- Email: [email protected]
High-sensitivity photonic crystal fiber force sensor based on Sagnac interferometer for weighing
Optics and Laser Technology xxx (xxxx) xxxx
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
High-sensitivity photonic crystal fiber force sensor based on Sagnac interferometer for weighing ⁎
Qiang Liu , Liang Xing, Zhaoxia Wu, Lu Cai, Zerui Zhang, Jincheng Zhao School of Control Engineering, Northeastern University at Qinhuangdao, 066004, People’s Republic of China
H I GH L IG H T S
high sensitivity is up to 16.32 nm/N as the force varies from 0 N to 0.392 N. • The find the sensitivity of the sensor increases as the length of the PM-PCF decreases. • We • The sensor is very weakly affected by ambient temperature.
A R T I C LE I N FO
A B S T R A C T
Keywords: Sagnac interferometer Photonic crystal fiber Force sensor Temperature-insensitive
Based on Sagnac interferometer, we proposed a force sensor with simple structure by embedding a short of polarization-maintaining photonic crystal fiber (PM-PCF) into Sagnac loop. It can be used to weigh small objects. Experiments were carried out with PM-PCF of different lengths. The results show that as the length of PM-PCF decreases, the sensitivity of the sensor will increase. As the length of PCF is 3 cm, the sensitivity reaches to 16.32 nm/N as the force varies from 0 N to 0.392 N. Due to the ultralow thermal coefficient of the quartz crystal, the force sensor is insensitive to temperature and therefore does not have to be taken into account the effect of temperature on the sensor.
1. Introduction In recent years, optical fiber sensors have attracted much research interests due to their high sensitivity, strong anti-interference ability, and reusability. Fiber optic sensors have important applications in many aspects such as power engineering, marine shipping, military defense, and biomedical, etc [1–5]. At present, the most widely used optical fiber force sensors are usually wavelength detection technologies of fiber Bragg grating (FBG) and long-period fiber grating (LPFG) [6–9]. These methods are complex in system, expensive in cost, and greatly affected by external environment (such as temperature, electric field, magnetic field, etc.), which will lead to the problem of crosssensitivity. Therefore, it is of great significance to develop a high-sensitivity optical fiber force sensor that is simple in structure and is not affected by changes in ambient temperature. Photonic crystal fiber (PCF) [10–12] is a kind of special fiber, there are many air holes distributed on the cross section. Lots of schemes for force measurement have been reported based on PCF. Xinyong Dong et al. used a short length of PM-PCF as the sensing element inserted in a Sagnac loop interferometer [13], but the sensitivity of the sensor is only
⁎
0.23 pm/με. Jiarong Zheng et al. demonstrated a strain sensor based on a PCF in line Mach–Zehnder interferometer [14], the sensitivity is just 2.1 pm/με, and the sensitivity of the temperature is 13.24 pm/℃. Tingting Han et al. proposed a simultaneous temperature and force measurement sensor by using Fabry-Perot interferometer and bandgap effect of a fluid-filled PCF inserted in a fiber loop to act as the sensing head [15], although the temperature sensitivity more than −1.94 dB/ °C is achieved, the force sensitivity of the sensor is only 3.25 nm/N. Hu Liang et al created a temperature and force simultaneous measurement sensors by filling different refractive index liquids into PCF [16]. Despite the high sensitivity of this sensor, it is difficult to fill liquids with different refractive indices into air holes, thus its application prospects are limited. Sagnac interferometer fiber optic sensor is widely used for many sensing applications because of its simplicity and high sensitivity [17–25]. Weiguo Chen et al. using side-leakage PCF proposed a highly sensitive torsion sensor based on Sagnac interferometer [21]. Chunliu Zhao et al. filled alcohol into a high birefringence PCF with a length of 6.1 cm and measured the temperature change using a Sagnac interference structure [22]. Lok-Hin Cho et al. developed a pressure sensor
Corresponding author. E-mail address: [email protected] (Q. Liu).
https://doi.org/10.1016/j.optlastec.2019.105939 Received 18 September 2019; Received in revised form 21 October 2019; Accepted 1 November 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Qiang Liu, et al., Optics and Laser Technology, https://doi.org/10.1016/j.optlastec.2019.105939
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
origin after a circumference, the optical path difference between them changes with the rotation of the closed optical path relative to the inertial space, thereby causing interference [25]. The schematic diagram based on fiber Sagnac interferometer to measure force shown in Fig. 3. The light from the amplification spontaneous emissions (ASE) broadband source passes through a 3 dB coupler (50:50) and split into two equal light with opposite directions. Two beams travel the same optical path. Introducing PM-PCF into the Sagnac loop, a phase difference is produced due to the birefringence characteristics of PM-PCF. Transmission spectrum can be expressed by [15]
T=
(2)
where φ=2πLB/λ is the phase difference of the interference ring, L is the length of PM-PCF, B is the birefringence value of PM-PCF, it can be described as B = ny-nx. That is the difference between the effective refractive indices of the modes in the fast and slow axis. λ is the wavelength of the light wave in the vacuum. The interval between adjacent peaks can be expressed as:
Fig. 1. Microscopic cross-section of PM-PCF. The diameters of large and small holes are about 4.01 μm and 1.74 μm, the lattice size is about 6.54 μm.
based on Sagnac structure, the sensitivity reaches 9.47 nm/MPa when the operating wavelength is 850 nm, and the sensitivities of different working wavelengths are different [23]. In this paper, we reported a temperature-insensitive force sensor based on Sagnac interferometer by inserting a short of PM-PCF into Sagnac loop interferometer. The sensor performs different sensitivities when the PM-PCF’s length changes. As the length of PM-PCF decrease, the sensitivity of sensor will increase. As the length of the fiber is 3 cm, the sensitivity of the sensor is up to 16.32 nm/N. The force measurement is intrinsic temperature insensitive because of the ultralow thermal coefficient of PM-PCF based on Sagnac interferometers, it is only −0.045 nm/℃, which improves the accuracy of the force measurement and eliminates the necessarity of temperature compensation.
