Abstract

A temperature compensated magnetic field strength optical fiber sensor has been proposed and experimentally demonstrated. A fiber Bragg grating (FBG) is cascaded to modal interferometer (MI), which is fabricated by dual S-bend splicing between thin fiber (TF) and single mode fiber (SMF) with intentionally controlled misalignment between cores. We established a modified numerical model to describe the multi-mode interference of this exceptional S-bend and misalignment structure, together with the simulation based on beam propagation method to gain insight into its operation mechanism. The FBG is used to interrogate the temperature change, and then compensate the perturbation of temperature on transmission of the MI. Thanks to the proposed dual S-bend structure and the diameter-thinned TF used here; we have obtained high magnetic sensitivity of −0.0678 dB/Oe using only 4 mm TF after the elimination of ambient temperature change.

© 2014 Optical Society of America

1. Introduction

Optical fiber based magnetic field sensors filled with magnetic fluid (MF) have been intensively investigated in last few years owning to their advantages like compact, stable, precise, reliable, adapting to harsh environments and capable of remote sensing, etc. Among which, magnetic fluid is a kind of colloid constituted by nanoscale magnetic ferrite particles dispersing in a carrier fluid with surfactant. It exhibits characteristics of the fluidity of liquid and the magnetism of solid magnet. MF is superparamagnetic without showing hysteresis and it possesses diverse optical effect such as thermal-optical effect [1], Faraday and birefringence effect [2, 3], tunable refractive index [4, 5], field dependent absorption and scattering [1, 6], etc. The combination of magnetic and optical characteristics make MF a distinguished functional material for developing magneto-optical sensors [3, 5], magneto-optical modulators [2, 4, 6], optical switch [7], tunable filters [1, 8], and so on.

Versatile configurations of optical magnetic field sensors based on MF have been proposed, such as optical fiber Fabry-Perot interferometer [9], optical fiber modal interferometer [10], optical fiber Sagnac interferometer [3], optical fiber Michelson interferometer [11], fiber grating [12, 13], fiber end Fresnel reflection [5], microstructure fiber with MF infiltrated [14, 15], etched and tapered fiber [16, 17], etc. For a specific MF with a constant concentration, its physical properties (especially the refractive index) are dependent on both the applied magnetic field strength with positive correlation [6, 9, 18] and temperature with negative correlation [1, 5]. Miao et al. [1] has demonstrated a transmission-type power thermal-controlled photonic device, which has potential application as tunable attenuator or edge filter. Obviously, the thermo-optical effect of any practical MF-based optical fiber magnetic field sensor will introduce considerable impact such that the performance of magnetic field measurement will be degraded and inaccurate. Recently, Zhao et al. [19] proposed a FBG assisted fiber optic Fabry-Perot interferometer to perform a temperature compensated magnetic field measurement, which shows important perspective and good experimental result. However, the tens of micrometers scale cavity length of the Fabry–Perot is very difficult to be realized without any specific facility. In addition, the package of this magnetic fluid infiltrated micro-cavity structure also increase the difficulty of operation. Besides, as far as we know, the cross-sensitivity issue between magnetic field and temperature for a MF-based optical fiber magnetic sensor has not been fully addressed for developing a temperature compensated optical fiber magnetic field sensor.

In this work, we proposed and demonstrated a magnetic fluid coated S-bend fiber modal interferometer cascaded to fiber Bragg grating for temperature compensated magnetic field strength measurement. A short section of only 4 mm thin fiber is sandwiched by single mode fibers with S-bend at two splicing regions. A modified numerical model of this multi-mode interference due to S-bend and misalignment between cores is established, and simulation based on beam propagation method has been implemented to look into the field distribution of the proposed structure. The variation of temperature can be measured using FBG as it is insensitive to the magnetic field. Since the temperature response of the modal interferometer can be easily obtained by monitoring its transmission spectrum without magnetic field applied, it will be convenient to compensate the perturbation of temperature on the transmission spectrum of modal interferometer thus to realize a temperature insensitive magnetic field measurement. Both the thin fiber and the S-bend structure contribute significantly to enhance the interaction between evanescent field of light and surrounding magnetic fluid. Thus high magnetic field sensitivity can be achieved within such a miniature fiber sensing head.

2. System configuration, principle and simulation analysis

The thin fiber we used in this proposed structure has a cladding diameter of 80 μm and a mode field diameter of ~9.5 um at 1.55 um. The core refractive index of the thin fiber is 1.4735. In order to fabricate an S-bend structure by fusion splicing the thin fiber and conventional single mode fiber (SMF), the manual mode operation of a fusion splicer (Fitel S153A) was adopted [20, 21]. The thin fiber is firstly spliced to a SMF with well-controlled lateral offset between cores of them, as shown in Fig. 1(a), after that one fiber clamp is manually controlled to apply another slight offset and additional “add” arc charge is performed to form the S-structure, as seen by Fig. 1(b). The discharge power is optimized to be “+00100” with the duration time of 2400 ms, and the added discharge time is set to be 500 ms. Subsequently, as presented in Fig. 1(c), the thin fiber is cut by fiber cleaver at another end, and is spliced with another SMF in the same way. Since the step pitch of stepper motor inside the fusion splicer can be adjusted and read from the screen, the whole process is repeatable and stable. The fabricated sensing head section is then inserted into a 2 cm long capillary tube with 1 mm inner diameter and 3 mm outer diameter, the tube is sealed with AB-epoxy glue at its two ends after filling with magnetic fluid (EMG 705, Ferrotec, USA), as schematically illustrated in Fig. 2(a). A fiber Bragg grating is then cascaded to the dual S-bend based modal interferometer and it is kept separated from MF. We spliced the modal interferometer with the FBG. Due to the existence of capillary tube (2 cm) used in current experiment setup, the minimum distance is about 1 cm in our case. Thus it’s very convenient for us to locate the FBG close to the modal interferometer to ensure that they are subjected to the same local temperature.

 

Fig. 1 (a) Illustration diagrams of the fabrication procedure of the S-bend structure. (a) and (b) are performed in fusion splicer, and (c) is in the fiber cleaver.

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Fig. 2 (a) Schematic diagram of the dual S-bend fiber modal interferometer. Inset: optical microscope image of the S-bend splicing region and the electromagnets used for provide accurate magnetic field strength; (b) junction of the S-bend structure.

