sensors Article
Ultrasensitive Magnetic Field Sensing Based on Refractive-Index-Matched Coupling Jie Rao 1 , Shengli Pu 1,2, * 1 2
*
, Tianjun Yao 1 and Delong Su 1
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China; [email protected] (J.R.); [email protected] (T.Y.); [email protected] (D.S.) Shanghai Key Laboratory of Modern Optical System, University of Shanghai for Science and Technology, Shanghai 200093, China Correspondence: [email protected]; Tel.: +86-21-6566-6454
Received: 22 May 2017; Accepted: 3 July 2017; Published: 7 July 2017
Abstract: An ultrasensitive magnetic field sensor is proposed and investigated experimentally. The no-core fiber is fusion-spliced between two pieces of single-mode fibers and then immersed in magnetic fluid with an appropriate value of refractive index. Under the refractive-index-matched coupling condition, the guided mode becomes leaky and a coupling wavelength dip in the transmission spectrum of the structure is observed. The coupling wavelength dip is extremely sensitive to the ambient environment. The excellent sensitivity to the refractive index is measured to be 116.681 µm/RIU (refractive index unit) in the refractive index range of 1.45691–1.45926. For the as-fabricated sensors, the highest magnetic field sensing sensitivities of 6.33 and 1.83 nm/mT are achieved at low and high fields, respectively. The sensitivity is considerably enhanced compared with those of previously designed, similar structures. Keywords: magnetic field sensor; magnetic fluid; singlemode-no-core-singlemode fiber structures; refractive-index-matched coupling
1. Introduction Magnetic fluid (MF) is a novel kind of functional material, which presents solid-magneticmaterial-like magnetism and liquid-like fluidity. It consists of magnetic nanoparticles dispersed in a suitable liquid carrier. The magnetic nanoparticles are coated with surfactant to form a stable colloidal system [1]. The microstructures within MF are diverse under the external applied magnetic field. This will lead to many unique optical properties of MF under an applied magnetic field, such as tunable refractive index (RI), tunable birefringence, and tunable transmittance [2]. Until now, many optical devices and applications based on MF have been proposed and demonstrated, for example, optical gratings [3,4], optical switches [5], magnetic field sensors [1,6–16], tunable filters [17], tunable slow light [18], and couplers [19]. Recently, the singlemode-multimode-singlemode (SMS) or singlemode-no-core-singlemode (SNS) fiber structures have been designed to sense temperature, RI, chemical concentration, strain and magnetic field [1,6,20–23]. They are low-cost and easy to fabricate. The fundamental sensing principle is the multimode interference within the multimode fiber or no-core fiber (NCF). The sensitivity of these structures depends on the difference of response to ambient variation between the involved modes. On the other hand, refractive-index-matched coupling (RIMC) is attractive for widely tunable filtering and ultrasensitive sensing applications [24–27]. The fundamental principle is based on the material dispersion effect. In this work, an MF with an appropriate RI value is utilized to cover the SNS fiber structure to realize magnetic field sensing with ultrahigh sensitivity. Different from the conventional SMS/SNS
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placed in a capillary tube, which is filled with MF. Both ends of the capillary tube are sealed with UV glue to prevent the MF from leaking and evaporating. Therefore, the cladding of the NCF is actually the ambient MF. The as-fabricated sensor is shown in Figure 1b. When the incident light is broadband and propagates within the NCF, there are three possible cases depending Sensors 2017, 17, 1590 on the relative relationship between the RI of NCF and that of MF: guided, index2 of 9 matched, and leaky (see Figure 1a). Due to the different dispersion properties of NCF and MF, their dispersion profiles may intersect at a certain wavelength range. The guided condition means that the fiber structures, the sensing of this work isnbased on RIMC. At RIMC, the guided modes nNCF (1 ) internal total reflection (ITR) principle happens, i.e., S (1 ) , where nNCF (1 ) and nS (1 ) are the RIs within the NCF become leaky, which yield a coupling wavelength dip (CWD) in the transmission of NCF and MF at , respectively. At a specific wavelength (for example 2 ), nNCF (2 ) nS (2 ) spectrum. The CWD 1will shift significantly, and even the ambient environment changes slightly. and the