S=
λ2 . LB
(3)
The spectral spacing S represents the period of the sinusoidal interference spectrum and also represents the dynamic range of the sensor. When the Sagnac fiber optic ring is stationary, the optical path that propagates in clockwise in the fiber and the one that propagates in counterclockwise in the fiber are exactly identical, the polarization state and amplitude are also the same by using the conventional singlemode fiber, so the phase difference is zero. While PM-PCF possessing birefringence is used, the phase difference is produced. When the force is applied, the PM-PCF is subjected to the force, causing the air holes changing, therefore internal structure and fiber length change, and the value B of the birefringence changes, so the phase difference also changes. The following relationship can be obtained by
2. Principle and experiment setup The cross-sectional view of the PM-PCF under a microscope shown in Fig. 1. The PM-PCF has a hexagonal structure, and the diameter of PM-PCF is 125 μm. The fundamental material is fused silica. From the figure, we can see that there are two large airs near the core of PM-PCF compared with ordinary single-mode photonic crystal fiber. For the holes, the diameter of the large holes is measured to be about 4.01 μm, the diameter of the small holes is about 1.74 μm, and the lattice size is about 6.54 μm. This leads to the geometric asymmetry of PM-PCF, which makes the orthogonal polarization directions of the fibers have different refractive indices, forming the fast axis and the slow axis, which produces the birefringence effect of PM-PCF. The simulation of the mode field distributions of PM-PCF, which is calculated by finite element method shown in Fig. 2. The size of the perfect matching layer is reduced to save calculation time. The temperature is set as 25 ℃. The dispersion relation of silica is calculated by Sellmeier equation [24]
Δϕ =
2π (LΔB + ΔLB ) . λ
(4)
The phase difference transform brings the wavelength shift.Δλ=SΔφ/2π. The force can be measured by detecting changes in wavelength. Hence, the Sagnac interferometer can be applied for force measurement. 3. Results and discussions In our experiment, the used ASE broadband source is manufactured by CONQUER company, the wavelength range is 1510–1630 nm. The splitting ratio of 3 dB coupler is 1:1, which divides the incident light into two beams of equal intensity and opposite directions. The polarization controller is mainly composed of a linear polarizer, a quarter wave plate and a half wave plate. By rotating the λ/4 and λ/2 wave plates, the fast axis can be rotated at any angle with respect to the direction of the linearly polarized light, thereby any desired polarization state can be obtained. The three-dimensional moving state is used to fix the PM-PCF. Both ends of the PM-PCF are connected to the 3 dB coupler through a fusion splicer. There is mismatch in numerical aperture (NA) between single-mode fiber (SMF) and PM-PCF, Therefore, there will be a bit of loss at the fusion joint. Fig. 4 shows the PM-PCF and SMF fusion diagram. We adjust the appropriate discharge intensity and discharge time with the FITEL s179c type fusion splicer on experiment time after time. We finally acquired a good result making the air holes of PM-PCF collapse as minimum as possible and having low loss of light during propagation. For the force measurement, we expressed the force according to the mass of the weight. Both ends of PM-PCF are mounted on two threedimensional moving states under indoor temperature. The weight is
n2 (λ, T ) = (1.31552 + 6.90754 × 10−6T ) (0.788404 + 23.5835 × 10−6T ) λ2 + 2 λ − (0.0110199 + 0.584758 × 10−6T ) (0.91316 + 0.548368 × 10−6T ) λ2 + . λ2 − 100
1 − cos ϕ 2
(1)
Fig. 2(a) shows the mode field distribution of the X-polarization mode at the wavelength of 1550 nm, and Fig. 2(b) shows the mode field distribution of the Y-polarization mode at the same wavelength. The refractive index of the Y-polarization mode is higher than that the Xpolarization direction, and the refractive indices are 1.437019 and 1.436585 respectively. In 1931, the French Sagnac first proposed the Sagnac effect, which is an optical effect: in a closed light path, light from a certain source simultaneously propagates in the opposite direction, and returns to the 2
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
Fig. 2. Mode field distributions of X-polarization (a) and Y-polarization (b) modes.
Fig. 3. The schematic diagram based on Sagnac interferometer for the experiment setup.
Fig. 4. Micrograph of the SMF and PM-PCF splicing point.
suspended at the center of the PM-PCF. The mass of the weight is at a range of 0–40 g per 10 g, which equal to 0–0.392 N, and the forces acting on the fiber are different, so that the fiber has different degrees of shape change. Transmission spectrum of the force sensor was obtained by an optical spectrum analyzer (OSA) with resolution of 0.02 nm (YOKOGAWA company AQ6370D). Fig. 5 shows the transmission spectra of PM-PCF with various lengths based on Sagnac loop, the force is 0 N. From the figure we could obviously see that, in the range of 1530–1620 nm wavelength, when the length of PM-PCF is 10 cm, 7.4 cm and 3 cm respectively, the transmission spectrum has different numbers of dips, the increase in fiber length causes the phase difference
Fig. 5. Transmission spectra of PM-PCF with different lengths by experiments. The number of dip wavelengths increases with length increasing.