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Due to the mode mismatch, cladding modes of TF will be excited at the first splicing region along with the propagation direction. The core mode and cladding modes will interfere at the second splicing region after through different optical paths, thus the modal interference takes place. A numerical model describing multi-mode interference has been widely used to provide insight into the mechanism of single-mode–multimode–single-mode fiber structure with ideally alignment [17, 22]; however, it can’t be used here directly without modification because the S-bend structure will give rise to the bending loss and excite asymmetric modes [23]. What’s more, the intentional misalignment within the splicing region should be taken into consideration. For simplicity, we treat the S-bend as a curve-to-curve structure with uniform curvature of R1 and R2, respectively, as shown in Fig. 2(b). Assuming the input light at the straight section of the lead-in SMF has a fundamental mode field profile E(r, 0), the field in a curved section can be given by [24, 25]

E(r,z)=E(r,0)[1+(κ0ncw0)2r/R]
Whereκ0=2π/λ0, nc is the refractive index of fiber core, w0is the waist width of the mode, andR=R1,R2. Due to the S-bend, as well as misalignment between cores, a series of guided modes will be excited in the thin fiber. Assuming they have the field profile ofψm(r) and the splicing point between SMF and TF is at Z=Z0, the input field at the thin fiber can be written as [23]
E(r,z0)=m=1Mcmψm(r)
Where cmis the excitation coefficient of each mode, Mis the total modes number in TF, cmis the excitation coefficient of the m-th mode in TF and it can be obtained by calculating the overlap integral between E(r,z0) and ψm(r):
cm=-+E(r,z0)ψm(r)rdr-+ψm(r)ψm(r)rdr
The field distribution of light propagating at a distance of Z in the TF can be expressed as
ETF(r,z)=m=1Mcmψm(r)exp(jβmz)
Where βm is the propagation constant of the m-th mode. Supposing that the core offset between SMF and TF is a, as labeled in Fig. 2(b), the S-structure induced transmission loss (in dB) can be calculated from the overlap integral
TS-bend=10log10(|-+E1(r,z)E2*(a-r,z)dr|2-+E1(r,z)E1*(r,z)dr-+E2(r,z)E2*(r,z)dr)
Where E1 and E2 are got from Eq. (1) with R=R1 andR=R2, respectively. It should be noted that the transmission is dependent on curve radius and core offset. Additionally, the interferometric phase difference ϕ between the core mode and the m-th cladding mode is given as ϕ=2πΔneffL0/λ with Δneff to be their effective refractive index difference, and L0 is the interferometric length.

Simulation based on beam propagation method (BPM) has been performed to investigate the modal distribution along the dual S-bend modal interferometer, in which the arc type is set as S-bend with a length of 300 um, as marked by L in Fig. 2(b). Figure 3(a) shows the simulated electric field intensity distribution with 10 um off-axis displacement at both ends showing in X-Z plane. The so- called off-axis displacement, which is labeled as b in Fig. 2(b), along with theL, can characterize the feature of curve R1 and R2. It’s clearly seen that a considerable part of light field spread into the cladding, which acts as evanescent field susceptible to the surrounding refractive index thus its magnetic field sensing response is expected to be improved. The off-axis displacement dependence of transmission loss in the output fiber core of the dual S-bend MI is shown in Fig. 3(b). Although the loss curve is not monotonically decreasing as the displacement increases, a larger displacement will excite more higher-order modes in the cladding region thus provide higher sensitivity to the surrounding environment. A proper off-axis displacement should be carefully chosen to get trade-off between the transmission loss and the sensitivity.

 

Fig. 3 (a) Simulated electric field intensity distribution with 10 um off-axis displacement at both ends shown in X-Z plane. (b) Transmission loss in the output fiber core dependent on the off-axis displacement between TF and SMF calculated from beam propagation method. (c) The transmission spectrum of the fiber Bragg grating.

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Thanks to the diameter decreased TF used here assisted with the dual S-bend structure, enhanced interaction between evanescent field of light and surrounding magnetic fluid can be achieved. Good working efficiency can thus be achieved by using shorter fiber embedded within a compact sensing head. The variation of applied magnetic field will induce changes of both the refractive index and the absorption/scattering coefficients of MF bonded with the sensing head. The changing surrounding refractive index will have great impact on cladding modes but less on core mode of TF. The interferometric phase differenceϕwill thus be changed and the wavelength shift of the transmission spectrum can be observed. On the other hand, the absorption and scattering coefficients will increase as the applied magnetic field increases [6]. This phenomenon results from the fact that when the applied external magnetic field exceeds a certain critical value, agglomerations will be formed within the MF thus leads to light attenuation.

The FBG is temperature-sensitive as its transmission dip will shift with the variation of temperature, but it is an intrinsic insensitive device to magnetic field. However, the MF-coated TF-constituted dual S-bend fiber modal interferometer is sensitive to both temperature and applied magnetic field. The change of temperature can be obtained by measuring the wavelength shift of FBG from the following equation

ΔλTFBG=αTFBGΔKTEM
Where ΔλTFBG is the measured wavelength shift of FBG, αTFBG is its temperature coefficient, and ΔKTEMis the temperature change. For a specific wavelength, the transmission of the MI responses to both temperature and applied magnetic field as represented by:
ΔTMI=ηTEMΔKTEM+ηHΔH
Where ΔTMIis the transmission variation of MI at a certain wavelength, ηTEM, ηH are its temperature and magnetic coefficients, respectively. ΔHis the variation of applied magnetic field strength. By measuring the response of FBG, we will know the temperature change; and with the help of Eq. (7), the perturbation of temperature on transmission of MI can be compensated. In this way, a temperature insensitive magnetic field sensor can be realized.

3. Experimental result and discussion

A section of only 4 mm TF is spliced between two SMF with ~42 μm off-axis displacement, ~7 μm core offset, and 324μm in length of the S-bend. The fabricated MI is then immersed into magnetic fluid (EMG 705) and protected by capillary tube. The water-based EMG 705 magnetic fluid has 10 nm nominal diameter of nanoparticle, 3.6% volume concentration, < 5 cp viscosity at 27° C, and the density is 1.19 gm/ml. A FBG with 0.2 nm-10 dB transmission bandwidth and ~55 dB in depth is cascaded to the modal interferometer and its transmission spectrum is shown in Fig. 3(c). The FBG has several cladding mode induced resonance dips in its transmission spectrum [26]. A broad band light source with wavelength range from 1510 to 1600 nm, and an optical spectrum analyzer (OSA, Yokogawa AQ6370C) with 0.02 nm best resolution are used for measurement. Figure 4(a) shows the transmission spectra of the MI with being exposed to air and being immersed into MF, respectively. It’s noted that the spectrum is a superposition of multiple interferences when the MI is exposed to air; however, this multimode interference phenomenon is not obvious after immersing into MF, in addition, the transmission loss increased. This is because some higher order cladding modes leaked when expose to high refractive index MF, which has been confirmed by the Fast Fourier Transform (FFT) calculated spatial frequency spectrum, as shown in Fig. 4(b).

