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Abstract
In this paper, cascaded modal interferometers constructed by strongly-coupled seven-core fiber (SC-SCF) with different lengths are demonstrated for enhanced bending sensing based on Vernier effect. The free spectral range (FSR) of a single SC-SCF interferometer is determined by the length of SC-SCF. Two SC-SCF interferometers with different FSRs are cascaded, in which, one functions as the sensor while the other functions as the reference. The wavelength shift of the envelope of the output spectrum is much larger than that of a single SC-SCF interferometer due to the Vernier effect. Therefore, enhanced sensing can be achieved. Experimental results show that the bending sensitivity of the proposed sensor is improved from −2.20 nm/m−1 (single SC-SCF interferometer) to 42.32 nm/m−1 (cascaded SC-SCF interferometers). The temperature response of the sensor is also investigated. Our proposed cascaded SC-SCF sensor has advantages of high sensitivity, ease of fabrication, and low cost. It is attractive for high precision bending sensing applications.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Since the successful development of low-loss optical fiber, it has opened the door to optical fiber communications and paved the way for optical fiber sensing which is still one of the most active branches of optoelectronic technology development [1]. Multicore optical fiber sensors are widely used in the measurement of curvature [2], bending [3], temperature [4], and other physical quantities due to their compact structure, high sensitivity, long-term durability, and anti-electromagnetic interference [3]. Various optical fiber-based bending and temperature sensors have been proposed in recent years. For the bending sensing, the bending sensor based on multi-core optical fiber (MCF) [5], long-period fiber gratings (LPFGs) [6], fiber Bragg gratings (FBGs) [7], photonic crystal fiber (PCF) [8] have been proposed. For temperature sensing, the temperature sensor based on long-period gratings [9], fiber Bragg gratings [10], and multi-core optical fiber [11] have been proposed. In 2021, Zhou et al. proposed a highly sensitive bending sensor based on a seven-core optical fiber with a bending sensitivity of 2.65 dB/m−1 and a temperature sensitivity of 0.021 nm/°C [3]. Later, Shao et al. proposed a Mach-Zehnder interferometer based on seven-core fiber, which had a curvature sensitivity of −26.5517 dB/m−1 and a temperature sensitivity of 0.0753 nm/°C, in 2023 [12].
However, optical fiber sensing technology still has shortcomings in some special applications, such as seismic wave detection [13], natural disaster precursor observation [14], and other fields requiring high resolution. Traditional sensing mechanisms may not meet the detection requirements, and improving the sensitivity is one of the effective ways to realize high-resolution sensors. At present, various enhanced sensing schemes based on the optical Vernier effect have been proposed [15]. This sensitization mechanism has been widely adopted in Mach-Zehnder interferometers (MZIs) [16], Sagnac interferometers (SIs) [17], fiber-optic rings [18], Fabry-Perot interferometers (FPIs) [19], etc., and successfully applied in the detection of airflow [19], curvature [20], temperature [17]. In 2014, Shao et al. proposed a sensitivity-enhanced temperature sensor based PMF with cascaded fiber optic SIs based on Vernier effect, which had a temperature sensitivity of −13.36 nm/°C [17]. Later, Liao et al. proposed an MZIs sensor based SMF with a modified Vernier effect that had a temperature sensitivity of 397.36 pm/°C and curvature sensitivity of −36.26 nm/m−1 in 2017 [16]. In 2021, Zhao et al. proposed a temperature sensor that had a sensitivity of 78.98 nm/°C with the Vernier effect based on Michelson interferometer [21]. However, the Vernier effect of cascaded multicore fiber interferometers for enhanced bending sensing is not yet studied, to the best of our knowledge.