to change, resulting in more dips. The wavelength spacing between the two dips is about 25.7 nm when the fiber is 10 cm. However, when the fiber length is 7.4 cm, it has larger distance between the dips, it is about 35.2 nm. That makes the sensor more sensitive to force. The 3 cm PMPCF has the highest extinction ratio of 22.5 dB. The dip positions of the 10 cm PM-PCF are 1552.6 nm, 1578.3 nm and 1604 nm respectively. 3
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
PCF and an increase in the optical path. The 1552 nm band was selected as the interference observation point, and the experimental data of the sensor was extracted for curve fitting. The dip wavelengths are 1552.6–1557.1 nm as the force varies from 0 to 0.392 N. The dip wavelength dependence on the force is shown in Fig. 7(b). The linear fit of experimental value is made. We got a wavelength-strain sensitivity of 8.16 nm/N from experimental data and the value of R2 is 0.9638, which indicates that the linearity of the wavelength to force response is wonderful. In contrast, we also studied the force sensors with different lengths of PM-PCF based on Sagnac interferometer. Fig. 8 and Fig. 9 show respectively the transmission spectra of 7.4 cm and 3 cm PM-PCF and the dip wavelengths varying with force. The dip wavelengths are 1540 nm, 1541.2 nm, 1541.9 nm, 1543.2 nm and 1544.1 nm as the force increases shown in Fig. 8(a), the FWHM and transmittance are not changed obviously. The dip wavelengths are 1548.2 nm, 1549.1 nm, 1551.5 nm, 1553 nm and 1554.6 nm as the force increases shown in Fig. 9(a), the FWHM is increased and the transmittance is not changed regularly. It could be found that the sensitivities of the 7.4 cm and 3 cm PM-PCF are 11.22 nm/N and 16.32 nm/N, and the linear fit values of R2 are 0.9919 and 0.9808 respectively. All the sensitivities of the sensors are higher than that of using a photonic crystal fiber-based Sagnac loop in reference [26]. On the basis of experiment result, we may conclude that, the sensitivity of the force sensor will increase with the decrease of PMPCF length. When the fiber is 3 cm, the sensitivity of the sensor is the highest, therefore that provides new ideas for improving sensor’s sensitivity. Because the three sample sensors have different sensitivities, therefore the resolution is different. The resolution of the three force sensors are 0.024 N, 0.017 N, 0.012 N respectively, under the limited resolution of 0.02 nm of the OSA. To confirm that the PM-PCF is insensitive to temperature because of its ultralow thermal coefficient, we used a 3 cm PM-PCF as an example to test the temperature sensitive characteristics of the sensor in a constant temperature and humidity chamber, the temperature varies from 20 ℃ to 80 ℃. The experimental results are shown in Fig. 10. On account of changes in the environment, when temperature is measured, the transmission spectrum obtained is slightly different from the force measured before, but this does not affect the accuracy of temperature sensitivity of the sensor. There is a blue shift of the wavelength when the temperature increases. The sensitivity of the PCF sensor to temperature is only −0.045 nm/℃, The R2 of the linear fitting curve obtained from the experimental results is really high up to 0.99745, so that the influence of this low temperature sensitivity to the sensor can be ignored.
Fig. 6. Transmission spectrum of 10 cm PM-PCF embedded into Sagnac loop by simulation. The dip positions are 1546 nm and 1584 nm respectively.
The dip positions of the 7.4 cm PM-PCF are about 1540 nm and 1575.2 nm. The corresponding position of the 3 cm PM-PCF is 1547.6 nm. We made a simulation of the transmission characteristics based on the Sagnac principle with the software of comsol 3.5 and the force is 0 N. The corresponding PM-PCF parameters are introduced in paragraph-1 and section-2. The transmission spectrum is shown in Fig. 6. There are two dips in this wavelength range, and the dip wavelengths are about 1546 nm and 1584 nm respectively. The distance between the troughs is 38 nm, and the extinction ratio is high up to 37.5 dB. Compared with the experimental results, there is a certain deviation, the first dip moves to the left and the second moves to the right, and there is no dip at 1604 nm, and the transmission curve is smoother than experimental results, but this deviation has no effect on the force measurement experiment. This result may be caused by the parameter changes of PM-PCF and single-mode fiber by the fusion and the loss of the optical path during the experiment. Fig. 7(a) shows the transmission spectrum obtained by measuring the force with a 10 cm PM-PCF. It can be seen from the figure that as the force of the weight increases from 0 N to 0.392 N, the transmission spectrum is red-shifted. Furthermore, the light transmittance is increased, and the full width at half maximum (FWHM) is reduced. The performance of the sensor is not affected by the amplitude of the transmission, mainly by monitoring the wavelength shift to measure force. Due to the gravity of the weight, the air holes inside of the PCF are compressed, causing a change in the birefringence value of the PM-
Fig. 7. (a) Transmission spectra of 10 cm PM-PCF inserted in the Sagnac loop under different forces. (b) Dip wavelength versus force at 1552.6 nm, the average sensitivity is 8.16 nm/N. 4
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
Fig. 8. (a) Transmission spectra of 7.4 cm PM-PCF inserted in the Sagnac loop under different forces. (b) Dip wavelength versus force at 1540 nm, the average sensitivity is 11.22 nm/N.
Fig. 9. (a) Transmission spectra of 3 cm PM-PCF inserted in the Sagnac loop under different forces. (b) Dip wavelength versus force at 1548.2 nm, the average sensitivity is 16.32 nm/N.
4. Conclusions
sensitivity. The lengths of PM-PCF are 10 cm, 7.4 cm and 3 cm, the sensitivities of the sensor are 8.16 nm/N, 11.22 nm/N and 16.32 nm/N respectively as the force varies from 0 N to 0.392 N. Compared with the previous fiber Bragg grating and long period grating sensors, the proposed force sensor have simple structure and it is instinctive insensitive to temperature. These advantages have great potential for sensor applications.