index-matched is satisfied. This field is thesensor RIMC, which can cause a high loss at this Therefore, the sensitivitycondition of the proposed magnetic can be markedly enhanced. specific wavelength. The leaky case implies nNCF (3 ) nS (3 ) and the Fresnel reflection (FR) will 2. SensoratStructure and Sensing Principle happen this wavelength. Figure 1c–e) displays the simulations of energy distribution within the NCF for the three cases, respectively. It is clear from Figure 1c–e that the light is effectively confined Figure 1a shows the schematic diagram of the proposed sensor. A section of NCF with a diameter within the NCF when nNCF (1 ) nS (1 ) . Strong interference is obvious. Under the index-matched of 125 µm is fusion spliced between two pieces of singlemode fibers. The whole structure is placed n ( ) n ( ), thewith energy leaksends out of ofthe NCF along tube withare thesealed light with propagation. condition ( NCF 2 S 2 in a capillary tube, which is)filled MF. Both capillary UV glue (3 )evaporating. nS (3 ) ), partTherefore, Meanwhile, forMF thefrom FR case ( nNCFand of energythe returns to theoffiber. Then,isweak light is to prevent the leaking cladding the NCF actually the ambient The the as-fabricated sensorinisFigure shown1e. in Figure 1b. observedMF. within NCF as shown
Figure 1. (a) Schematic of the proposed sensor; (b) picture of the as-fabricated sensor; (c) simulation Figure 1. (a) Schematic of the proposed sensor; (b) picture of the as-fabricated sensor; (c) simulation of energy distribution within the no-core fiber (NCF) for the guided ( nNCF (1 ) nS (1 ) ); (d) indexof energy distribution within the no-core fiber (NCF) for the guided (n NCF (λ1 ) > nS (λ1 )); (d) 2 ) (nλS ()2=) )nand matched ( nNCF ((n (e) leaky ( nNCF (3 ) nS (3 ) ) cases, respectively. index-matched NCF 2 S ( λ2 )) and (e) leaky (n NCF ( λ3 ) < nS ( λ3 )) cases, respectively.
When the incident light is broadband and propagates within the NCF, there are three possible cases depending on the relative relationship between the RI of NCF and that of MF: guided, index-matched, and leaky (see Figure 1a). Due to the different dispersion properties of NCF and MF, their dispersion profiles may intersect at a certain wavelength range. The guided condition means that the internal total reflection (ITR) happens, i.e., n NCF (λ1 ) > nS (λ1 ), where n NCF (λ1 ) and nS (λ1 ) are the RIs of NCF and MF at λ1 , respectively. At a specific wavelength (for example λ2 ), n NCF (λ2 ) = nS (λ2 ) and the index-matched condition is satisfied. This is the RIMC, which can cause a high loss at this specific wavelength. The leaky case implies n NCF (λ3 ) < nS (λ3 ) and the Fresnel reflection (FR) will happen at this wavelength. Figure 1c–e) displays the simulations of energy distribution within the NCF for the three cases, respectively. It is clear from Figure 1c–e that the light is effectively confined within the NCF when n NCF (λ1 ) > nS (λ1 ). Strong interference is obvious. Under the index-matched condition (n NCF (λ2 ) = nS (λ2 )), the energy leaks out of NCF along with the light propagation. Meanwhile, for
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the FR case (n NCF (λ3 ) < nS (λ3 )), part of energy returns to the fiber. Then, weak light is observed Sensors 2017, 17, 1590 3 of 9 within the NCF as shown in Figure 1e. The with the the index-match index-matchbetween betweenthe theNCF NCFand andthe thesurrounding surrounding media (MF) The CWD CWD is is related related with media (MF) at at a specific wavelength. The RI of the MF changes with the external magnetic field, but that of the a specific wavelength. The RI of the MF changes with the external magnetic field, but that of the NCF NCF is independent of magnetic So,index-matched the index-matched wavelength will with shift the withmagnetic the magnetic is independent of magnetic field.field. So, the wavelength will shift field. field. Due to the low dispersion of the NCF and MF, i.e., small slopes of the dispersion profiles, the Due to the low dispersion of the NCF and MF, i.e., small slopes of the dispersion profiles, the indexindex-matched wavelength will shift significantly, and even the ambient environment varies slightly. matched wavelength will shift significantly, and even the ambient environment varies slightly. Thus, Thus, the magnetic sensing ultrahigh sensitivity be realized through observing shift the magnetic field field sensing withwith ultrahigh sensitivity can can be realized through observing thethe shift of of the CWD. the CWD. 3. Experimental Results and Discussion 3. Experimental