In this paper, we have proposed and demonstrated a sensitivity enhanced sensor using cascaded SC-SCF interferometers based on the Vernier effect. By splicing a section of SC-SCF between two single-mode fibers (SMF) and cascading two SC-SCFs with small difference in length, the sensitivity can be greatly improved due to the Vernier effect. A 9 cm SC-SCF was used as the sensing interferometer. And the length of the SC-SCF of the reference interferometer was changed to 8, 8.5, and 8.7 cm, respectively. For these three cascading schemes, experimental results show that the bending sensitivity is 8.36 nm/m−1, 12.53 nm/m−1, 42.32 nm/m−1, and the temperature sensitivity is 59.6 pm/°C, 261.1 pm/°C, and 481.8 pm/°C, respectively. For a single 9 cm SC-SCF interferometer, its bending and temperature sensitivities are −2.20 nm/m−1, and 14.1 pm/°C, respectively.
2. Sensor structure and principle of operation
2.1 Sensor structure
The SC-SCF used in the experiment was purchased from Futong Optical Technologies Ltd., China. Figure 1(a) shows the scanning electron microscope photo of the cross-section of SC-SCF. It has pure silica cladding with a diameter of 125 ± 2 µm and seven identical germanium-doped cores. Hexagonally arranged six outer cores surround its central core. The diameter of the cores is 8.2 ± 0.5 µm. The refractive index difference between the core and the cladding (ncore − nclad)/ncore is 0.0049 ± 0.0005. The center distances between all adjacent cores are 11.0 ± 0.7 µm. The numerical aperture and normalized V-parameter of every individual core is calculated to be 0.14 and 2.38 at the wavelength of 1550 nm, respectively.
Fig. 1. (a) Scanning electronic microscope photo of the cross section of the SC-SCF. (b) & (c) Electrical field distributions of HE11-like and HE12-like supermodes of the SC-SCF, respectively.
A section SC-SCF was spliced between two SMFs via central alignment at both joints, i.e., the central core of the SC-SCF was aligned to the core of the SMF, forming an SMF-SCSCF-SMF structure. Such a structure results in an interference fringe pattern in the transmission spectrum owing to the modal interference between the supermodes excited and guided in the SCF [4,22–25]. The SC-SCF length of the sensing interferometer was set to 9 cm, while the SC-SCF length of the cascaded reference interferometer was 8 cm, 8.5 cm, and 8.7 cm, forming an SMF-SCSCF-SMF-SCSCF-SMF structure. The price of the SC-SCF we used is 50 CNY per meter. The total length of SC-SCF used for the sensor is less than 0.2 m with a cost of less than 10 CNY. The fabrication of the sensor only involves a commercial fusion splicer. Therefore, our sensor head is cost effective and easy to fabricate.
2.2 Principle of operation
According to the coupled-mode theory [26], when the core of the two SMFs is aligned with the central core of the SC-SCF at both ends, two supermodes of SC-SCF shown in Fig. 1(b) and (c) will be excited. Mode fields of these two supermodes are similar to that of HE11 mode and HE12 mode of a step-index fiber, so we name them HE11-like and HE12-like supermodes [11], respectively. Therefore, the transmission spectrum of the interferometer based on the SMF-SCSCF-SMF structure can be expressed as follows [24,25]:
The transmission spectra are like a ruler in which the free spectral range (FSR) remains as wide as the range of this ruler. Thus, we can enhance the sensitivity by constructing a “Vernier ruler” with cascaded dual SC-SCF interferometers. FSR of the interferometer is controlled by the SC-SCF length. The transmission spectrums of 9 cm and 8 cm long SC-SCF interferometers are shown in Fig. 2(a) and (b).
Fig. 2. (a) Transmission spectrum of 9 cm SC-SCF interferometer. (b) Transmission spectrum of 8 cm SC-SCF interferometer. (c) Transmission spectra of 9 cm and 8 cm SC-SCF cascades. (d) Cascaded transmission spectra and filter curves in linear coordinates.
