Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects Wei Lin, Yinping Miao, Hao Zhang, Bo Liu, Yange Liu et al. Citation: Appl. Phys. Lett. 103, 151101 (2013); doi: 10.1063/1.4824470 View online: http://dx.doi.org/10.1063/1.4824470 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v103/i15 Published by the AIP Publishing LLC.
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APPLIED PHYSICS LETTERS 103, 151101 (2013)
Fiber-optic in-line magnetic field sensor based on the magnetic fluid and multimode interference effects Wei Lin,1 Yinping Miao,2,a) Hao Zhang,1 Bo Liu,1 Yange Liu,1 and Binbin Song1 1
Key Laboratory of Optical Information Science and Technology, Ministry of Education, Institute of Modern Optics, Nankai University, Tianjin 300071, China 2 School of Electronics Information Engineering, Tianjin Key Laboratory of Film Electronic and Communication Device, Tianjin University of Technology, Tianjin 300384, China
(Received 14 June 2013; accepted 22 September 2013; published online 7 October 2013) A compact magnetic field sensor has been proposed based on multimode interference effects. It consists of typical multimode interferometer (MMI) immersed into the magnetic fluid (MF) which is formed by a section of square no-core fiber (NCF) spliced between two single-mode fibers. The transmission spectral characteristics of this MMI have been analyzed, and the spectral magnetic response of the proposed sensor has been investigated by immersing the NCF into the MF environment. The transmission response of the interference maxima exhibits a sensitivity of 0.01939 dB/Oe in the relatively linear range. Due to its low cost and compactness, this sensor C 2013 AIP Publishing LLC. would find potential applications in the measurement of magnetic field. V [http://dx.doi.org/10.1063/1.4824470] The magnetic field sensors have important research significance due to the importance of this physical parameter in many fields. Compared with the other magnetic field sensors, fiberbased sensors have been extensively investigated owing to their portability, high geometric adaptability, anti-interference, and resistance to high pressure and corrosion. The fiber magnetic field sensor can be achieved by magnetic moment,1 magnetostrictive effect,2 and magneto-optical effect.3,4 Since indirect measurement based on magnetic moment and magnetostrictive effect severely limit the sensitivity of these kinds of sensors, the fiber magnetometers based on magneto-optical effects have been widely investigated as well. Recently, fiber magnetic field sensors based on magnetic fluid (MF) have attracted consistent research interests owing the fluidity of the MF which makes it easier to be integrated with fibers owing to its variety of magneto-optical properties. The MF-based sensors usually exploit two types of magnetic effects: magneto-optic effect5–10 and magnetic traction.11 The magneto-optic-effect-based sensors can be constructed by utilizing the adjustable refractive index (RI).5–9 Tunable birefringence of the MF can also be utilized to design the magneto-optic-effect-based sensors by inserting a MF film into a fiber sagnac interferometer.10 The Photonic Crystal Fiber (PCF) filled with MF would change its relative position to the microstructure optical fiber Bragg grating and influence the spectrum, achieving a high measurement range.11 Compared with other fiber-based sensors, multimode interferometric sensors have attracted a growing interest in recent years owing to their excellent properties, including ease of fabrication, capability of simultaneous multiparameter measurement, etc.12 The multimode interferometer (MMI) can be fabricated by simply splicing a section of a step-index multimode fiber in between two common singlemode fibers (SMFs). It has been demonstrated that this structure is also sensitive to the external RI by removing the cladding or using a no-core fiber (NCF) instead,13–15 which a)
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provides a possibility to design a compact magnetic field sensor by immersing this structure into the MF. In this Letter, a compact magnetic field sensor is proposed based on MMI immersing in the MF. The sensor is fabricated by simply splicing a section of square NCF between two SMFs, which is later immersed into the MF. The magnetic field sensing characteristics have been experimentally investigated. Based on intensity-based interrogation approach, magnetic field measurement with high sensitivity within the saturation region could be achieved. The experimental setup of the proposed magnetic field sensor is shown in Fig. 1(a). It consists of a supercontinuum broadband source (SBS), an optical spectrum