Results and Discussion The schematic of the experimental setup for investing the sensing properties is shown in Figure 2. The schematic of the experimental setup for investing the sensing properties is shown in Figure Light from the supercontinuum broadband source (SBS, Wuhan Yangtze Soton Laser Co., Ltd., Wuhan, 2. Light from the supercontinuum broadband source (SBS, Wuhan Yangtze Soton Laser Co., Ltd., China) is launched into the sensing structure and the output light is monitored and analyzed by an Wuhan, China) is launched into the sensing structure and the output light is monitored and analyzed optical spectrum analyzer (OSA, Yokogawa AQ6370C, Tokyo, Japan). The magnetic field strength by an optical spectrum analyzer (OSA, Yokogawa AQ6370C, Tokyo, Japan). The magnetic field is adjusted by changing the magnitude of the supply current and calibrated by a gauss meter. The strength is adjusted by changing the magnitude of the supply current and calibrated by a gauss meter. magnetic field direction is perpendicular to the optical fiber axis. During our experiments, the ambient The magnetic field direction is perpendicular to the optical fiber axis. During our experiments, the temperature is kept constant. ambient temperature is kept constant.
Figure 2. 2. Schematic Schematic diagram diagram of of the the experimental experimental setup setupfor forinvestigating investigatingthe thesensing sensingproperties. properties. Figure
The NCF with a diameter of 125 μm was provided by Yangtze Optical Fibre and Cable Joint The NCF with a diameter of 125 µm was provided by Yangtze Optical Fibre and Cable Joint Stock Stock Limited Company (Wuhan, China). The RI of the oil-based MF (EXP08103, Ferrotec, Chiba, Limited Company (Wuhan, China). The RI of the oil-based MF (EXP08103, Ferrotec, Chiba, Japan) Japan) with volume fraction of 5.62% used in this work is measured to be 1.56403 by a refractometer with volume fraction of 5.62% used in this work is measured to be 1.56403 by a refractometer (A670, (A670, Hanon, Jinan, China). For the easy occurrence of the abovementioned three cases, the initial Hanon, Jinan, China). For the easy occurrence of the abovementioned three cases, the initial MF is MF is diluted with ethyl oleate to around 0.4% volume fraction, whose RI approaches that of the NCF. diluted with ethyl oleate to around 0.4% volume fraction, whose RI approaches that of the NCF. The The diluted MFs with RIs of 1.45468, 1.45691, 1.45786, and 1.45926 (measured by the same diluted MFs with RIs of 1.45468, 1.45691, 1.45786, and 1.45926 (measured by the same refractometer) refractometer) are obtained through finely tuning the volume fraction further, which are then utilized are obtained through finely tuning the volume fraction further, which are then utilized to fabricate to fabricate the proposed sensing structures. The corresponding transmission spectra are shown in the proposed sensing structures. The corresponding transmission spectra are shown in Figure 3a. Figure 3a. Figure 3a indicates that the spectra for the MF-covered SNS structures is much smoother Figure 3a indicates that the spectra for the MF-covered SNS structures is much smoother than that than that without the MF. This may be due to the RI of the MF approaching that of the NCF, which without the MF. This may be due to the RI of the MF approaching that of the NCF, which leads to the leads to the weakly guided case. More high-order modes radiate into the MF and become lossy, which weakly guided case. More high-order modes radiate into the MF and become lossy, which weakens the weakens the modal interference effect. For clarity, the spectra at short and long wavelength regimes modal interference effect. For clarity, the spectra at short and long wavelength regimes are replotted in are replotted in Figure 3b,c respectively. Figure 3b shows that the spectrum red-shifts with the RI of Figure 3b,c respectively. Figure 3b shows that the spectrum red-shifts with the RI of the MF (see the the MF (see the red arrow). This is qualitatively consistent with that in [6]. Therefore, the mode red arrow). This is qualitatively consistent with that in [6]. Therefore, the mode interference dominates interference dominates the spectrum at the short wavelength regime. The total wavelength shift is the spectrum at the short wavelength regime. The total wavelength shift is 40.2 nm. For the RI ranging 40.2 nm. For the RI ranging from 1.45468 to 1.45926, the obtained wavelength shift is 13.8 nm and the corresponding average RI sensing sensitivity is 3013 nm/RIU (refractive index unit).