For a single SCF modal interferometer, when the phase difference satisfies 2πΔn(λ)L/λ = (2m + 1)π, the wavelength of the trough is:
where m is an integer. The FSR of the interferometer is:According to the formula, the FSR is inversely proportional to the length of SC-SCF. In the same wavelength range, the long one has more periods than the short one, so the free spectral range is smaller. The envelope FSR of cascaded configuration can be expressed as [15]:
where $FS{R_s}$ and $FS{R_r}$ are the sensing interferometer and the reference interferometer, respectively. When the spectrum of the sensing element moves slightly, and the reference element remains stable, the transmission spectrum envelope of the cascaded interferometer will show multiple wavelength shifts. The cascaded transmission spectrum is shown in Fig. 2(c). The amplification factor M amplifies the sensitivity of the sensor compared with that of a single sensing arm, which can be described as [15]:We can know from Eq. (6) that the closer the FSRr of the reference interferometer and the FSRs of the sensing interferometer, the larger the value of the amplification factor M. Similarly, the envelope shift of the Vernier configuration is magnified M times compared to individual one that can be given as:
Therefore, when the sensing interferometer experiences a dip shift Δλ with bending variation ΔC or temperature variation ΔT, the Vernier configuration will undergo an envelope shift MΔλ, which can profoundly enhance the sensitivity.
Because the FSRe of the cascaded spectrum is relatively large, the spectral quality obtained by using envelope fitting is relatively poor. Fast Fourier transform (FFT) filter [27] has a very good effect on the demodulation of mixed signals. Therefore, we used an FFT filter to demodulate the transmission spectrum. The output spectrum formula is as follow:
Logarithmic coordinate system to linear coordinate system conversion formula is as follow:
The converted spectrum and the bandpass filter curve are shown in Fig. 2(d). The transmission spectrum of a single interferometer is represented by Eq. (1), and then the cascaded spectrum can be expressed as [27]:
For the convenience of calculation, let $A = {I_1} + {I_2},\;B = 2\sqrt {{I_1} \cdot {I_2}} $, then we get
The substitution of Eq. (11) into Eq. (10) results in the following expression:
We can see from Eq. (12) that the superimposed spectrum is composed of four frequency components: fS, fR, fS + fR, |fS - fR|, where fS and fR are the spatial frequency of sensing and reference interferometer. The frequency components fS, fR and fS + fR are the comb-like fine spectrum, while the lowest frequency component |fS - fR| corresponds to the envelope with the largest FSR.
The spectrums of Fig. 2(a) and (b) are converted from logarithmic coordinates to linear coordinates by Eq. (9), as shown in Fig. 3(a) and (b). The frequency analysis of Fig. 2(d) and Fig. 3(a) and (b) are performed using FFT, and the results are shown in Fig. 3. For a single SC-SCF interferometer, Eq. (4) indicates that the FSR is not a constant and it varies with the change of λ. As shown in Fig. 2(a) and (b), the FSRs of 9 cm and 8 cm SC-SCF interferometer vary from 12 nm to 16 nm and from 13 nm to 19 nm over the wavelength range of 1250 nm to 1650 nm, respectively. Therefore, in the FFT frequency domain as shown in Fig. 3(c) and (d), the frequency peaks are broadened due to the non-uniformity of the FSR. Figure 3(e) is FFT of the cascaded interferometers spectrum. In order to acquire the envelope, the frequency of |fS - fR| is filtered out by FFT band pass filter of the Origin software.
Fig. 3. (a) Transmission spectrum of 9 cm SC-SCF interferometer in linear coordinates. (b) Transmission spectrum of 8 cm SC-SCF interferometer in linear coordinates. (c) FFT of 9 cm SC-SCF in linear coordinates. (d) FFT of 8 cm SC-SCF in linear coordinates. (e) FFT of cascaded interferometer.
3. Experiment and results
In the experiment, a broadband light source (BBS) with a 400 nm wavelength range from 1250 nm to 1650 nm is utilized as an input light source. An optical spectrum analyzer (Yokogawa AQ6370D) with a wavelength resolution of 0.1 nm is used to measure the transmission spectra. We measured the sensing sensitivity of single and cascade SC-SCFs respectively. First, a single SC-SCF with a length of 9 cm was used for measurement, and then an SC-SCF with a length of 9 cm was used as the sensing interferometer, and an SC-SCF with a length of 8 cm was used as the reference interferometer. Finally, change the SC-SCF length of the reference interferometer to 8.5 cm and 8.7 cm, respectively.