 

Fig. 4 (a) Transmission spectra of the modal interferometer with being exposed to air and being immersed into MF; (b) the corresponding FFT-spatial frequency spectrum.

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The sensing head is then placed between two electromagnets with the fiber axis perpendicular to the magnetic field direction to investigate its magnetic response. The electromagnets, as shown in the inset of Fig. 2(a), are powered by a programmable power supply. One can adjust the magnetic field strength by changing the input current with a linear responsivity of 20 Oe/A. The transmission spectra under different magnetic field strength with an increment of 10 Oe from 0 Oe to 230 Oe have been recorded, as shown in Fig. 5(a). It can be noticed that the transmission loss increases as the applied magnetic field strength increases. This is because, as analyzed before, the absorption and scattering coefficients become larger at higher magnetic field strength hence increases light attenuation. It also shows wavelength shift with different field strength, which is due to the variation of interferometric phase difference caused by the varied refractive index of MF. However, the FBG spectrum shows no dependence of applied magnetic field. We have chosen two specific wavelengths at 1526.72 nm and 1563.72 nm, as respectively marked for “WL A” and “WL B” in Fig. 5(a), for indicators to measure their magnetic response. Figure 5(b) shows the magnetic field strength dependence on the transmission power around two selected wavelength regions. It’s found that the transmission loss keeps almost unchanged at low magnetic field strength below 50 Oe, which should be attributed to the process of initial magnetization of the MF. Owing to the saturated magnetization of MF, the transmission tends to be constant again when the magnetic field intensity exceeds 210 Oe. The measured magnetic sensitivities are −0.0525 dB/Oe and −0.0678 dB/Oe for wavelength at 1526.72nm and 1563.72nm, respectively. Thanks to the proposed dual S-bend structure and the used diameter-thinned TF, we obtained higher magnetic sensitivity with using only 4 mm TF compared with some previously reported results [10, 17].

 

Fig. 5 (a) Measured transmission spectrums under different magnetic field strengths from 0 Oe to 230 Oe; (b) magnetic response of the MI at two specific wavelengths (1526.72 nm and 1563.72 nm, respectively).

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The measurement of temperature response has also been implemented by placing the sensing head between a contact-type dual-copper plate structure, which is constructed by thermoelectric cooler (TEC) [20]. Temperature from 20 °C to 60 °C with a step of 5 °C was generated and the corresponding transmission spectra were recorded, as shown in Fig. 6(a). Figure 6(b) is the partially enlarged view at the transmission dip range of FBG with different temperature. Figure 6(c) and (d) show the temperature dependence of transmission loss of the MI, and wavelength shift of the FBG, respectively, in which the same wavelength at 1526.72nm and 1563.72nm are chosen to measure the temperature response of the MI. The wavelengths at transmission of −42 dB of the FBG are selected as indicators to interrogate its temperature response. The refractive index of MF has negative response on temperature and the transmission loss should be decreased since less power will leak into the surrounding MF with decreased refractive index. However, in our experiments the transmission loss is a combined effect of refractive index induced mode leakage and magnetic enhanced absorption/scattering induced attenuation as also discovered by zu et al. [2]. The latter one takes advantages over the former factor thus the overall temperature response of the transmission loss presents a positive relationship. The obtained temperature sensitivities are −0.0325 dB/°C for wavelength at 1526.72nm, and −0.04 dB/ °C for wavelength at 1563.72nm, respectively. And the temperature sensitivity of FBG is measured to be 10.1 pm/ °C.

 

Fig. 6 (a) Measured transmission spectrums with different temperature; (b) enlarged view of spectrums in the range of FBG transmission dip; (c) temperature response of the MI at two specific wavelengths (1526.72 nm and 1563.72 nm, respectively); (d) temperature dependence of wavelength shift of the FBG.

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With the MI/FBG’s response on the temperature/magnetism uncovered, it’s clear for us to realize the temperature compensated magnetic field sensing. The variation of temperature can be interrogated by measuring the wavelength shift of FBG. By substituting the obtained response coefficients into Eqs. (6) and (7), we can obtain an accurate magnetic field fiber sensor that is immune to the ambient temperature vibration. Let’s take the wavelength at 1563.72nm for example, we have the following equation for precise magnetic field strength measurement at any temperature:

ΔλTFBG=0.0101ΔKTEMΔTMI=0.04ΔKTEM0.0678ΔH

Since the best resolution of optical spectrum analyzer is 0.02nm, the temperature resolution is thus 1.98 °C with 10.1 pm/ °C sensitivity, which results in 1.168 Oe uncertainty of magnetic field measurement. A thinner and longer sandwiched fiber is expected to provide higher magnetic sensitivity, since both will increase the interaction between evanescent field and surrounding magnetic fluid. However, an excessively thinned fiber should be avoided because it will be fragile with the existence of the dual S-bend structure. What’s more, a finer S-taper will also contribute to improve its magnetic response and this can be easily realized by creating a larger axis offset in our experiment. On the other hand, larger axis offset may degrade its mechanical robustness thus it should not exceed 50 um for the ease of the implementation of the cleaving operation of a millimeter-scale sandwiched thin fiber.

3. Conclusion

We proposed and demonstrated a temperature compensated magnetic field strength sensor by cascading a FBG to dual S-bend fiber modal interferometer. The modal interferometer is constituted by S-bend splicing between thin fiber and single mode fiber. A modified numerical model of multi-mode interference with S-bend and misalignment has been established, and the simulation based on beam propagation method is performed to reveal the field distribution of this proposed structure. Both the dual S-bend structure and the diameter-thinned TF used in this experiment contribute significantly to improve the magnetic sensitivity. Since the modal interferometer responses to both the applied magnetic field and temperature, the FBG is used to interrogate the temperature change by measuring its wavelength shift thus the perturbation of temperature on transmission of the MI can be compensated. In this way, a temperature compensated magnetic field strength sensor has been experimentally demonstrated and specific magnetic response (−0.0678 dB/Oe) and temperature response (−0.04 dB/ °C) are successfully realized at the monitoring wavelength of 1563.72 nm. Our proposed structure will be very useful for any practical fiber based magnetic field strength sensor to provide highly sensitive and convinced measurement results along with the inevitable environmental temperature change.

