than 0.5% and 2.5%, respectively.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

All-fiber Fabry-Perot interferometer (FPI) has been comprehensively investigated for its convenience on various physical parameters measurement, such as temperature, strain [1,2], pressure [3], refractive index [4], magnetic field [5], and vibration [6], owing to its advantages of miniature size, linear response, high sensitivity, and in-line configuration. Because of extremely low temperature sensitivity of silica based FPI with the air-cavity (10−1pm/°C), it has been widely used in relatively temperature insensitive scenarios [6,7]. However, when such a fiber optical sensor is used in harsh environment, such as oil and gas drilling [5], thermal fluctuation over a wide temperature range will bring severe measurement error. An effective way to resolve this problem is to realize discriminative sensing for the temperature sensitive measurement. Consequently, various all-fiber FPI configurations have been proposed, including multiple-FPI cascaded structure and FPI cascaded with fiber Bragg grating (FBG) structure, which utilize different responses of FPI or FBG to realize the dual-parameter sensing. It is reported that with the help of hybrid fiber fusion splicing [1,2,8] or laser induced air-hole technique [4], several multiple-FPI structures are fabricated by two cascaded cavities in the fiber axial direction. However, the corresponding interferometric spectrum needs additional signal processing to recover response of each cavity, and expensive specialty fiber like photonic crystal fiber or hollow-core fiber is used. Although FPI cascaded with a FBG can realize a discriminative measurement [3,9,10], such a dual-parameter fiber optical sensor requires an optical spectrum analyzer (OSA) with a wide wavelength range or two separated OSAs to resolve both the FPI and FBG response, leading to high implementation cost. More importantly, both cascaded FPI structures are spatially separated along the fiber axial direction, leading to the reduction of spatial measurement accuracy and occurrence of cross-sensitivity headache. In addition, for multiple-parameter sensing, current FPI cascaded structures are insufficient to provide the scalability. Consequently, more cascaded structures are indispensable, leading to a complicated configuration and further reduction of the spatial measurement accuracy.

Owing to the flexibility to introduce permanent refractive index change or structural damage, femtosecond laser micro-machining has been proposed for the FPI fabrication. Several FPI structures have been demonstrated by femtosecond laser micro-machining, such as intrinsic mirrors enabled FPI structure [11] and air-hole FPI structure [12–14]. Although femtosecond laser micro-machining is a powerful fabrication platform, the problems of discriminative dual-parameter sensing still exist, especially for traditional FPI structure arising in standard single mode fiber (SSMF). Multicore fiber, which is an effective solution for solving the capacity crunch of SSMF, has been widely investigated for optical sensing [15,16], because it provides multiple parallel channels for independent measurement. Therefore, parallel FPIs arising in single multicore fiber are promising for discriminative dual-parameters sensing.

In this submission, parallel FPIs at the same axial position of multicore fiber with good spatial measurement accuracy are demonstrated by femtosecond laser selective micro-machining and fiber fusion splicing. By with use of the image processing algorithm, location of each core can be precisely locked, and micro-hole can be fabricated at an arbitrary core of multicore-fiber. Owing to the uneven arc distribution along the fiber axial direction, FPI with variable cavity lengths from 16µm to 61µm can be obtained at an arbitrary core of multicore fiber, resulting in parallel FPIs structure. Finally, parallel FPIs with different responses are simultaneously fabricated at the central core and surrounding core of seven-core fiber, leading to different responses for both temperature and strain. FPI fabricated at the central core has a temperature sensitivity of 0.74 pm/°C and a strain sensitivity of 8.3pm/µɛ, while FPI at the surrounding core has a temperature sensitivity of 1.37pm/°C and a strain sensitivity of 3.7pm/µɛ. As a result, the cross-sensitivity between dual parameters can be successfully mitigated. With micro-hole diameters managed, more parallel FPIs with variable cavity length are possible, which makes it possible to realize a multiple-parameter discriminative sensing. Besides, parallel FPIs can offer a dual-parameters sensing at fixed location, leading to less spatial measurement error, in comparison with the cascaded FPIs along fiber axial direction [3,10,11].