In conclusion, a temperature-insensitive force sensor by inserting a bit of PM-PCF into Sagnac interferometer loop has been demonstrated. According to the experiment results, we figured that the length of PMPCF influences the sensitivity of the sensor. Force sensors based on Sagnac interferometer with shorter PM-PCF lengths usually have higher
Fig. 10. (a) Transmission spectra result of 3 cm PM-PCF inserted to the Sagnac loop under different temperatures. (b) Dip wavelength versus temperature at 1548 nm, the average sensitivity is 0.045 nm/℃. 5
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
Acknowledgments
[13] X.Y. Dong, H.Y. Tam, P. Shum, Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer, Appl. Phys. Lett. 90 (2007) 151113, https://doi.org/10.1063/1.2722058. [14] J.R. Zheng, P.G. Yan, Y.Q. Yu, Z.L. Ou, J.S. Wang, X. Chen, C.L. Du, Temperature and index insensitive strain sensor based on a photonic crystal fiber in line MachZehnder interferometer, Opt. Commun. 297 (2013) 7–11, https://doi.org/10.1016/ j.optcom.2013.01.063. [15] T.T. Han, Y.G. Liu, Z. Wang, Z.F. Wu, S.X. Wang, S. Li, Simultaneous temperature and force measurement using Fabry-Perot interferometer and bandgap effect of a fluid-filled photonic crystal fiber, Opt. Express 20 (12) (2012) 13320–13325, https://doi.org/10.1364/OE.20.013320. [16] H. Liang, W.G. Zhang, P.C. Geng, Simultaneous measurement of temperature and force with high sensitivities based on filling different index liquids into photonic crystal fiber, Opt. Lett. 38 (7) (2013) 1071–1073, https://doi.org/10.1364/OL.38. 001071. [17] Q. Liu, S.G. Li, X. Wang, Sensing characteristics of a MF-filled photonic crystal fiber Sagnac interferometer for magnetic field detecting, Sens. Actuat. B 242 (2017) 949–955, https://doi.org/10.1016/j.snb.2016.09.160. [18] Q. Liu, S.G. Li, H. Chen, Enhanced sensitivity of temperature sensor by a PCF with a defect core based on Sagnac interferometer, Sens. Actuat. B 254 (2018) 636–641, https://doi.org/10.1016/j.snb.2017.07.120. [19] Q. Liu, L. Xin, Z.X. Wu, Refractive index sensor of a photonic crystal fiber Sagnac interferometer based on variable polarization states, Appl. Phys Express 12 (6) (2019) 062009, https://doi.org/10.7567/1882-0786/ab1ffc. [20] Y.E. Monfared, C. Liang, R. Khosravi, B. Kacerovska, S. Yang, Selectively toluenefilled photonic crystal fiber Sagnac interferometer with high sensitivity for temperature sensing applications, Res. Phys. 13 (2019) 102297, https://doi.org/10. 1016/j.rinp.2019.102297. [21] W.G. Chen, S.Q. Lou, L.W. Wang, H. Zou, W.L. Lu, S.S. Jian, Highly sensitive torsion sensor based on Sagnac interferometer using Side-Leakage photonic crystal fiber, IEEE Photon. Technol. Lett. 23 (21) (2011) 1639–1641, https://doi.org/10.1109/ LPT.2011.2166062. [22] W.W. Qian, C.L. Zhao, S.L. He, High-sensitivity temperature sensor based on an alcohol-filled photonic crystal fiber loop mirror, Opt. Lett. 36 (9) (2011) 1548–1550, https://doi.org/10.1364/OL.36.001548. [23] L.H. Cho, C. Wu, C. Lu, H.Y. Tam, A highly sensitive and Low-Cost Sagnac loop based pressure sensor, IEEE Sens. J. 13 (8) (2013) 3073–3078, https://doi.org/10. 1109/JSEN.2013.2261291. [24] G. Ghosh, M. Endo, T. Lwasaki, Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glass, J. Lightw. Technol. 12 (1994) 1338–1342, https://doi.org/10.1109/50.317500. [25] H.J. Arditty, H.C. Leèfovre, Sagnac effect in fiber gyroscopes, Opt. Lett. 6 (8) (1981) 401–403, https://doi.org/10.1364/OL.6.000401. [26] P. Zu, C.C. Chan, Y.X. Jin, Y.F. Zhang, X.Y. Dong, Fabrication of a temperatureinsensitive transverse mechanical load sensor by using a photonic crystal fiberbased Sagnac loop, Meas. Sci. Technol. 22 (2) (2011) 025204, https://doi.org/10. 1088/0957-0233/22/2/025204.
This research was funded by the National Natural Science Foundation of China (Grant No. 51907017), the Key Science and Technology Research Projects of Higher Education Institutions in Hebei Province of China (Grant No. ZD2019304), the Fundamental Research Funds for the Central Universities of China (Grant No. N182304011), the Key Program of the Natural Science Foundation of Hebei Province of China (Grant No. F2017203193). References [1] Y. Zhao, Z.Q. Deng, J. Li, Photonic crystal fiber based surface plasmon resonance chemical sensors, Sens. Actuat. B 202 (2014) 557–567, https://doi.org/10.1016/j. snb.2014.05.127. [2] F.A. José, C.Z. Dimitrios, T. Alberto, P. David, M.S.P. José, Infiltrated photonic crystal fibers for sensing applications, Sensors 18 (12) (2018) 4263, https://doi. org/10.3390/s18124263. [3] F. Eric, K.S. Carlos, Optical fiber force myography sensor for identification of hand postures, J. Sensors 8940373 (2018), https://doi.org/10.1155/2018/8940373. [4] Y. Zhao, R.J. Tong, M. Chen, F. Xia, Relative humidity sensor based on hollow core fiber filled with GQDs-PVA, Sens. Actuat. B 284 (2019) 96–102, https://doi.org/10. 1016/j.snb.2018.12.130. [5] Y. Zhao, R.J. Tong, F. Xia, Y. Peng, Current status of optical fiber biosensor based on surface plasmon resonance, Biosens. Bioelectron 142 (2019) 111505, https://doi. org/10.1016/j.bios.2019.111505. [6] T. Mawatari, D. Nelson, A multi-parameter Bragg grating fiber optic sensor and triaxial strain measurement, Smart. Mater. Struct 17 (3) (2008) 035033, https:// doi.org/10.1088/0964-1726/17/3/035033. [7] G. Thomas, L. Geert, V. Eli, N. Tomasz, Transversal load sensing with fiber Bragg grating in Microstructured Optical Fibers, IEEE Photon. Technol. Lett. 21 (1) (2009) 6–8, https://doi.org/10.1109/LPT.2008.2007915. [8] Y. Wang, D.N. Wang, W. Jin, Y. Rao, Asymmetric transverse-load characteristics and polarization dependence of long-period fiber gratings written by a focused CO2 laser, Appl. Opt. 46 (2007) 3079–3086, https://doi.org/10.1364/AO.46.003079. [9] V.I. Del, O. Fuentes, F. Chiavaioli, Optimized strain long-period fiber grating (LPFG) sensors operating at the dispersion turning point, J. Lightw. Technol. 36 (11) (2018) 2240–2247, https://doi.org/10.1109/JLT.2018.2790434. [10] T.A. Birks, J.C. Knight, P.S.J. Russell, Endlessly single-mode photonic crystal fiber, Opt. Lett. 22 (13) (1997) 961–963, https://doi.org/10.1364/OL.22.000961. [11] P. Russell, Photonic crystal fibers, Science 299 (5605) (2003) 358–362, https://doi. org/10.1126/science.1079280. [12] M. Andreana, T. Le, W. Drexler, A. Unterhuber, Ultrashort pulse Kagome hollowcore photonic crystal fiber delivery for nonlinear optical imaging, Opt. Lett. 44 (7) (2019) 1588–1591, https://doi.org/10.1364/OL.44.001588.