Acknowledgments

The work presented in this paper is supported by the 863 High Technology Plan of China (2013AA013402), the National Natural Science Foundation of China (NSFC) under Grant No. 61107087 and 61331010, the Fundamental Research Funds for the Central Universities’, HUST: 2013TS052, and the Program for New Century Excellent Talents in University (NCET-13-0235). The authors would like to extend their appreciation to Dr. Weijun Tong for his support to this work.

References and links

1. Y. Miao, B. Liu, K. Zhang, Y. Liu, and H. Zhang, “Temperature tunability of photonic crystal fiber filled with Fe3O4 nanoparticle fluid,” Appl. Phys. Lett. 98(2), 021103 (2011). [CrossRef]  

2. P. Zu, C. C. Chan, L. W. Siang, Y. Jin, Y. Zhang, L. H. Fen, L. Chen, and X. Dong, “Magneto-optic fiber Sagnac modulator based on magnetic fluids,” Opt. Lett. 36(8), 1425–1427 (2011). [CrossRef]   [PubMed]  

3. P. Zu, C. C. Chan, W. S. Lew, Y. Jin, Y. Zhang, H. F. Liew, L. H. Chen, W. C. Wong, and X. Dong, “Magneto-optical fiber sensor based on magnetic fluid,” Opt. Lett. 37(3), 398–400 (2012). [CrossRef]   [PubMed]  

4. H. E. Horng, J. J. Chieh, Y. H. Chao, S. Y. Yang, C. Y. Hong, and H. C. Yang, “Designing optical-fiber modulators by using magnetic fluids,” Opt. Lett. 30(5), 543–545 (2005). [CrossRef]   [PubMed]  

5. L. X. Chen, X. G. Huang, J. H. Zhu, G. C. Li, and S. Lan, “Fiber magnetic-field sensor based on nanoparticle magnetic fluid and Fresnel reflection,” Opt. Lett. 36(15), 2761–2763 (2011). [PubMed]  

6. S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006). [CrossRef]  

7. H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004). [CrossRef]  

8. W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005). [CrossRef]  

9. R. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry-Perot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26(3), 217–219 (2014). [CrossRef]  

10. W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013). [CrossRef]  

11. M. Deng, X. Sun, M. Han, and D. Li, “Compact magnetic-field sensor based on optical microfiber Michelson interferometer and Fe3O4 nanofluid,” Appl. Opt. 52(4), 734–741 (2013). [CrossRef]   [PubMed]  

12. J. Zheng, X. Dong, P. Zu, L. Y. Shao, C. C. Chan, Y. Cui, and P. P. Shum, “Magnetic field sensor using tilted fiber grating interacting with magnetic fluid,” Opt. Express 21(15), 17863–17868 (2013). [PubMed]  

13. J. Zheng, X. Dong, P. Zu, J. Ji, H. Su, and P. P. Shum, “Intensity-modulated magnetic field sensor based on magnetic fluid and optical fiber gratings,” Appl. Phys. Lett. 103(18), 183511 (2013). [CrossRef]  

14. H. V. Thakur, S. M. Nalawade, S. Gupta, R. Kitture, and S. N. Kale, “Photonic crystal fiber injected with Fe3O4 nanofluid for magnetic field detection,” Appl. Phys. Lett. 99(16), 161101 (2011). [CrossRef]  

15. R. Gao, Y. Jiang, and S. Abdelaziz, “All-fiber magnetic field sensors based on magnetic fluid-filled photonic crystal fibers,” Opt. Lett. 38(9), 1539–1541 (2013). [CrossRef]   [PubMed]  

16. H. Wang, S. Pu, N. Wang, S. Dong, and J. Huang, “Magnetic field sensing based on singlemode-multimode-singlemode fiber structures using magnetic fluids as cladding,” Opt. Lett. 38(19), 3765–3768 (2013). [CrossRef]   [PubMed]  

17. J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014). [CrossRef]  

18. H. E. Horng, C. Hong, S. Y. Yang, and H. C. Yang, “Designing the refractive indices by using magnetic fluids,” Appl. Phys. Lett. 82(15), 2434–2436 (2003). [CrossRef]  

19. Y. Zhao, R. Lv, D. Wang, and Q. Wang, “Fiber Optic Fabry-Perot magnetic field sensor with temperature compensation using a fiber Bragg grating,” IEEE Trans. Instrum. Meas. 63(9), 2210–2214 (2014). [CrossRef]  

20. Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013). [CrossRef]  

21. J. Chen, J. Zhou, and X. Yuan, “Mach-Zehnder interferometer constructed by two S-bend fibers for displacement and force measurements,” IEEE Photon. Technol. Lett. 26(8), 837–840 (2014). [CrossRef]  

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23. A. M. Hatta, G. Farrell, P. Wang, G. Rajan, and Y. Semenova, “Misalignment limits for a singlemode–multimode–singlemode fiber-based edge filter,” J. Lightwave Technol. 27(13), 2482–2488 (2009). [CrossRef]  