2. Operation principle

Figure 1 shows the experimental setup of both temperature and strain simultaneous sensing by the use of the parallel FPIs fabricated in seven-core fiber. Light from the broadband light source covering the wavelength from 1500 nm to 1600 nm goes through a circulator and introduces into single specific core of seven-core fiber with the help of the self-developed Fan-in device [17]. Then, light is reflected by the micro-cavity of FPI leading to an interference pattern and recorded by OSA, and the other end of multicore fiber is not connected with the Fan-out device. Connecting each input port of Fan-in device with corresponding core of seven-core fiber enables different FPI reflection spectrum can to be obtained, and the shift of two dip wavelengths toward temperature and strain variations to be monitored. In order to realize discriminative sensing of both temperature and strain, a matrix of the strain and temperature sensitivities for two resonant wavelength shifts is necessary, as shown in Eq. (1)

$$\left( {\begin{array}{c} {\Delta \varepsilon }\\ {\Delta T} \end{array}} \right) = {\left( {\begin{array}{cc} {C_\varepsilon^1}&{C_T^1}\\ {C_\varepsilon^2}&{C_T^2} \end{array}} \right)^{ - 1}}\left( {\begin{array}{c} {\Delta {\lambda_1}}\\ {\Delta {\lambda_2}} \end{array}} \right) = {A^{ - 1}}\left( {\begin{array}{c} {\Delta {\lambda_1}}\\ {\Delta {\lambda_2}} \end{array}} \right)$$
where Δɛ and ΔT are the environmental variation of strain and temperature, $C_\varepsilon ^1$ and $C_\varepsilon ^2$ are the strain sensitivities of two resonant wavelengths, $C_T^1$ and $C_T^2$ are the temperature sensitivities of two resonant wavelengths, Δλ1 and Δλ2 are the measured wavelength shifts of two FPIs, the superscripts 1 and 2 represent each FPI at different cores, respectively. Once two resonant wavelength shifts are obtained, the inverse sensitivity matrix (A−1) is able to mitigate the cross-sensitivity between temperature and strain. Generally, the stability of sensitivity matrix plays a great role in the simultaneous measurement, which can be evaluated by the condition number of sensitivity matrix [18–20]. The condition number of sensitivity matrix A is defined as
$$Con{d_2}(A) = ||A|{|_2}||{A^{ - 1}}|{|_2}$$
where ||A||2 is second order norm of the sensitivity matrix, as shown in Eq. (3)
$$||A|{|_2}\textrm{ = }{\left( {\sum\limits_i {|{a_i}{|^2}} } \right)^{1/2}}$$
where ai is the matrix elements of the sensitivity matrix. By substituting Eq. (3) into Eq. (2), the matrix condition number can be written as
$$Con{d_2}(A) = ||A|{|_2}||{A^{ - 1}}|{|_2}\textrm{ = }\frac{{{{({C_\varepsilon^1} )}^2} + {{({C_T^1} )}^2} + {{({C_\varepsilon^2} )}^2} + {{({C_T^2} )}^2}}}{{|C_\varepsilon ^1C_T^2 - C_\varepsilon ^2C_T^1|}}$$

 figure: Fig. 1.

Fig. 1. Experimental setup for parallel FPIs based discriminative sensing for both temperature and strain.