6
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
High-sensitivity photonic crystal fiber force sensor based on Sagnac interferometer for weighing ⁎
Qiang Liu , Liang Xing, Zhaoxia Wu, Lu Cai, Zerui Zhang, Jincheng Zhao School of Control Engineering, Northeastern University at Qinhuangdao, 066004, People’s Republic of China
H I GH L IG H T S
high sensitivity is up to 16.32 nm/N as the force varies from 0 N to 0.392 N. • The find the sensitivity of the sensor increases as the length of the PM-PCF decreases. • We • The sensor is very weakly affected by ambient temperature.
A R T I C LE I N FO
A B S T R A C T
Keywords: Sagnac interferometer Photonic crystal fiber Force sensor Temperature-insensitive
Based on Sagnac interferometer, we proposed a force sensor with simple structure by embedding a short of polarization-maintaining photonic crystal fiber (PM-PCF) into Sagnac loop. It can be used to weigh small objects. Experiments were carried out with PM-PCF of different lengths. The results show that as the length of PM-PCF decreases, the sensitivity of the sensor will increase. As the length of PCF is 3 cm, the sensitivity reaches to 16.32 nm/N as the force varies from 0 N to 0.392 N. Due to the ultralow thermal coefficient of the quartz crystal, the force sensor is insensitive to temperature and therefore does not have to be taken into account the effect of temperature on the sensor.
1. Introduction In recent years, optical fiber sensors have attracted much research interests due to their high sensitivity, strong anti-interference ability, and reusability. Fiber optic sensors have important applications in many aspects such as power engineering, marine shipping, military defense, and biomedical, etc [1–5]. At present, the most widely used optical fiber force sensors are usually wavelength detection technologies of fiber Bragg grating (FBG) and long-period fiber grating (LPFG) [6–9]. These methods are complex in system, expensive in cost, and greatly affected by external environment (such as temperature, electric field, magnetic field, etc.), which will lead to the problem of crosssensitivity. Therefore, it is of great significance to develop a high-sensitivity optical fiber force sensor that is simple in structure and is not affected by changes in ambient temperature. Photonic crystal fiber (PCF) [10–12] is a kind of special fiber, there are many air holes distributed on the cross section. Lots of schemes for force measurement have been reported based on PCF. Xinyong Dong et al. used a short length of PM-PCF as the sensing element inserted in a Sagnac loop interferometer [13], but the sensitivity of the sensor is only
⁎
0.23 pm/με. Jiarong Zheng et al. demonstrated a strain sensor based on a PCF in line Mach–Zehnder interferometer [14], the sensitivity is just 2.1 pm/με, and the sensitivity of the temperature is 13.24 pm/℃. Tingting Han et al. proposed a simultaneous temperature and force measurement sensor by using Fabry-Perot interferometer and bandgap effect of a fluid-filled PCF inserted in a fiber loop to act as the sensing head [15], although the temperature sensitivity more than −1.94 dB/ °C is achieved, the force sensitivity of the sensor is only 3.25 nm/N. Hu Liang et al created a temperature and force simultaneous measurement sensors by filling different refractive index liquids into PCF [16]. Despite the high sensitivity of this sensor, it is difficult to fill liquids with different refractive indices into air holes, thus its application prospects are limited. Sagnac interferometer fiber optic sensor is widely used for many sensing applications because of its simplicity and high sensitivity [17–25]. Weiguo Chen et al. using side-leakage PCF proposed a highly sensitive torsion sensor based on Sagnac interferometer [21]. Chunliu Zhao et al. filled alcohol into a high birefringence PCF with a length of 6.1 cm and measured the temperature change using a Sagnac interference structure [22]. Lok-Hin Cho et al. developed a pressure sensor
Corresponding author. E-mail address: [email protected] (Q. Liu).
https://doi.org/10.1016/j.optlastec.2019.105939 Received 18 September 2019; Received in revised form 21 October 2019; Accepted 1 November 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Qiang Liu, et al., Optics and Laser Technology, https://doi.org/10.1016/j.optlastec.2019.105939
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
origin after a circumference, the optical path difference between them changes with the rotation of the closed optical path relative to the inertial space, thereby causing interference [25]. The schematic diagram based on fiber Sagnac interferometer to measure force shown in Fig. 3. The light from the amplification spontaneous emissions (ASE) broadband source passes through a 3 dB coupler (50:50) and split into two equal light with opposite directions. Two beams travel the same optical path. Introducing PM-PCF into the Sagnac loop, a phase difference is produced due to the birefringence characteristics of PM-PCF. Transmission spectrum can be expressed by [15]
T=
(2)
where φ=2πLB/λ is the phase difference of the interference ring, L is the length of PM-PCF, B is the birefringence value of PM-PCF, it can be described as B = ny-nx. That is the difference between the effective refractive indices of the modes in the fast and slow axis. λ is the wavelength of the light wave in the vacuum. The interval between adjacent peaks can be expressed as:
Fig. 1. Microscopic cross-section of PM-PCF. The diameters of large and small holes are about 4.01 μm and 1.74 μm, the lattice size is about 6.54 μm.
based on Sagnac structure, the sensitivity reaches 9.47 nm/MPa when the operating wavelength is 850 nm, and the sensitivities of different working wavelengths are different [23]. In this paper, we reported a temperature-insensitive force sensor based on Sagnac interferometer by inserting a short of PM-PCF into Sagnac loop interferometer. The sensor performs different sensitivities when the PM-PCF’s length changes. As the length of PM-PCF decrease, the sensitivity of sensor will increase. As the length of the fiber is 3 cm, the sensitivity of the sensor is up to 16.32 nm/N. The force measurement is intrinsic temperature insensitive because of the ultralow thermal coefficient of PM-PCF based on Sagnac interferometers, it is only −0.045 nm/℃, which improves the accuracy of the force measurement and eliminates the necessarity of temperature compensation.