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from 1.45468 to 1.45926, the obtained wavelength shift is 13.8 nm and the corresponding average RI is 3013 nm/RIU (refractive index unit). 4 of 9
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Figure 3. (a) Transmission spectra of the as-fabricated sensing structures, (b) the corresponding spectra Figure 3. (a) Transmission spectra of the as-fabricated sensing structures, (b) the corresponding at the short wavelength regime and (c) at the long wavelength regime. spectra at the short wavelength regime and (c) at the long wavelength regime.
At the long wavelength regime, there is a newly emerging dip wavelength occurring around 1480 nm when the RI of the MF is increased to 1.45691 (see Figure 3c). When the RI of the MF further increases, the newly emerging emerging dip wavelength wavelength shifts shifts toward toward the short wavelength wavelength side side (see (see the red increases, arrow in Figure 3c), which is is opposite opposite to to the the mode mode interference interference effect effect at atthe theshort shortwavelength wavelengthregime. regime. This newly newly emerging emergingdip dipwavelength wavelengthcorresponds correspondstotothe theCWD. CWD.AtAt this specific wavelength, this specific wavelength, thethe RI RI of of the equals that NCF. illustratethe theshift shiftofofthe theCWD CWDexplicitly, explicitly, Figure Figure 44 schematically the MFMF equals that of of thethe NCF. ToToillustrate plots the dispersion profiles of the NCF and MFs with different RIs. The intersection point between dispersion profiles of the NCF and MF corresponds to the CWD. Figure 4 clearly indicates that the dispersion the intersection point shifts toward the short wavelength side as the RI of the MF increases. This is in agreement with the experimental results shown in Figure 3c.
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Figure 4. 4. Dispersion Dispersion profiles of the and magnetic with different refractive Figure profiles of the the NCFNCF and magnetic magnetic fluidsfluids (MFs) (MFs) with different different refractive indices Figure 4. Dispersion profiles of NCF and fluids (MFs) with refractive indices indices (RIs). (RIs). (RIs).
At the the long wavelength regime, the the totaltotal wavelength shift is is 274.2 nm in the the range of range 1.45691– thelong longwavelength wavelength regime, wavelength shift is nm 274.2 nmrange in the of At regime, the total wavelength shift 274.2 in of 1.45691– 1.45926, which which corresponds corresponds to an an average average RI sensing sensing sensitivity of 116.681 116.681 μm/RIU. Hence, the 1.45691–1.45926, which corresponds to an average RI sensing sensitivity of 116.681 µm/RIU. Hence, 1.45926, to RI sensitivity of μm/RIU. Hence, the sensitivity based on the thethe RIMC (leak of guided guided modes) is is around 3939times times higher than that based on the sensitivity based on RIMC (leak of guided modes) around39 timeshigher higherthan thanthat thatbased based on sensitivity based on RIMC (leak of modes) is around mode interference. Thus, the proposed structure can be employed to realize a magnetic field sensor Thus,the the proposed structure can be employed to realize a magnetic field sensor mode interference. Thus, ultrahigh sensitivity sensitivity through through interrogating interrogating the the CWD. CWD. with ultrahigh with In of the the proposed structure in in order to investigate the magnetic field sensing characteristics of proposed structure In order to investigate the magnetic field sensing characteristics detail, the the MF MF with with an an RI first employed, of NCF RI of of 1.45786 1.45786 is is first employed, and and two two structures structures consisting consisting of NCF with with detail, lengths of of 2.5 2.5 and The experimental experimental results results are are shown 5. Figure Figure 5a,b and 3.5 3.5 cm cm are are fabricated. fabricated. The shown in in Figure Figure 5. 