3.1 Bending response
The schematic diagram of the proposed sensor based on cascaded SC-SCFs is illustrated in Fig. 4. The right translation stage uses a clamp to fix the fiber, while the left one does not fix the fiber. A 10-gram weight is suspended from the fiber on the left side to ensure that the SCF is straight along the steel beam and with the same axial tense during bending [28]. By moving the right translation stage to the left, pressure is applied to the cantilever beam to bend it upwards with a total displacement of 10 mm and a step of 1 mm. Firstly without cascading the reference interferometer, the bending sensitivity of the SC-SCF with a length of 9 cm was measured and the transmission spectrum is shown in Fig. 5(a). We obtained a bending sensitivity of –2.20 nm/m−1 for a single SC-SCF interferometer. Three wavelength ranges are selected for measurement here to investigate the dispersion of the bending sensitivity of the sensor since both Δn(λ) and the FSR depend on λ. The measurement results show that the bending sensitivity in the short wavelength part is higher, so the sensitivity measured by Dip_1 is selected for comparison in subsequent experiments. Subsequently, the 8 cm reference arm was cascaded and measured, and the transmission spectra are shown in Fig. 5(c.1). Changing the length of the reference arm, 8.5 cm and 8.7 cm SC-SCFs were cascaded with the sensing arm respectively, and the transmission spectra correspond to Fig. 5(c.2) and (c.3).
Fig. 5. (a) Bending measurement of single SC-SCF. (b) Wavelength shift of single SC-SCF as a function of bending for three interferometer dips. (c) Transmission spectra of three cascaded combinations. (d) Transmission spectra of three cascaded combinations under a linear coordinate transformation. (e) FFT bandpass filtered spectrum in linear coordinates. (f) Wavelength shift of three cascaded combinations as a function of bending for interferometer dip.
Initially, the cantilever beam with a length of 530 mm was horizontally straight and its curvature was zero. Then, the right translation stage was moved gradually towards the left one so that their distance became smaller, making the cantilever beam and the SC-SCF bent. The curvature of the bent SC-SCF is the reciprocal of its bending radius, and can be calculated from the following equation:
The bending sensitivities were calculated to be 8.36 nm/${\textrm{m}^{ - 1}}$, 12.53 nm/${\textrm{m}^{ - 1}}$, and 42.32 nm/${\textrm{m}^{ - 1}} $ for reference arms of 8 cm, 8.5 cm, and 8.7 cm, respectively. As can be seen from Fig. 5(f), the sensitivity and amplification factor were enhanced as the length difference of the SC-SCFs was reduced. Bending sensitivity is increased from −2.20 nm/${\textrm{m}^{ - 1}} $ for single SC-SCF to 42.32 nm/${\textrm{m}^{ - 1}}$ for cascaded structure.
3.2 Temperature response
To investigate the temperature response of our sensor, we placed its sensing arm in a tube oven while the reference arm was placed in a room temperature environment with both SC-SCFs kept taut. There was a thermocouple temperature sensor with a resolution of 0.5 °C to monitor the temperature change in the oven. The temperature was changed from 35 °C to 90 °C with a step of 5 °C. At each temperature, it was maintained for 10 min to make sure the temperature was stable. Figure 6(a) demonstrates the transmission spectra of three cascaded combinations of 9 cm for the sensing arm and 7.9 cm, 8.5 cm, and 8.7 cm for the reference arm, respectively. And Fig. 6(b) shows the transformed spectrum in linear coordinates of the corresponding length. The temperature wavelength drift FFT filtered curves for three combinations is shown in Fig. 6(c). The temperature sensitivity of the three combinations corresponded to 59.6 pm/°C, 261.1 pm/°C, and 481.8 pm/°C. The temperature sensitivity of a single SC-SCF is 14.1 pm/°C. As shown in Fig. 6(d), the sensitivity and amplification factor were enhanced as the length difference of the SC-SCFs was reduced. Temperature sensitivity is increased from 14.1 pm/°C (single SC-SCF) to 481.8 pm/°C (cascaded SC-SCFs).