S=
λ2 . LB
(3)
The spectral spacing S represents the period of the sinusoidal interference spectrum and also represents the dynamic range of the sensor. When the Sagnac fiber optic ring is stationary, the optical path that propagates in clockwise in the fiber and the one that propagates in counterclockwise in the fiber are exactly identical, the polarization state and amplitude are also the same by using the conventional singlemode fiber, so the phase difference is zero. While PM-PCF possessing birefringence is used, the phase difference is produced. When the force is applied, the PM-PCF is subjected to the force, causing the air holes changing, therefore internal structure and fiber length change, and the value B of the birefringence changes, so the phase difference also changes. The following relationship can be obtained by
2. Principle and experiment setup The cross-sectional view of the PM-PCF under a microscope shown in Fig. 1. The PM-PCF has a hexagonal structure, and the diameter of PM-PCF is 125 μm. The fundamental material is fused silica. From the figure, we can see that there are two large airs near the core of PM-PCF compared with ordinary single-mode photonic crystal fiber. For the holes, the diameter of the large holes is measured to be about 4.01 μm, the diameter of the small holes is about 1.74 μm, and the lattice size is about 6.54 μm. This leads to the geometric asymmetry of PM-PCF, which makes the orthogonal polarization directions of the fibers have different refractive indices, forming the fast axis and the slow axis, which produces the birefringence effect of PM-PCF. The simulation of the mode field distributions of PM-PCF, which is calculated by finite element method shown in Fig. 2. The size of the perfect matching layer is reduced to save calculation time. The temperature is set as 25 ℃. The dispersion relation of silica is calculated by Sellmeier equation [24]
Δϕ =
2π (LΔB + ΔLB ) . λ
(4)
The phase difference transform brings the wavelength shift.Δλ=SΔφ/2π. The force can be measured by detecting changes in wavelength. Hence, the Sagnac interferometer can be applied for force measurement. 3. Results and discussions In our experiment, the used ASE broadband source is manufactured by CONQUER company, the wavelength range is 1510–1630 nm. The splitting ratio of 3 dB coupler is 1:1, which divides the incident light into two beams of equal intensity and opposite directions. The polarization controller is mainly composed of a linear polarizer, a quarter wave plate and a half wave plate. By rotating the λ/4 and λ/2 wave plates, the fast axis can be rotated at any angle with respect to the direction of the linearly polarized light, thereby any desired polarization state can be obtained. The three-dimensional moving state is used to fix the PM-PCF. Both ends of the PM-PCF are connected to the 3 dB coupler through a fusion splicer. There is mismatch in numerical aperture (NA) between single-mode fiber (SMF) and PM-PCF, Therefore, there will be a bit of loss at the fusion joint. Fig. 4 shows the PM-PCF and SMF fusion diagram. We adjust the appropriate discharge intensity and discharge time with the FITEL s179c type fusion splicer on experiment time after time. We finally acquired a good result making the air holes of PM-PCF collapse as minimum as possible and having low loss of light during propagation. For the force measurement, we expressed the force according to the mass of the weight. Both ends of PM-PCF are mounted on two threedimensional moving states under indoor temperature. The weight is
n2 (λ, T ) = (1.31552 + 6.90754 × 10−6T ) (0.788404 + 23.5835 × 10−6T ) λ2 + 2 λ − (0.0110199 + 0.584758 × 10−6T ) (0.91316 + 0.548368 × 10−6T ) λ2 + . λ2 − 100
1 − cos ϕ 2
(1)
Fig. 2(a) shows the mode field distribution of the X-polarization mode at the wavelength of 1550 nm, and Fig. 2(b) shows the mode field distribution of the Y-polarization mode at the same wavelength. The refractive index of the Y-polarization mode is higher than that the Xpolarization direction, and the refractive indices are 1.437019 and 1.436585 respectively. In 1931, the French Sagnac first proposed the Sagnac effect, which is an optical effect: in a closed light path, light from a certain source simultaneously propagates in the opposite direction, and returns to the 2
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
Fig. 2. Mode field distributions of X-polarization (a) and Y-polarization (b) modes.
Fig. 3. The schematic diagram based on Sagnac interferometer for the experiment setup.
Fig. 4. Micrograph of the SMF and PM-PCF splicing point.
suspended at the center of the PM-PCF. The mass of the weight is at a range of 0–40 g per 10 g, which equal to 0–0.392 N, and the forces acting on the fiber are different, so that the fiber has different degrees of shape change. Transmission spectrum of the force sensor was obtained by an optical spectrum analyzer (OSA) with resolution of 0.02 nm (YOKOGAWA company AQ6370D). Fig. 5 shows the transmission spectra of PM-PCF with various lengths based on Sagnac loop, the force is 0 N. From the figure we could obviously see that, in the range of 1530–1620 nm wavelength, when the length of PM-PCF is 10 cm, 7.4 cm and 3 cm respectively, the transmission spectrum has different numbers of dips, the increase in fiber length causes the phase difference
Fig. 5. Transmission spectra of PM-PCF with different lengths by experiments. The number of dip wavelengths increases with length increasing.