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References

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  1. Y. Miao, B. Liu, K. Zhang, Y. Liu, and H. Zhang, “Temperature tunability of photonic crystal fiber filled with Fe3O4 nanoparticle fluid,” Appl. Phys. Lett. 98(2), 021103 (2011).
    [Crossref]
  2. P. Zu, C. C. Chan, L. W. Siang, Y. Jin, Y. Zhang, L. H. Fen, L. Chen, and X. Dong, “Magneto-optic fiber Sagnac modulator based on magnetic fluids,” Opt. Lett. 36(8), 1425–1427 (2011).
    [Crossref] [PubMed]
  3. P. Zu, C. C. Chan, W. S. Lew, Y. Jin, Y. Zhang, H. F. Liew, L. H. Chen, W. C. Wong, and X. Dong, “Magneto-optical fiber sensor based on magnetic fluid,” Opt. Lett. 37(3), 398–400 (2012).
    [Crossref] [PubMed]
  4. H. E. Horng, J. J. Chieh, Y. H. Chao, S. Y. Yang, C. Y. Hong, and H. C. Yang, “Designing optical-fiber modulators by using magnetic fluids,” Opt. Lett. 30(5), 543–545 (2005).
    [Crossref] [PubMed]
  5. L. X. Chen, X. G. Huang, J. H. Zhu, G. C. Li, and S. Lan, “Fiber magnetic-field sensor based on nanoparticle magnetic fluid and Fresnel reflection,” Opt. Lett. 36(15), 2761–2763 (2011).
    [PubMed]
  6. S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
    [Crossref]
  7. H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
    [Crossref]
  8. W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005).
    [Crossref]
  9. R. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry-Perot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26(3), 217–219 (2014).
    [Crossref]
  10. W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013).
    [Crossref]
  11. M. Deng, X. Sun, M. Han, and D. Li, “Compact magnetic-field sensor based on optical microfiber Michelson interferometer and Fe3O4 nanofluid,” Appl. Opt. 52(4), 734–741 (2013).
    [Crossref] [PubMed]
  12. J. Zheng, X. Dong, P. Zu, L. Y. Shao, C. C. Chan, Y. Cui, and P. P. Shum, “Magnetic field sensor using tilted fiber grating interacting with magnetic fluid,” Opt. Express 21(15), 17863–17868 (2013).
    [PubMed]
  13. J. Zheng, X. Dong, P. Zu, J. Ji, H. Su, and P. P. Shum, “Intensity-modulated magnetic field sensor based on magnetic fluid and optical fiber gratings,” Appl. Phys. Lett. 103(18), 183511 (2013).
    [Crossref]
  14. H. V. Thakur, S. M. Nalawade, S. Gupta, R. Kitture, and S. N. Kale, “Photonic crystal fiber injected with Fe3O4 nanofluid for magnetic field detection,” Appl. Phys. Lett. 99(16), 161101 (2011).
    [Crossref]
  15. R. Gao, Y. Jiang, and S. Abdelaziz, “All-fiber magnetic field sensors based on magnetic fluid-filled photonic crystal fibers,” Opt. Lett. 38(9), 1539–1541 (2013).
    [Crossref] [PubMed]
  16. H. Wang, S. Pu, N. Wang, S. Dong, and J. Huang, “Magnetic field sensing based on singlemode-multimode-singlemode fiber structures using magnetic fluids as cladding,” Opt. Lett. 38(19), 3765–3768 (2013).
    [Crossref] [PubMed]
  17. J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
    [Crossref]
  18. H. E. Horng, C. Hong, S. Y. Yang, and H. C. Yang, “Designing the refractive indices by using magnetic fluids,” Appl. Phys. Lett. 82(15), 2434–2436 (2003).
    [Crossref]
  19. Y. Zhao, R. Lv, D. Wang, and Q. Wang, “Fiber Optic Fabry-Perot magnetic field sensor with temperature compensation using a fiber Bragg grating,” IEEE Trans. Instrum. Meas. 63(9), 2210–2214 (2014).
    [Crossref]
  20. Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
    [Crossref]
  21. J. Chen, J. Zhou, and X. Yuan, “Mach-Zehnder interferometer constructed by two S-bend fibers for displacement and force measurements,” IEEE Photon. Technol. Lett. 26(8), 837–840 (2014).
    [Crossref]
  22. L. B. Soldano and E. C. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
    [Crossref]
  23. A. M. Hatta, G. Farrell, P. Wang, G. Rajan, and Y. Semenova, “Misalignment limits for a singlemode–multimode–singlemode fiber-based edge filter,” J. Lightwave Technol. 27(13), 2482–2488 (2009).
    [Crossref]
  24. W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14(5), 130–132 (1978).
    [Crossref]
  25. V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15(6), 990–997 (1997).
    [Crossref]
  26. J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photon. Rev. 7(1), 83–108 (2013).
    [Crossref]

2014 (4)

R. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry-Perot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26(3), 217–219 (2014).
[Crossref]

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

Y. Zhao, R. Lv, D. Wang, and Q. Wang, “Fiber Optic Fabry-Perot magnetic field sensor with temperature compensation using a fiber Bragg grating,” IEEE Trans. Instrum. Meas. 63(9), 2210–2214 (2014).
[Crossref]

J. Chen, J. Zhou, and X. Yuan, “Mach-Zehnder interferometer constructed by two S-bend fibers for displacement and force measurements,” IEEE Photon. Technol. Lett. 26(8), 837–840 (2014).
[Crossref]

2013 (8)

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photon. Rev. 7(1), 83–108 (2013).
[Crossref]

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

R. Gao, Y. Jiang, and S. Abdelaziz, “All-fiber magnetic field sensors based on magnetic fluid-filled photonic crystal fibers,” Opt. Lett. 38(9), 1539–1541 (2013).
[Crossref] [PubMed]

H. Wang, S. Pu, N. Wang, S. Dong, and J. Huang, “Magnetic field sensing based on singlemode-multimode-singlemode fiber structures using magnetic fluids as cladding,” Opt. Lett. 38(19), 3765–3768 (2013).
[Crossref] [PubMed]

W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013).
[Crossref]

M. Deng, X. Sun, M. Han, and D. Li, “Compact magnetic-field sensor based on optical microfiber Michelson interferometer and Fe3O4 nanofluid,” Appl. Opt. 52(4), 734–741 (2013).
[Crossref] [PubMed]

J. Zheng, X. Dong, P. Zu, L. Y. Shao, C. C. Chan, Y. Cui, and P. P. Shum, “Magnetic field sensor using tilted fiber grating interacting with magnetic fluid,” Opt. Express 21(15), 17863–17868 (2013).
[PubMed]

J. Zheng, X. Dong, P. Zu, J. Ji, H. Su, and P. P. Shum, “Intensity-modulated magnetic field sensor based on magnetic fluid and optical fiber gratings,” Appl. Phys. Lett. 103(18), 183511 (2013).
[Crossref]

2012 (1)

2011 (4)

Y. Miao, B. Liu, K. Zhang, Y. Liu, and H. Zhang, “Temperature tunability of photonic crystal fiber filled with Fe3O4 nanoparticle fluid,” Appl. Phys. Lett. 98(2), 021103 (2011).
[Crossref]

P. Zu, C. C. Chan, L. W. Siang, Y. Jin, Y. Zhang, L. H. Fen, L. Chen, and X. Dong, “Magneto-optic fiber Sagnac modulator based on magnetic fluids,” Opt. Lett. 36(8), 1425–1427 (2011).
[Crossref] [PubMed]

H. V. Thakur, S. M. Nalawade, S. Gupta, R. Kitture, and S. N. Kale, “Photonic crystal fiber injected with Fe3O4 nanofluid for magnetic field detection,” Appl. Phys. Lett. 99(16), 161101 (2011).
[Crossref]

L. X. Chen, X. G. Huang, J. H. Zhu, G. C. Li, and S. Lan, “Fiber magnetic-field sensor based on nanoparticle magnetic fluid and Fresnel reflection,” Opt. Lett. 36(15), 2761–2763 (2011).
[PubMed]

2009 (1)

2006 (1)

S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
[Crossref]

2005 (2)

H. E. Horng, J. J. Chieh, Y. H. Chao, S. Y. Yang, C. Y. Hong, and H. C. Yang, “Designing optical-fiber modulators by using magnetic fluids,” Opt. Lett. 30(5), 543–545 (2005).
[Crossref] [PubMed]

W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005).
[Crossref]

2004 (1)

H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
[Crossref]

2003 (1)

H. E. Horng, C. Hong, S. Y. Yang, and H. C. Yang, “Designing the refractive indices by using magnetic fluids,” Appl. Phys. Lett. 82(15), 2434–2436 (2003).
[Crossref]

1997 (1)

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15(6), 990–997 (1997).
[Crossref]

1995 (1)

L. B. Soldano and E. C. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

1978 (1)

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14(5), 130–132 (1978).
[Crossref]

Abdelaziz, S.