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The condition number indicates the sensitivity towards the matrix calculation error. The smaller the sensitivity matrix condition number is, the more stable measurement can be expected. From Eq. (4), we can find that, it is desired to obtain a large difference among diagonal elements of sensitivity matrix A−1, which is described in Eq. (5).

$$D = \textrm{|}C_\varepsilon ^1C_T^2 - C_\varepsilon ^2C_T^1\textrm{|}$$
Now, we investigate the relationship between the sensitivity and the FPI structure. The intensity of FPI induced interference signal is:
$$I = {I_1} + {I_2} + 2\sqrt {{I_1}{I_2}} \cos \left( {\frac{{4\pi nL}}{\lambda } + {\varphi_0}} \right)$$
where I1 and I2 are the intensity of the reflected beams by two FPI surfaces, λ is operation wavelength of incident light, n is the refractive index of the cavity, L is cavity length, and φ0 is the initial phase of the interference. At the spectrum fringe dip position, the phase difference of two reflected beams satisfies Eq. (7)
$$\frac{{4\pi nL}}{{{\lambda _m}}} + {\varphi _0} = ({2m + 1} )\pi$$
where m is an integer and λm is the wavelength of the mth order interference dip. For a FPI based temperature and strain sensor, both temperature and strain sensitivity can be derived as
$${C_T} = \frac{{d{\lambda _m}}}{{dT}} = \frac{4}{{2m + 1}}\left( {\frac{{dn}}{{dT}}L + \frac{{dL}}{{dT}}n} \right)$$
$$ {C_\varepsilon } = \frac{{d{\lambda _m}}}{{dS}} = \frac{4}{{2m + 1}}\left( {\frac{{dn}}{{dS}}L + \frac{{dL}}{{dS}}n} \right)$$
where ${{dn} \mathord{\left/ {\vphantom {{dn} {dT}}} \right.} {dT}}$ is the thermo-optic coefficient of cavity medium, and ${{dn} \mathord{\left/ {\vphantom {{dn} {dS}}} \right.} {dS}}$ is the elastic-optic coefficient of the cavity medium. Since both can be negligible under the condition of air medium [14], Eqs. (8) and (9) can be derived as
$${C_T} = \frac{{d{\lambda _m}}}{{dT}} = \frac{4}{{2m + 1}}\frac{{dL}}{{dT}}n$$
$${C_\varepsilon } = \frac{{d{\lambda _m}}}{{dS}} = \frac{4}{{2m + 1}}\frac{{dL}}{{dS}}n$$
where ${{dL} \mathord{\left/ {\vphantom {{dL} {dT}}} \right.} {dT}}$ is the thermal-expansion coefficient of fiber material and ${{dL} \mathord{\left/ {\vphantom {{dL} {dS}}} \right.} {dS}}$ is elastic coefficient of the fiber material. For parallel FPIs arising in the multicore fiber, temperature sensitivity may not possess too much difference. While for the elastic coefficient ${{dL} \mathord{\left/ {\vphantom {{dL} {dS}}} \right.} {dS}}$, it is directly related with the air cavity length [7,21]. Specifically, the air cavity with longer cavity length possesses a larger ellipticity, which is less sensitive to the fiber axial strain. Alternatively, the air cavity with shorter cavity length possesses a smaller ellipticity, which is more sensitive to the fiber axial strain. Therefore, in order to obtain a large D and improve the measurement stability of dual-parameter monitoring, parallel FPIs with large cavity length difference arising in the multicore fiber are ideally desired.

3. Parallel FPIs fabrication

Experimental setup of femtosecond laser enabled parallel micro-holes drilling on the seven-core fiber facet is schematically shown in Fig. 2. A femtosecond laser (Satsuma, Amplitude System) with an operation wavelength of 1030nm, a pulsewidth of 270fs, and a repetition rate of 1kHz, is used as the fabrication source. The energy of laser pulse can be attenuated by a combination of half wave plate and Glan prism, and then focused by a 20X objective (NA = 0.4) onto the seven-core fiber facet placed on the three-dimensional (3D) motion stage. Two CCDs are used to monitor the fabrication process and provide a reference for the image processing algorithm. The flowchart in Fig. 2 shows the improved image algorithm and Fig. 3 shows the identification process of seven cores. First, calibration points are arbitrarily drilled on the seven-core fiber facet, and the seven-core fiber with calibration points is captured by CCD as the stored image, as show in Fig. 3(a). The calibration points are denoted with a red circle, while the rest points are fiber cores. The calibration points at the seven-core fiber facet provide a reference of each core location. Then, with image correlation analysis between the stored image and the new image of multicore fiber to be processed, each core location of multicore fiber to be processed can be precisely locked. Compared with our early image processing algorithm [22], with the help of image correlation analysis, the calibration point drilling is avoided, leading to efficient identification of core location before the micro-hole drilling. The whole fabrication system possesses a fabrication accuracy of 0.5µm, which guarantees the sensor fabrication repeatability.