Fig. 6. (a) Transmission spectra of three cascaded combinations. (b) Transmission spectra of three cascaded combinations under a linear coordinate transformation. (c) FFT band pass filtered spectrum in linear coordinates. (d) Wavelength shift of single SC-SCF and three cascaded combinations as a function of temperature for interferometer dip.
3.3 Discussion
The Vernier effect is successfully introduced into the strong coupling seven-core fiber super-mode interferometer. Since the FSR of the interferometer changes with wavelength over the wide operation wavelength range, the amplification M of this sensor cannot be accurately calculated theoretically. Nevertheless, Eq. (6) indicates that a smaller difference in the FSR (i.e., the lengths of the SC-SCFs of the two interferometers) gives rise to a larger value of M. Our experimental results demonstrate that the sensitivity of the combination of 8.7 + 9 cm is much larger than that of the combination of 8 + 9 cm, which is consistent with the theory. The bending sensor proposed in this paper achieves a 19-fold increase in sensitivity. Table 1 is a survey of recent research on fiber bending sensors based on composite optical fiber interferometers. Our sensor only involves splicing two short pieces of SC-SCF without offset splicing or other treatments. It is mechanically robust and easy to fabricate.
Table 1. Bending sensors based on composite optical fiber interferometers
As the bending sensitivity has an enhanced effect, the temperature sensing aspect is also enhanced, so it is necessary to conduct a temperature cross-sensitivity analysis. For the sensor with 8.7 + 9 cm combination, its Vernier bending sensitivity and temperature sensitivity are 42.32 nm/m−1 and 0.48 nm/°C, respectively, corresponding to a cross sensitivity of 0.011 m−1/°C. As we know, the Vernier temperature sensitivity of 0.48 nm/°C was measured when the temperature changes of the reference interferometer and the sensing interferometer are different. Actually, for bending sensing, temperature is an environmental variable, i.e., the temperature changes for the two interferometers are usually the same. In this case, the Vernier temperature sensitivity is much smaller than 0.48 nm/°C [31]. Therefore, the actual cross sensitivity is much smaller than 0.011 m−1/°C.
4. Conclusion
In summary, we have proposed and demonstrated a sensitivity enhanced sensor based on the Vernier effect using cascaded SC-SCF interferometers. The Vernier effect is formed by cascaded dual SC-SCF interferometers with slightly different FSRs. One SC-SCF interferometer is used for the sensing element, while the other SC-SCF interferometer serves as the reference. We investigate the principle of the Vernier configuration theoretically. The bending and temperature characteristics of the proposed sensor are experimentally investigated. The signal is demodulated by coordinate conversion and FFT bandpass filtering to track the wavelength drift. The experimental results show that by optimizing the length difference of SC-SCF from 1 cm to 0.3 cm, the bending sensitivity of the proposed sensor can be improved from −2.20 nm/m−1 (single SC-SCF) to 42.32 nm/m−1 (cascaded SC-SCFs), and the temperature sensitivity can be improved from 14.1 pm/°C (single SC-SCF) to 481.8 pm/°C (cascaded SC-SCFs). The proposed SC-SCF interferometer sensitivity-enhanced sensor has higher bending and temperature sensitivities. Therefore, it is promising for bending and temperature measurements on high-precision infrastructures.
Funding
National Natural Science Foundation of China (62075087, 62175089); Natural Science Foundation of Guangdong Province (2014A030306040, 2018A030313440); Pearl River S and T Nova Program of Guangzhou Municipality (201806010197); Guangdong Provincial Pearl River Talents Program (2019BT02X105); Guangzhou Science and Technology Program Key Projects (201904020032).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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