Albert, J.

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photon. Rev. 7(1), 83–108 (2013).
[Crossref]

Boyd, J. T.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15(6), 990–997 (1997).
[Crossref]

Caucheteur, C.

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photon. Rev. 7(1), 83–108 (2013).
[Crossref]

Chan, C. C.

Chao, Y. H.

Chen, C. S.

H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
[Crossref]

Chen, J.

J. Chen, J. Zhou, and X. Yuan, “Mach-Zehnder interferometer constructed by two S-bend fibers for displacement and force measurements,” IEEE Photon. Technol. Lett. 26(8), 837–840 (2014).
[Crossref]

Chen, L.

P. Zu, C. C. Chan, L. W. Siang, Y. Jin, Y. Zhang, L. H. Fen, L. Chen, and X. Dong, “Magneto-optic fiber Sagnac modulator based on magnetic fluids,” Opt. Lett. 36(8), 1425–1427 (2011).
[Crossref] [PubMed]

S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
[Crossref]

Chen, L. H.

Chen, L. X.

Chen, X.

S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
[Crossref]

W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005).
[Crossref]

Chen, Y.

S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
[Crossref]

W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005).
[Crossref]

Cheng, Y.

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

Chieh, J. J.

H. E. Horng, J. J. Chieh, Y. H. Chao, S. Y. Yang, C. Y. Hong, and H. C. Yang, “Designing optical-fiber modulators by using magnetic fluids,” Opt. Lett. 30(5), 543–545 (2005).
[Crossref] [PubMed]

H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
[Crossref]

Cui, Y.

De Brabander, G. N.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15(6), 990–997 (1997).
[Crossref]

Deng, M.

Dong, S.

Dong, X.

Fang, K. L.

H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
[Crossref]

Farrell, G.

Fen, L. H.

Fu, S.

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

Gambling, W. A.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14(5), 130–132 (1978).
[Crossref]

Gao, R.

Gupta, S.

H. V. Thakur, S. M. Nalawade, S. Gupta, R. Kitture, and S. N. Kale, “Photonic crystal fiber injected with Fe3O4 nanofluid for magnetic field detection,” Appl. Phys. Lett. 99(16), 161101 (2011).
[Crossref]

Han, M.

Hatta, A. M.

Hong, C.

H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
[Crossref]

H. E. Horng, C. Hong, S. Y. Yang, and H. C. Yang, “Designing the refractive indices by using magnetic fluids,” Appl. Phys. Lett. 82(15), 2434–2436 (2003).
[Crossref]

Hong, C. Y.

Horng, H. E.

H. E. Horng, J. J. Chieh, Y. H. Chao, S. Y. Yang, C. Y. Hong, and H. C. Yang, “Designing optical-fiber modulators by using magnetic fluids,” Opt. Lett. 30(5), 543–545 (2005).
[Crossref] [PubMed]

H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
[Crossref]

H. E. Horng, C. Hong, S. Y. Yang, and H. C. Yang, “Designing the refractive indices by using magnetic fluids,” Appl. Phys. Lett. 82(15), 2434–2436 (2003).
[Crossref]

Huang, J.

Huang, X. G.

Ji, J.

J. Zheng, X. Dong, P. Zu, J. Ji, H. Su, and P. P. Shum, “Intensity-modulated magnetic field sensor based on magnetic fluid and optical fiber gratings,” Appl. Phys. Lett. 103(18), 183511 (2013).
[Crossref]

Jiang, Y.

Jin, Y.

Kale, S. N.

H. V. Thakur, S. M. Nalawade, S. Gupta, R. Kitture, and S. N. Kale, “Photonic crystal fiber injected with Fe3O4 nanofluid for magnetic field detection,” Appl. Phys. Lett. 99(16), 161101 (2011).
[Crossref]

Kitture, R.

H. V. Thakur, S. M. Nalawade, S. Gupta, R. Kitture, and S. N. Kale, “Photonic crystal fiber injected with Fe3O4 nanofluid for magnetic field detection,” Appl. Phys. Lett. 99(16), 161101 (2011).
[Crossref]

Lan, S.

Lew, W. S.

Li, D.

Li, G. C.

Li, Q.

W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005).
[Crossref]

Liao, W.

S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
[Crossref]

W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005).
[Crossref]

Liew, H. F.

Lin, W.

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013).
[Crossref]

Liu, B.

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013).
[Crossref]

Y. Miao, B. Liu, K. Zhang, Y. Liu, and H. Zhang, “Temperature tunability of photonic crystal fiber filled with Fe3O4 nanoparticle fluid,” Appl. Phys. Lett. 98(2), 021103 (2011).
[Crossref]

Liu, D.

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

Liu, S.

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

Liu, Y.

W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013).
[Crossref]

Y. Miao, B. Liu, K. Zhang, Y. Liu, and H. Zhang, “Temperature tunability of photonic crystal fiber filled with Fe3O4 nanoparticle fluid,” Appl. Phys. Lett. 98(2), 021103 (2011).
[Crossref]

Lv, R.

R. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry-Perot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26(3), 217–219 (2014).
[Crossref]

Y. Zhao, R. Lv, D. Wang, and Q. Wang, “Fiber Optic Fabry-Perot magnetic field sensor with temperature compensation using a fiber Bragg grating,” IEEE Trans. Instrum. Meas. 63(9), 2210–2214 (2014).
[Crossref]

Matsumura, H.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14(5), 130–132 (1978).
[Crossref]

Miao, Y.

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013).
[Crossref]

Y. Miao, B. Liu, K. Zhang, Y. Liu, and H. Zhang, “Temperature tunability of photonic crystal fiber filled with Fe3O4 nanoparticle fluid,” Appl. Phys. Lett. 98(2), 021103 (2011).
[Crossref]

Naghski, D. H.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15(6), 990–997 (1997).
[Crossref]

Nalawade, S. M.