 figure: Fig. 2.

Fig. 2. Experiment setup for parallel micro-holes drilling.

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 figure: Fig. 3.

Fig. 3. Image correlation analysis between (a) multicore fiber with calibration point, (b) multicore fiber to be processed.

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The cladding of the used seven-core fiber is 150µm, and the spacing between two adjacent cores is 42µm, as shown in Fig. 4(a). Each core with a diameter of 9µm is surrounded by a low refractive index trench. In a seven-core fiber with hexagon arrangement, there exists four kinds of parallel micro-holes arrangement, as shown in Figs. 4(a)–4(d). The parallel FPIs fabrication process is described as follows. First, with a pulse energy of ∼2.5µJ and a laser fabrication time of 1s, two micro-holes are drilled at different cores of a cleaved seven-core fiber facet, as shown in Figs. 4(a)–4(d). Then, seven-core fiber with micro-holes is spliced with another seven-core fiber without micro-holes by a fusion splicer (Fujikura, 100P+). Due to the micro-holes suddenly heated, two micro-holes rapidly expand to an elliptically hollow sphere, as show in Figs. 4(e)–4(h).

 figure: Fig. 4.

Fig. 4. (a)-(d) End view of four kinds of parallel micro-holes arrangements on the cleaved seven-core fiber facet. (e)-(h) Optical microscopic image of the fabricated parallel FPIs.

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During the parallel FPIs fabrication, we investigate the influence of parallel micro-holes location and fiber splice duration time on the fabricated parallel FPIs, in order to maximize the cavity length difference of parallel FPIs. All parallel micro-holes, as shown in Figs. 4(a)–4(d), are fabricated under conditions of the same laser pulse energy and laser fabrication time. Then, parallel micro-holes on Figs. 4(a) and 4(b) experience a fusion duration time of 1s, while micro-holes on Fig. 4(c) experience a fusion duration time of 1.2s.

We experimentally identify that, the increase of fusion splicing time is helpful to enlarge the cavity length of parallel FPIs. However, for the parallel micro-holes with centrally symmetrical distribution in Figs. 4(a)–4(c), the cavity length at the parallel FPIs is almost the same, due to almost the same arc-discharge distribution. Therefore, in order to fabricate parallel FPIs with different cavity length, the parallel micro-holes are fabricated at the core 1 and core 2 to bring a different arc-discharge distribution along the fiber radial direction, and the fusion duration time is set as 1.5s. Finally, parallel FPIs with different cavity lengths are simultaneously fabricated, as shown in Fig. 4(h). The micro-hole at core 1 experiences a relatively small arc discharge, resulting in a small FPI with a cavity length of 26µm. While for the micro-hole at the surrounding core, large arc discharge results in an FPI with a cavity length of 61µm. Next, the sensing characteristics of parallel FPIs with different cavity lengths can be investigated.