to change, resulting in more dips. The wavelength spacing between the two dips is about 25.7 nm when the fiber is 10 cm. However, when the fiber length is 7.4 cm, it has larger distance between the dips, it is about 35.2 nm. That makes the sensor more sensitive to force. The 3 cm PMPCF has the highest extinction ratio of 22.5 dB. The dip positions of the 10 cm PM-PCF are 1552.6 nm, 1578.3 nm and 1604 nm respectively. 3
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
PCF and an increase in the optical path. The 1552 nm band was selected as the interference observation point, and the experimental data of the sensor was extracted for curve fitting. The dip wavelengths are 1552.6–1557.1 nm as the force varies from 0 to 0.392 N. The dip wavelength dependence on the force is shown in Fig. 7(b). The linear fit of experimental value is made. We got a wavelength-strain sensitivity of 8.16 nm/N from experimental data and the value of R2 is 0.9638, which indicates that the linearity of the wavelength to force response is wonderful. In contrast, we also studied the force sensors with different lengths of PM-PCF based on Sagnac interferometer. Fig. 8 and Fig. 9 show respectively the transmission spectra of 7.4 cm and 3 cm PM-PCF and the dip wavelengths varying with force. The dip wavelengths are 1540 nm, 1541.2 nm, 1541.9 nm, 1543.2 nm and 1544.1 nm as the force increases shown in Fig. 8(a), the FWHM and transmittance are not changed obviously. The dip wavelengths are 1548.2 nm, 1549.1 nm, 1551.5 nm, 1553 nm and 1554.6 nm as the force increases shown in Fig. 9(a), the FWHM is increased and the transmittance is not changed regularly. It could be found that the sensitivities of the 7.4 cm and 3 cm PM-PCF are 11.22 nm/N and 16.32 nm/N, and the linear fit values of R2 are 0.9919 and 0.9808 respectively. All the sensitivities of the sensors are higher than that of using a photonic crystal fiber-based Sagnac loop in reference [26]. On the basis of experiment result, we may conclude that, the sensitivity of the force sensor will increase with the decrease of PMPCF length. When the fiber is 3 cm, the sensitivity of the sensor is the highest, therefore that provides new ideas for improving sensor’s sensitivity. Because the three sample sensors have different sensitivities, therefore the resolution is different. The resolution of the three force sensors are 0.024 N, 0.017 N, 0.012 N respectively, under the limited resolution of 0.02 nm of the OSA. To confirm that the PM-PCF is insensitive to temperature because of its ultralow thermal coefficient, we used a 3 cm PM-PCF as an example to test the temperature sensitive characteristics of the sensor in a constant temperature and humidity chamber, the temperature varies from 20 ℃ to 80 ℃. The experimental results are shown in Fig. 10. On account of changes in the environment, when temperature is measured, the transmission spectrum obtained is slightly different from the force measured before, but this does not affect the accuracy of temperature sensitivity of the sensor. There is a blue shift of the wavelength when the temperature increases. The sensitivity of the PCF sensor to temperature is only −0.045 nm/℃, The R2 of the linear fitting curve obtained from the experimental results is really high up to 0.99745, so that the influence of this low temperature sensitivity to the sensor can be ignored.
Fig. 6. Transmission spectrum of 10 cm PM-PCF embedded into Sagnac loop by simulation. The dip positions are 1546 nm and 1584 nm respectively.
The dip positions of the 7.4 cm PM-PCF are about 1540 nm and 1575.2 nm. The corresponding position of the 3 cm PM-PCF is 1547.6 nm. We made a simulation of the transmission characteristics based on the Sagnac principle with the software of comsol 3.5 and the force is 0 N. The corresponding PM-PCF parameters are introduced in paragraph-1 and section-2. The transmission spectrum is shown in Fig. 6. There are two dips in this wavelength range, and the dip wavelengths are about 1546 nm and 1584 nm respectively. The distance between the troughs is 38 nm, and the extinction ratio is high up to 37.5 dB. Compared with the experimental results, there is a certain deviation, the first dip moves to the left and the second moves to the right, and there is no dip at 1604 nm, and the transmission curve is smoother than experimental results, but this deviation has no effect on the force measurement experiment. This result may be caused by the parameter changes of PM-PCF and single-mode fiber by the fusion and the loss of the optical path during the experiment. Fig. 7(a) shows the transmission spectrum obtained by measuring the force with a 10 cm PM-PCF. It can be seen from the figure that as the force of the weight increases from 0 N to 0.392 N, the transmission spectrum is red-shifted. Furthermore, the light transmittance is increased, and the full width at half maximum (FWHM) is reduced. The performance of the sensor is not affected by the amplitude of the transmission, mainly by monitoring the wavelength shift to measure force. Due to the gravity of the weight, the air holes inside of the PCF are compressed, causing a change in the birefringence value of the PM-
Fig. 7. (a) Transmission spectra of 10 cm PM-PCF inserted in the Sagnac loop under different forces. (b) Dip wavelength versus force at 1552.6 nm, the average sensitivity is 8.16 nm/N. 4
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
Fig. 8. (a) Transmission spectra of 7.4 cm PM-PCF inserted in the Sagnac loop under different forces. (b) Dip wavelength versus force at 1540 nm, the average sensitivity is 11.22 nm/N.
Fig. 9. (a) Transmission spectra of 3 cm PM-PCF inserted in the Sagnac loop under different forces. (b) Dip wavelength versus force at 1548.2 nm, the average sensitivity is 16.32 nm/N.
4. Conclusions
sensitivity. The lengths of PM-PCF are 10 cm, 7.4 cm and 3 cm, the sensitivities of the sensor are 8.16 nm/N, 11.22 nm/N and 16.32 nm/N respectively as the force varies from 0 N to 0.392 N. Compared with the previous fiber Bragg grating and long period grating sensors, the proposed force sensor have simple structure and it is instinctive insensitive to temperature. These advantages have great potential for sensor applications.
In conclusion, a temperature-insensitive force sensor by inserting a bit of PM-PCF into Sagnac interferometer loop has been demonstrated. According to the experiment results, we figured that the length of PMPCF influences the sensitivity of the sensor. Force sensors based on Sagnac interferometer with shorter PM-PCF lengths usually have higher
Fig. 10. (a) Transmission spectra result of 3 cm PM-PCF inserted to the Sagnac loop under different temperatures. (b) Dip wavelength versus temperature at 1548 nm, the average sensitivity is 0.045 nm/℃. 5