H. V. Thakur, S. M. Nalawade, S. Gupta, R. Kitture, and S. N. Kale, “Photonic crystal fiber injected with Fe3O4 nanofluid for magnetic field detection,” Appl. Phys. Lett. 99(16), 161101 (2011).
[Crossref]

Pennings, E. C.

L. B. Soldano and E. C. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

Pu, S.

H. Wang, S. Pu, N. Wang, S. Dong, and J. Huang, “Magnetic field sensing based on singlemode-multimode-singlemode fiber structures using magnetic fluids as cladding,” Opt. Lett. 38(19), 3765–3768 (2013).
[Crossref] [PubMed]

S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
[Crossref]

W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005).
[Crossref]

Ragdale, C. M.

W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,” Electron. Lett. 14(5), 130–132 (1978).
[Crossref]

Rajan, G.

Semenova, Y.

Shao, L. Y.

Shum, P. P.

J. Zheng, X. Dong, P. Zu, J. Ji, H. Su, and P. P. Shum, “Intensity-modulated magnetic field sensor based on magnetic fluid and optical fiber gratings,” Appl. Phys. Lett. 103(18), 183511 (2013).
[Crossref]

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

J. Zheng, X. Dong, P. Zu, L. Y. Shao, C. C. Chan, Y. Cui, and P. P. Shum, “Magnetic field sensor using tilted fiber grating interacting with magnetic fluid,” Opt. Express 21(15), 17863–17868 (2013).
[PubMed]

Siang, L. W.

Soldano, L. B.

L. B. Soldano and E. C. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

Song, B.

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013).
[Crossref]

Su, H.

J. Zheng, X. Dong, P. Zu, J. Ji, H. Su, and P. P. Shum, “Intensity-modulated magnetic field sensor based on magnetic fluid and optical fiber gratings,” Appl. Phys. Lett. 103(18), 183511 (2013).
[Crossref]

Subramaniam, V.

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15(6), 990–997 (1997).
[Crossref]

Sun, X.

Tang, M.

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

Thakur, H. V.

H. V. Thakur, S. M. Nalawade, S. Gupta, R. Kitture, and S. N. Kale, “Photonic crystal fiber injected with Fe3O4 nanofluid for magnetic field detection,” Appl. Phys. Lett. 99(16), 161101 (2011).
[Crossref]

Tong, W.

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

Wang, D.

Y. Zhao, R. Lv, D. Wang, and Q. Wang, “Fiber Optic Fabry-Perot magnetic field sensor with temperature compensation using a fiber Bragg grating,” IEEE Trans. Instrum. Meas. 63(9), 2210–2214 (2014).
[Crossref]

R. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry-Perot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26(3), 217–219 (2014).
[Crossref]

Wang, H.

Wang, N.

Wang, P.

Wang, Q.

Y. Zhao, R. Lv, D. Wang, and Q. Wang, “Fiber Optic Fabry-Perot magnetic field sensor with temperature compensation using a fiber Bragg grating,” IEEE Trans. Instrum. Meas. 63(9), 2210–2214 (2014).
[Crossref]

R. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry-Perot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26(3), 217–219 (2014).
[Crossref]

Wei, H.

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

Wong, W. C.

Wu, J.

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

Xia, Y.

S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
[Crossref]

W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005).
[Crossref]

Xu, Y.

S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
[Crossref]

Yang, H. C.

H. E. Horng, J. J. Chieh, Y. H. Chao, S. Y. Yang, C. Y. Hong, and H. C. Yang, “Designing optical-fiber modulators by using magnetic fluids,” Opt. Lett. 30(5), 543–545 (2005).
[Crossref] [PubMed]

H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
[Crossref]

H. E. Horng, C. Hong, S. Y. Yang, and H. C. Yang, “Designing the refractive indices by using magnetic fluids,” Appl. Phys. Lett. 82(15), 2434–2436 (2003).
[Crossref]

Yang, S. Y.

H. E. Horng, J. J. Chieh, Y. H. Chao, S. Y. Yang, C. Y. Hong, and H. C. Yang, “Designing optical-fiber modulators by using magnetic fluids,” Opt. Lett. 30(5), 543–545 (2005).
[Crossref] [PubMed]

H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
[Crossref]

H. E. Horng, C. Hong, S. Y. Yang, and H. C. Yang, “Designing the refractive indices by using magnetic fluids,” Appl. Phys. Lett. 82(15), 2434–2436 (2003).
[Crossref]

Yao, J.

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

Yuan, X.

J. Chen, J. Zhou, and X. Yuan, “Mach-Zehnder interferometer constructed by two S-bend fibers for displacement and force measurements,” IEEE Photon. Technol. Lett. 26(8), 837–840 (2014).
[Crossref]

Zhang, H.

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013).
[Crossref]

Y. Miao, B. Liu, K. Zhang, Y. Liu, and H. Zhang, “Temperature tunability of photonic crystal fiber filled with Fe3O4 nanoparticle fluid,” Appl. Phys. Lett. 98(2), 021103 (2011).
[Crossref]

Zhang, K.

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

Y. Miao, B. Liu, K. Zhang, Y. Liu, and H. Zhang, “Temperature tunability of photonic crystal fiber filled with Fe3O4 nanoparticle fluid,” Appl. Phys. Lett. 98(2), 021103 (2011).
[Crossref]

Zhang, Y.

Zhao, Y.

R. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry-Perot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26(3), 217–219 (2014).
[Crossref]

Y. Zhao, R. Lv, D. Wang, and Q. Wang, “Fiber Optic Fabry-Perot magnetic field sensor with temperature compensation using a fiber Bragg grating,” IEEE Trans. Instrum. Meas. 63(9), 2210–2214 (2014).
[Crossref]

Zhao, Z.

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

Zheng, J.

J. Zheng, X. Dong, P. Zu, J. Ji, H. Su, and P. P. Shum, “Intensity-modulated magnetic field sensor based on magnetic fluid and optical fiber gratings,” Appl. Phys. Lett. 103(18), 183511 (2013).
[Crossref]

J. Zheng, X. Dong, P. Zu, L. Y. Shao, C. C. Chan, Y. Cui, and P. P. Shum, “Magnetic field sensor using tilted fiber grating interacting with magnetic fluid,” Opt. Express 21(15), 17863–17868 (2013).
[PubMed]

Zhou, J.

J. Chen, J. Zhou, and X. Yuan, “Mach-Zehnder interferometer constructed by two S-bend fibers for displacement and force measurements,” IEEE Photon. Technol. Lett. 26(8), 837–840 (2014).
[Crossref]

Zhu, J. H.