4. Parallel FPIs based temperature and strain sensing

The reflection responses of dip wavelengths A and B for each FPI are shown in Fig. 5, for the purpose of simultaneous measurement of both temperature and strain. Since we only use single one broadband source (BBS) and OSA, the spectrum of parallel FPIs is separately interrogated. In order to overcome such issue, another setup including light source and OSA can be used to monitor each FPI cavity simultaneously. Besides, multichannel wavelength interrogation equipment can also be used to make a real-time dual-parameter discriminative sensing. The FPI dip wavelength A of core 1 is 1564.75nm, and dip wavelength B of core 2 is 1559.22nm. Both ends of seven-core fiber are fixed by the fiber clamp, and seven-core fiber having parallel FPIs is placed on the thermoelectric cooler (TEC) with a resolution of 0.1°C to carry out the temperature measurement. When the strain is 0µɛ, the temperature of TEC is increased from 20°C to 80°C with a step of 10°C, wavelength shifts of two FPIs with respect to the temperature are shown in Figs. 6(a) and 6(b). Both FPIs possess a relative low temperature sensitivity, due to the extremely low thermo-optic coefficient of silica with the air cavity. The temperature sensitivity of core 1 is about 0.74pm/°C, while FPI at core 2 possesses a temperature sensitivity of 1.37pm/°C. As for the strain measurement of parallel FPIs, both ends of seven-core fiber are fixed on the translation stage when the temperature is fixed at 30°C by the TEC. The strain varies from 0µɛ to 1000µɛ with a step of 200µɛ. The wavelength shifts of two FPIs with respect to the strain are shown in Figs. 6(c) and 6(d), respectively. FPI at core 1 possesses a strain sensitivity of 8.3pm/µɛ, while the FPI at core 2 has a strain sensitivity of 3.7pm/µɛ.

 figure: Fig. 5.

Fig. 5. Optical spectral of parallel FPIs.

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 figure: Fig. 6.

Fig. 6. Temperature response of parallel FPIs on (a) core 1, and (b) core 2. Strain response of parallel FPIs at (c) core 1, and (d) core 2, insets are the corresponding spectrum shifting.

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Due to the totally different sensitivity of parallel FPIs towards the temperature and strain, a discriminative sensing of the temperature and strain can be realized by a sensitivity matrix, as shown in Eq. (12):

$$\left( {\begin{array}{c} {\Delta \varepsilon }\\ {\Delta T} \end{array}} \right) = {\left( {\begin{array}{cc} {C_\varepsilon^1}&{C_T^1}\\ {C_\varepsilon^2}&{C_T^2} \end{array}} \right)^{ - 1}}\left( {\begin{array}{c} {\Delta {\lambda_{core1}}}\\ {\Delta {\lambda_{core2}}} \end{array}} \right) = {\left( {\begin{array}{cc} {8.3}&{0.74}\\ {3.7}&{1.37} \end{array}} \right)^{ - 1}}\left( {\begin{array}{c} {\Delta {\lambda_{core1}}}\\ {\Delta {\lambda_{core2}}} \end{array}} \right)$$
The condition number of the obtained sensitivity matrix is 9.74. Since the core-spacing of the used seven-core fiber is fixed at 42µm, the maximum cavity length difference is limited for the purpose of achieving a small condition number. To further reduce the condition number, multicore-fiber with large core spacing is preferred. Meanwhile, heterogenous multicore fiber with large difference of thermal expansion coefficients may be helpful to further reduce the condition number. Moreover, by optimizing the fusion splicing parameters, the difference of cavity length can be further increased to improve the strain sensitivity difference [21].

Next, a proof-of-concept experiment is conducted to verify the sensing performance of parallel FPIs. The simultaneous measurement results are summarized in Table 1. In order to evaluate the performance of parallel FPIs, here we only present several typical results, including a low temperature with high strain and a high temperature with low strain. The wavelength shifting of two wavelength dips A and B at the FPI reflection spectrum is recorded. By substituting the corresponding values into the Eq. (12), the temperature and strain deviation from the set values can be obtained. The relative measurement error of the temperature sensing is smaller than 0.5%, and the relative error of the strain sensing is smaller than 2.5%. The sensor also has the capability to distinguish the linear strain from the bending or twist and torsion, due to the fact that linear strain has an equivalent effect on parallel FPIs, while both bending and twist has little effect on the FPI at the central core of multicore fiber.