5a,b lengths display that the CWDs (denoted as C) side field move to the short wavelength with the magnetic display that the CWDs (denoted as C) move to the short wavelength side with the magnetic field as B), B), which which is is contributed contributed to the increase of the RI of the MF with the magnetic field [28]. (denoted as contributedto tothe theincrease increaseof ofthe theRI RIof ofthe theMF MFwith withthe themagnetic magneticfield field[28]. [28]. (denoted be more more explicit, explicit, the the shift shift of of the the CWDs CWDs labeled labeled in in Figure Figure 5a,b field is To be 5a,b with with the the magnetic magnetic field is replotted replotted To in Figure Figure 5c. 5c. Figure Figure 5c 5c indicates indicates that that the the CWDs CWDs change change significantly significantly with with the the magnetic magnetic field field under under in the low field region region (≤6 mT). The corresponding sensitivities are 5.49 and 5.62 nm/mT, respectively. low field ((≤6 ≤6mT). mT).The Thecorresponding correspondingsensitivities sensitivitiesare are5.49 5.49and and5.62 5.62 nm/mT, nm/mT,respectively. respectively. the increase, shift becomes slight. This is due As the magnetic field continues to increase, the shift becomes slight. to the saturation As magnetic continues This is due to the saturation magnetization of the MF MF at at aa relatively relatively high high magnetic magnetic field. field. The The corresponding corresponding sensitivities sensitivities at at higher higher of the magnetization field regions mT) are are 1.51 1.51 and and 1.42 1.42 nm/mT, nm/mT, respectively. respectively. The experimental experimental results results indicate indicate that that regions (6–26 (6–26 mT) nm/mT, respectively. The field the length sensitivity of the SNS structure. of the NCF has a negligible effect on the sensitivity of the SNS structure. the length of the NCF
Figure 5. Cont.
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Figure 5. Transmission spectra of the sensing structures consisting of the NCF with lengths of (a) 2.5 cm and (b) 3.5 cm; (c) the relationship between the coupling wavelength dip (CWD) and the magnetic field intensity.
Furthermore, another two SNS structures are fabricated employing MFs with an RI of 1.45691 and 1.45926, respectively. The length of the NCF is kept at 3.5 cm. The very similar experimental results are obtained and shown in Figure 6.
Figure 5. 5. Transmission Transmissionspectra spectraofofthe thesensing sensingstructures structures consisting NCF with lengths of 2.5 (a) cm 2.5 Figure consisting of of thethe NCF with lengths of (a) cm and relationship between the couplingwavelength wavelengthdip dip(CWD) (CWD)and and the the magnetic magnetic and (b) (b) 3.5 3.5 cm;cm; (c) (c) thethe relationship between the coupling Figure 5. Transmission spectra of the sensing structures consisting of the NCF with lengths of (a) 2.5 field intensity. field intensity. cm and (b) 3.5 cm; (c) the relationship between the coupling wavelength dip (CWD) and the magnetic field intensity.
Furthermore, another two SNS structures are fabricated employing MFs with an RI of 1.45691 Furthermore, another two SNS structures are fabricated employing MFs with an RI of 1.45691 and and 1.45926, respectively. length of the NCF is kept 3.5 cm. The very similar experimental Furthermore, another two SNS structures areThe fabricated employing MFs with an RI at of 1.45691 1.45926, respectively. The length of the NCF is kept at 3.5 cm. The very similar experimental results are and 1.45926, respectively. Theobtained length of the is kept 3.5 cm.6. The very similar experimental results are andNCF shown inatFigure obtained andinshown results are obtained and shown Figure 6.in Figure 6.
6. Transmission spectra of the sensing structures with the RI of the MF of (a) 1.45691 and (b) Figure 6. Transmission spectra of theFigure sensing structures with the RI of the MF of (a) 1.45691 and (b) 1.45926. The length of the NCF is 3.5 cm. 1.45926. The length of the NCF is 3.5 cm.
According to Figures 5 and 6, the relationship between the CWDs and the magnetic field for the three structures with the same length of NCF (3.5 cm) covered with different RIs of the MF (1.45691, 1.45786, and 1.45926) is plotted in Figure 7. From Figure 7, the sensitivities of the three structures are 6.33, 5.62, and 5.50 nm/mT under the low magnetic field region (≤6 mT), respectively. Under the high magnetic field (6–26 mT), the decreased sensitivities of 1.83, 1.42, and 1.46 nm/mT are obtained, respectively. The structure covered with the lowest RI of the MF (1.45691) has the highest sensitivity. This may be due to the dispersion profile difference between the MFs with different RIs. Then, the intersection point of the dispersion profile between the NCF and MF shifts differently for different Figure 6. Transmission spectra of thethe sensing structures with the RI ofchange. the MF of (a) 1.45691 and (b) structures under same magnetic field 1.45926. The length of the NCF is 3.5 cm.