Optics and Laser Technology xxx (xxxx) xxxx
Q. Liu, et al.
Acknowledgments
[13] X.Y. Dong, H.Y. Tam, P. Shum, Temperature-insensitive strain sensor with polarization-maintaining photonic crystal fiber based Sagnac interferometer, Appl. Phys. Lett. 90 (2007) 151113, https://doi.org/10.1063/1.2722058. [14] J.R. Zheng, P.G. Yan, Y.Q. Yu, Z.L. Ou, J.S. Wang, X. Chen, C.L. Du, Temperature and index insensitive strain sensor based on a photonic crystal fiber in line MachZehnder interferometer, Opt. Commun. 297 (2013) 7–11, https://doi.org/10.1016/ j.optcom.2013.01.063. [15] T.T. Han, Y.G. Liu, Z. Wang, Z.F. Wu, S.X. Wang, S. Li, Simultaneous temperature and force measurement using Fabry-Perot interferometer and bandgap effect of a fluid-filled photonic crystal fiber, Opt. Express 20 (12) (2012) 13320–13325, https://doi.org/10.1364/OE.20.013320. [16] H. Liang, W.G. Zhang, P.C. Geng, Simultaneous measurement of temperature and force with high sensitivities based on filling different index liquids into photonic crystal fiber, Opt. Lett. 38 (7) (2013) 1071–1073, https://doi.org/10.1364/OL.38. 001071. [17] Q. Liu, S.G. Li, X. Wang, Sensing characteristics of a MF-filled photonic crystal fiber Sagnac interferometer for magnetic field detecting, Sens. Actuat. B 242 (2017) 949–955, https://doi.org/10.1016/j.snb.2016.09.160. [18] Q. Liu, S.G. Li, H. Chen, Enhanced sensitivity of temperature sensor by a PCF with a defect core based on Sagnac interferometer, Sens. Actuat. B 254 (2018) 636–641, https://doi.org/10.1016/j.snb.2017.07.120. [19] Q. Liu, L. Xin, Z.X. Wu, Refractive index sensor of a photonic crystal fiber Sagnac interferometer based on variable polarization states, Appl. Phys Express 12 (6) (2019) 062009, https://doi.org/10.7567/1882-0786/ab1ffc. [20] Y.E. Monfared, C. Liang, R. Khosravi, B. Kacerovska, S. Yang, Selectively toluenefilled photonic crystal fiber Sagnac interferometer with high sensitivity for temperature sensing applications, Res. Phys. 13 (2019) 102297, https://doi.org/10. 1016/j.rinp.2019.102297. [21] W.G. Chen, S.Q. Lou, L.W. Wang, H. Zou, W.L. Lu, S.S. Jian, Highly sensitive torsion sensor based on Sagnac interferometer using Side-Leakage photonic crystal fiber, IEEE Photon. Technol. Lett. 23 (21) (2011) 1639–1641, https://doi.org/10.1109/ LPT.2011.2166062. [22] W.W. Qian, C.L. Zhao, S.L. He, High-sensitivity temperature sensor based on an alcohol-filled photonic crystal fiber loop mirror, Opt. Lett. 36 (9) (2011) 1548–1550, https://doi.org/10.1364/OL.36.001548. [23] L.H. Cho, C. Wu, C. Lu, H.Y. Tam, A highly sensitive and Low-Cost Sagnac loop based pressure sensor, IEEE Sens. J. 13 (8) (2013) 3073–3078, https://doi.org/10. 1109/JSEN.2013.2261291. [24] G. Ghosh, M. Endo, T. Lwasaki, Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical fiber glass, J. Lightw. Technol. 12 (1994) 1338–1342, https://doi.org/10.1109/50.317500. [25] H.J. Arditty, H.C. Leèfovre, Sagnac effect in fiber gyroscopes, Opt. Lett. 6 (8) (1981) 401–403, https://doi.org/10.1364/OL.6.000401. [26] P. Zu, C.C. Chan, Y.X. Jin, Y.F. Zhang, X.Y. Dong, Fabrication of a temperatureinsensitive transverse mechanical load sensor by using a photonic crystal fiberbased Sagnac loop, Meas. Sci. Technol. 22 (2) (2011) 025204, https://doi.org/10. 1088/0957-0233/22/2/025204.
This research was funded by the National Natural Science Foundation of China (Grant No. 51907017), the Key Science and Technology Research Projects of Higher Education Institutions in Hebei Province of China (Grant No. ZD2019304), the Fundamental Research Funds for the Central Universities of China (Grant No. N182304011), the Key Program of the Natural Science Foundation of Hebei Province of China (Grant No. F2017203193). References [1] Y. Zhao, Z.Q. Deng, J. Li, Photonic crystal fiber based surface plasmon resonance chemical sensors, Sens. Actuat. B 202 (2014) 557–567, https://doi.org/10.1016/j. snb.2014.05.127. [2] F.A. José, C.Z. Dimitrios, T. Alberto, P. David, M.S.P. José, Infiltrated photonic crystal fibers for sensing applications, Sensors 18 (12) (2018) 4263, https://doi. org/10.3390/s18124263. [3] F. Eric, K.S. Carlos, Optical fiber force myography sensor for identification of hand postures, J. Sensors 8940373 (2018), https://doi.org/10.1155/2018/8940373. [4] Y. Zhao, R.J. Tong, M. Chen, F. Xia, Relative humidity sensor based on hollow core fiber filled with GQDs-PVA, Sens. Actuat. B 284 (2019) 96–102, https://doi.org/10. 1016/j.snb.2018.12.130. [5] Y. Zhao, R.J. Tong, F. Xia, Y. Peng, Current status of optical fiber biosensor based on surface plasmon resonance, Biosens. Bioelectron 142 (2019) 111505, https://doi. org/10.1016/j.bios.2019.111505. [6] T. Mawatari, D. Nelson, A multi-parameter Bragg grating fiber optic sensor and triaxial strain measurement, Smart. Mater. Struct 17 (3) (2008) 035033, https:// doi.org/10.1088/0964-1726/17/3/035033. [7] G. Thomas, L. Geert, V. Eli, N. Tomasz, Transversal load sensing with fiber Bragg grating in Microstructured Optical Fibers, IEEE Photon. Technol. Lett. 21 (1) (2009) 6–8, https://doi.org/10.1109/LPT.2008.2007915. [8] Y. Wang, D.N. Wang, W. Jin, Y. Rao, Asymmetric transverse-load characteristics and polarization dependence of long-period fiber gratings written by a focused CO2 laser, Appl. Opt. 46 (2007) 3079–3086, https://doi.org/10.1364/AO.46.003079. [9] V.I. Del, O. Fuentes, F. Chiavaioli, Optimized strain long-period fiber grating (LPFG) sensors operating at the dispersion turning point, J. Lightw. Technol. 36 (11) (2018) 2240–2247, https://doi.org/10.1109/JLT.2018.2790434. [10] T.A. Birks, J.C. Knight, P.S.J. Russell, Endlessly single-mode photonic crystal fiber, Opt. Lett. 22 (13) (1997) 961–963, https://doi.org/10.1364/OL.22.000961. [11] P. Russell, Photonic crystal fibers, Science 299 (5605) (2003) 358–362, https://doi. org/10.1126/science.1079280. [12] M. Andreana, T. Le, W. Drexler, A. Unterhuber, Ultrashort pulse Kagome hollowcore photonic crystal fiber delivery for nonlinear optical imaging, Opt. Lett. 44 (7) (2019) 1588–1591, https://doi.org/10.1364/OL.44.001588.
6