Tables Icon

Table 1. Discriminative temperature and strain measurement.

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5. Conclusion

In conclusion, we present the design, characterization, and fabrication of parallel FPIs arising in the seven-core fiber. Theoretical analysis shows that parallel FPIs with large difference of cavity length are preferred for stable dual-parameter discriminative sensing. Parallel FPIs on the seven-core fiber by femtosecond laser micro-machining and fiber fusion splicing are experimentally verified. With the micro-hole position and fiber fusion splicing time controlled, parallel FPIs with different cavity length can be obtained, and discriminative measurement of both temperature and strain becomes possible, due to different responses of parallel FPIs and the low condition number of sensitivity matrix. Our experimental results indicate that, relative temperature measurement error of parallel FPIs is smaller than 0.5%, and relative stain measurement error is smaller than 2.5%. Through drilling micro-holes with different depth on the multicore fiber, more FPIs with different cavity lengths can be fabricated at each core of multicore-fiber, for the easy realization of discriminative multiple-parameter sensing under harsh environment.

Funding

National key R&D Program of China (2018YFB1801002); National Natural Science Foundation of China (61875061); Fundamental Research Funds for the Central Universities (2019kfyRCPY006).

Disclosures

The authors declare no conflicts of interest.

References

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Figures (6)
Fig. 1.
Fig. 1. Experimental setup for parallel FPIs based discriminative sensing for both temperature and strain.

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Fig. 2.
Fig. 2. Experiment setup for parallel micro-holes drilling.

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Fig. 3.
Fig. 3. Image correlation analysis between (a) multicore fiber with calibration point, (b) multicore fiber to be processed.

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Fig. 4.
Fig. 4. (a)-(d) End view of four kinds of parallel micro-holes arrangements on the cleaved seven-core fiber facet. (e)-(h) Optical microscopic image of the fabricated parallel FPIs.

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Fig. 5.
Fig. 5. Optical spectral of parallel FPIs.

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Fig. 6.
Fig. 6. Temperature response of parallel FPIs on (a) core 1, and (b) core 2. Strain response of parallel FPIs at (c) core 1, and (d) core 2, insets are the corresponding spectrum shifting.

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Tables (1)

Tables Icon

Table 1. Discriminative temperature and strain measurement.

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Equations (12)

Equations on this page are rendered with MathJax. Learn more.

( Δ ε Δ T ) = ( C ε 1 C T 1 C ε 2 C T 2 ) − 1 ( Δ λ 1 Δ λ 2 ) = A − 1 ( Δ λ 1 Δ λ 2 )
C o n d 2 ( A ) = | | A | | 2 | | A − 1 | | 2
| | A | | 2  =  ( ∑ i | a i | 2 ) 1 / 2
C o n d 2 ( A ) = | | A | | 2 | | A − 1 | | 2  =  ( C ε 1 ) 2 + ( C T 1 ) 2 + ( C ε 2 ) 2 + ( C T 2 ) 2 | C ε 1 C T 2 − C ε 2 C T 1 |
D = | C ε 1 C T 2 − C ε 2 C T 1 |
I = I 1 + I 2 + 2 I 1 I 2 cos ⁡ ( 4 π n L λ + φ 0 )
4 π n L λ m + φ 0 = ( 2 m + 1 ) π
C T = d λ m d T = 4 2 m + 1 ( d n d T L + d L d T n )
C ε = d λ m d S = 4 2 m + 1 ( d n d S L + d L d S n )
C T = d λ m d T = 4 2 m + 1 d L d T n
C ε = d λ m d S = 4 2 m + 1 d L d S n
( Δ ε Δ T ) = ( C ε 1 C T 1 C ε 2 C T 2 ) − 1 ( Δ λ c o r e 1 Δ λ c o r e 2 ) = ( 8.3 0.74 3.7 1.37 ) − 1 ( Δ λ c o r e 1 Δ λ c o r e 2 )
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