Zu, P.

Appl. Opt. (1)

Appl. Phys. B (1)

Z. Zhao, M. Tang, S. Fu, S. Liu, H. Wei, Y. Cheng, W. Tong, P. P. Shum, and D. Liu, “All-solid multi-core fiber-based multipath Mach–Zehnder interferometer for temperature sensing,” Appl. Phys. B 112(4), 491–497 (2013).
[Crossref]

Appl. Phys. Lett. (7)

H. E. Horng, C. Hong, S. Y. Yang, and H. C. Yang, “Designing the refractive indices by using magnetic fluids,” Appl. Phys. Lett. 82(15), 2434–2436 (2003).
[Crossref]

J. Zheng, X. Dong, P. Zu, J. Ji, H. Su, and P. P. Shum, “Intensity-modulated magnetic field sensor based on magnetic fluid and optical fiber gratings,” Appl. Phys. Lett. 103(18), 183511 (2013).
[Crossref]

H. V. Thakur, S. M. Nalawade, S. Gupta, R. Kitture, and S. N. Kale, “Photonic crystal fiber injected with Fe3O4 nanofluid for magnetic field detection,” Appl. Phys. Lett. 99(16), 161101 (2011).
[Crossref]

Y. Miao, B. Liu, K. Zhang, Y. Liu, and H. Zhang, “Temperature tunability of photonic crystal fiber filled with Fe3O4 nanoparticle fluid,” Appl. Phys. Lett. 98(2), 021103 (2011).
[Crossref]

H. E. Horng, C. S. Chen, K. L. Fang, S. Y. Yang, J. J. Chieh, C. Hong, and H. C. Yang, “Tunable optical switch using magnetic fluids,” Appl. Phys. Lett. 85(23), 5592–5594 (2004).
[Crossref]

W. Liao, X. Chen, Y. Chen, S. Pu, Y. Xia, and Q. Li, “Tunable optical fiber filters with magnetic fluids,” Appl. Phys. Lett. 87(15), 151122 (2005).
[Crossref]

W. Lin, Y. Miao, H. Zhang, B. Liu, Y. Liu, and B. Song, “Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects,” Appl. Phys. Lett. 103(15), 151101 (2013).
[Crossref]

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[Crossref]

IEEE Photon. Technol. Lett. (3)

J. Wu, Y. Miao, W. Lin, K. Zhang, B. Song, H. Zhang, B. Liu, and J. Yao, “Dual-direction magnetic field sensor based on core-offset microfiber and ferrofluid,” IEEE Photon. Technol. Lett. 26(15), 1581–1584 (2014).
[Crossref]

J. Chen, J. Zhou, and X. Yuan, “Mach-Zehnder interferometer constructed by two S-bend fibers for displacement and force measurements,” IEEE Photon. Technol. Lett. 26(8), 837–840 (2014).
[Crossref]

R. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry-Perot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26(3), 217–219 (2014).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

Y. Zhao, R. Lv, D. Wang, and Q. Wang, “Fiber Optic Fabry-Perot magnetic field sensor with temperature compensation using a fiber Bragg grating,” IEEE Trans. Instrum. Meas. 63(9), 2210–2214 (2014).
[Crossref]

J. Appl. Phys. (1)

S. Pu, X. Chen, Y. Chen, Y. Xu, W. Liao, L. Chen, and Y. Xia, “Fiber-optic evanescent field modulator using a magnetic fluid as the cladding,” J. Appl. Phys. 99(9), 093516 (2006).
[Crossref]

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[Crossref]

A. M. Hatta, G. Farrell, P. Wang, G. Rajan, and Y. Semenova, “Misalignment limits for a singlemode–multimode–singlemode fiber-based edge filter,” J. Lightwave Technol. 27(13), 2482–2488 (2009).
[Crossref]

V. Subramaniam, G. N. De Brabander, D. H. Naghski, and J. T. Boyd, “Measurement of mode field profiles and bending and transition losses in curved optical channel waveguides,” J. Lightwave Technol. 15(6), 990–997 (1997).
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Laser Photon. Rev. (1)

J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photon. Rev. 7(1), 83–108 (2013).
[Crossref]

Opt. Express (1)

Opt. Lett. (6)

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Figures (6)

Fig. 1
Fig. 1 (a) Illustration diagrams of the fabrication procedure of the S-bend structure. (a) and (b) are performed in fusion splicer, and (c) is in the fiber cleaver.
Fig. 2
Fig. 2 (a) Schematic diagram of the dual S-bend fiber modal interferometer. Inset: optical microscope image of the S-bend splicing region and the electromagnets used for provide accurate magnetic field strength; (b) junction of the S-bend structure.
Fig. 3
Fig. 3 (a) Simulated electric field intensity distribution with 10 um off-axis displacement at both ends shown in X-Z plane. (b) Transmission loss in the output fiber core dependent on the off-axis displacement between TF and SMF calculated from beam propagation method. (c) The transmission spectrum of the fiber Bragg grating.
Fig. 4
Fig. 4 (a) Transmission spectra of the modal interferometer with being exposed to air and being immersed into MF; (b) the corresponding FFT-spatial frequency spectrum.
Fig. 5
Fig. 5 (a) Measured transmission spectrums under different magnetic field strengths from 0 Oe to 230 Oe; (b) magnetic response of the MI at two specific wavelengths (1526.72 nm and 1563.72 nm, respectively).
Fig. 6
Fig. 6 (a) Measured transmission spectrums with different temperature; (b) enlarged view of spectrums in the range of FBG transmission dip; (c) temperature response of the MI at two specific wavelengths (1526.72 nm and 1563.72 nm, respectively); (d) temperature dependence of wavelength shift of the FBG.

Equations (8)

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E(r,z)=E(r,0)[1+ ( κ 0 n c w 0 ) 2 r/R]
E( r, z 0 )= m=1 M c m ψ m ( r )
c m = - + E (r,z 0 ) ψ m ( r )rdr - + ψ m ( r ) ψ m ( r )rdr
E TF (r,z)= m=1 M c m ψ m ( r )exp(j β m z)
T S-bend =10 log 10 ( | - + E 1 (r,z)E 2 * (a-r,z)dr | 2 - + E 1 (r,z)E 1 * (r,z)dr - + E 2 (r,z)E 2 * (r,z)dr )
Δ λ TFBG = α TFBG Δ K TEM
Δ T MI = η TEM Δ K TEM + η H ΔH
Δ λ TFBG =0.0101Δ K TEM Δ T MI =0.04Δ K TEM 0.0678ΔH

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