analyzer (OSA: Yokogawa AQ6370C, operation wavelength ranges from 600 nm to 1700 nm) with a resolution of 0.1 nm, a sensor head based on a MMI and the MF, two electromagnets, and a tunable voltage source (TVS). The external magnetic field perpendicular to the fiber axis is generated by two electromagnets dynamically tuned by the TVS. A Tesla meter with a resolution of 0.1 Oe is used to measure the magnetic field intensity along the perpendicular axis. As shown in the inset of Fig. 1, the sensor head is formed by a MMI immersed in the MF. The MMI is constructed by splicing a section of square NCF (pure silica, with the cross section size of 90 lm 90 lm. 9 mm in length) between two SMFs (SMF-28e, Corning, Inc). The capillary is infiltrated with EMG605 (Ferrotec, Japan, the saturable magnetization increases from 200 Oe to about 300 Oe, owing to the clustering of the nanoparticles) and its both ends were sealed with paraffin. The capillary cavity could maintain sufficient fiber tension. Fig. 2 shows the transmission spectrum of the MMI before and after immersing into the MF. As shown in the Fig. 2, a red-shift occurs when the MMI is immersed into the MF, together with some transmission variation, which is in good agreement with Jung’s work.11 When the incident light is coupled from the lead-in SMF into the square NCF, several of high-order eigenmodes of the square NCF, i.e., Exmn and Eymn modes, are excited and cross-interference between different modes occur while the
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FIG. 1. Schematic diagram of the experimental setup.
light propagates along the NCF. The field profile of the light propagating in the NCF, defined as E(x, y, z), can be written as12 Eðx; y; zÞ ¼
M X N X
FIG. 2. Transmission spectrum of the MMI before and after immersing into the MF.
½amn wmn ðx; yÞexpðjbmn zÞ
ef f
Wef f ðrÞ W00
m¼0 n¼0
þ bmn w0 mn ðx; yÞexpðjb0 mn zÞ;
Xmn ¼
0 0 1 ð1 ð
Eðx; y; 0ÞWmn ðx; yÞdxdy
0
0
0
(5)
0 0
ðm þ 1Þ2 kp ef f 2 4n0 Wxm
(2)
ðn þ 1Þ2 kp ef f 2 4n0 Wyn
;
(3)
ef f where n0 is the refractive index of the square NCF and Wxm ef f and Wyn refer to the effective widths of the mn-order mode along x and y direction. For the square NCF, they can be written as13
8pn0 2
0
Wmn ðx; yÞWmn ðx; yÞdxdy
ðX ¼ a; W ¼ w or X ¼ b; W ¼ w’Þ;
k¼
ef f ef f ¼ Wef f ð1Þ , Wym ¼ Wef f ð0Þ for Exmn mode, and here, Wxm ef f ef f Wxm ¼ Wef f ð0Þ , Wym ¼ Wef f ð1Þ for Eymn mode, and next is the external refractive index. Defining the field profile of the lead-out SMF as E0(x, y), the transmission power at the place with a distance of L relative to the lead in plane can be written as12 0 1 ð 1 ð 1 2 Eðx; y; LÞE0 ðx; yÞdxdyj B C B C 0 0 ð1 ð1 Iout ¼ 10lgBð 1 ð 1 C: @ A jEðx; y; LÞj2 dxdy jE0 ðx; yÞj2 dxdy
;
bmn k0 nr
2
1 2
ðc þ 1Þ ðd þ 1Þ ðe þ 1Þ ðf þ 1Þ þ Wef f 2 ð0Þ Wef f 2 ð1Þ
(4)
(1)
where amn, wmn, and bmn are the excitation coefficient, field profile, and the propagation constant of the Exmn mode in the square NCF, respectively, and bmn, w0 mn, and b0 mn are the parameters corresponding to the Eymn mode, respectively. Here, the excitation coefficient and propagation constant can be expressed as12,13 1 ð1 ð
2r k next 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; þ p n0 n0 2 next 2
2L
;
Based on the self-image theory, when L equates to the single image distance, the output field from the NCF will be reimaged, which means the intensity of the output light will be highest. For the propagation constant of mn-order and uvorder modes, bmn and buv, respectively, if (buv-bmn) L ¼ 2pp (p is integer), the mn-order and uv-order modes will be reimaged, and the maxima will be observable in the transmission spectrum. In general, the uv-order mode is the most dominant radial mode in the MMF. The wavelength for the transmission maxima can be expressed as
p is integer and
Based on Eq. (6), we can estimate the order of the reimaged modes. As Weff (0) and Weff (1) increase with the increment of external RI, the wavelength of transmission maxima will accordingly experience red-shift. On the other hand, the change of the external RI will also affect the excitation coefficients of respective mode amn and bmn and the eigenmodes
8 c ¼ n; d ¼ v; e ¼ m; f > > < c ¼ m; d ¼ u; e ¼ n; f c ¼ n; d ¼ u; e ¼ m; f > > : c ¼ m; d ¼ v; e ¼ n; f
¼ u; ¼ v; ¼ v; ¼ u;
Exmn with Exmn Eymn with Eymn : Exmn with Eymn x x Emn with Emn
(6)
wmn and w0 mn, causing the change of output intensity. The spectra before and after immersing in the MF shown in Fig. 2 indicate a good agreement with the above analysis. By immersing the MMI section into the MF and exploiting RI tunability of the MF under varying magnetic field,6 a magnetic field sensor can be achieved.
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FIG. 3. Transmission characteristics of the magnetic field sensor. FIG. 4. Transmission spectral response of peak A and peak B to the change of magnetic field intensity.
TABLE I. Values of parameters used in the simulation.
Peak A Peak B
kexp (nm)a
c, d, e, f
p
Weff (0) and Weff(1)b
n0c
kcal (nm)d
1175.5 1293
4, 7, 6, 1 3, 1, 4, 1
1 4
91.0088 and 90.9426 91.1251 and 91.0532
1.4483 1.447
1175.6 1293.3
a exp
k is the wavelength measured by the OSA. ef f Weff is calculated by Eq. (4), with the RI of magnetic fluid next ¼ 1.40 and W00 ¼ 90 lm. c n0 is the RI of pure silica, calculated by the well-known Cauchy dispersion formula according to the wavelength kexp. d cal k is the wavelength calculated by Eq. (6). b
By tuning the TVS to change the magnetic field intensity, the transmission characteristics of the proposed sensor are shown in Fig. 3. One can see that the transmission spectrum changes gradually with the variation of magnetic field intensity. Peak A and peak B are selected to analyze the spectral response of the sensor to the change of magnetic field. Based on Eq. (6), part of the main reimaged modes can be estimated, as shown in Table I. The transmission spectral responses of peak A and peak B to the change of applied magnetic field intensity are shown in Fig. 4. The responses of these two peaks exhibit nonlinear behavior, which is similar to the Langevin function in Ref. 5. With the increment of magnetic field intensity, the external RI increases. And as a result, the excitation coefficient of the eigenmodes and the field profile will change accordingly. Hence, the output intensity calculated by Eq. (5) will vary. As the magnetic field intensity increases from 0 Oe to 500 Oe, the spectral transmission decreases from 28.075 dB to 31.099 dB and 21.954 dB to 25.391 dB for peak A and peak B, respectively. From 0 Oe to 100 Oe, spectral transmission changes slightly due to the effect of the initial magnetization of MF. And owing to the saturated magnetization of MF, the spectral transmission tends to be constant for the magnetic field intensity higher than 275 Oe. Peak A and peak B vary linearly with the magnetic field intensity for a range of 100 Oe 250 Oe. The sensitivity and R2 reach 0.01418 dB/Oe and 0.9927 for peak A and 0.01939 dB/Oe and 0.99285 for peak B. Within this linear
range, easy modulation methods could be employed to achieve the measurement of the magnetic field intensity. In this paper, a compact magnetic field sensor has been proposed based on square NCF MMI and the MF. Numerous high-order modes sensitive to external RI variation are excited in the square NCF. Different characteristics of different peaks are analyzed. The magnetic field sensitivities are 0.01418 dB/Oe and 0.01939 dB/Oe for peak A and peak B, respectively. Due to its low cost and compactness, this sensor would find potential applications in the measurement of magnetic field. This work was jointly supported by the National Natural Science Foundation of China under Grant Nos. 11004110, 11274182, and 11204212, the National Key Basic Research and Development Program of China under Grant No. 2010CB327605, Science & Technology Support Project of Tianjin under Grant No. 11ZCKFGX01800, China Postdoctoral Science Foundation Funded Project under Grant No. 2012M520024, and the Fundamental Research funds for the Central Universities. 1
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