Figure 6. Transmission spectra of the sensing structures with the RI of the MF of (a) 1.45691 and (b) 1.45926. The length of the NCF is 3.5 cm.
6.33, 5.62, and 5.50 nm/mT under the low magnetic field region (≤6 mT), respectively. Under the high magnetic field (6–26 mT), the decreased sensitivities of 1.83, 1.42, and 1.46 nm/mT are obtained, respectively. The structure covered with the lowest RI of the MF (1.45691) has the highest sensitivity. This may be due to the dispersion profile difference between the MFs with different RIs. Then, the Sensors 2017, 17,point 1590 of the dispersion profile between the NCF and MF shifts differently for different 7 of 9 intersection structures under the same magnetic field change.
Figure Figure 7. 7. Relationship Relationship between between the the CWD CWD and and the the magnetic magnetic field field intensity intensity for for the the sensing sensing structures structures covered covered with with an an MF MF of of different different RIs. RIs. The The length length of of the the NCF NCF is is 3.5 3.5 cm. cm.
Though the the low low concentration concentration MF MF is is utilized utilized in in this this work, work, the the sensitivity sensitivity has has been been improved improved Though significantly compared with those of previously used similar structures, based on mode interference. significantly compared with those of previously used similar structures, based on mode interference. The highest highest sensitivity sensitivity of of 6.33 6.33 nm/mT nm/mT was achieved under under the the low low magnetic magnetic field field region region ((≤6 The was achieved ≤6 mT), mT), which is is around around 38 38 times times and and 77 times timeshigher higherthan thanthose thoseof ofthe thevery verysimilar similarSMS SMS(0.1686 (0.1686nm/mT) nm/mT) and and which SNS (0.905 nm/mT) structures based on the multimode interference effect [1,6]. SNS (0.905 nm/mT) structures based on the multimode interference effect [1,6]. 4. Conclusions In conclusion, conclusion, a novel novel magnetic magnetic field field sensor sensor based based on on MF MF and and RIMC RIMC is proposed. proposed. The traditional SNS fiber structure structure is employed, employed, but the sensing principle is totally different from the previously employed multimode interference. The length of the NCF has a negligible effect on the sensitivity of the SNS SNS structure. structure. For For the the as-fabricated as-fabricated structures, structures, the the highest highest sensitivities sensitivities of of6.33 6.33and and1.83 1.83nm/mT nm/mT were ≤6 mT) mT) and and high magnetic magnetic field (6–26 mT) regions, were achieved achieved under under the the low low magnetic magnetic field field ((≤6 respectively. enhanced compared with those of respectively. The Themaximum maximumsensitivity sensitivityininthis thiswork workisisconsiderably considerably enhanced compared with those the previous designed, similar structures. By choosing an MF withwith highhigh saturation magnetization and of the previous designed, similar structures. By choosing an MF saturation magnetization and designing the initial RI MF of the MF zero (under zero magnetic field) with an appropriate value, the designing the initial RI of the (under magnetic field) with an appropriate value, the sensitivity sensitivity sensing of themagnetic proposedfield magnetic sensor canimproved. be further improved. and sensingand range of therange proposed sensorfield can be further Acknowledgments: Foundation of of China China (Grant (Grant No. No. Acknowledgments: This This research research is is supported supported by by National National Natural Natural Science Science Foundation 61675132), Shanghai “Shuguang Program” (Grant No. 16SG40), Shanghai Talent Development Fund (Grant No. 61675132), Shanghai “Shuguang Program” (Grant No. 16SG40), Shanghai Talent Development Fund (Grant No. 201529), Natural Science Foundation of Shanghai (Grant No. 13ZR1427400), Shanghai Key Laboratory of Specialty 201529), Natural ScienceAccess Foundation of (Grant Shanghai No. 13ZR1427400), Shanghai KeyofLaboratory of Fiber Optics and Optical Networks No. (Grant SKLSFO2014-05), and Hujiang Foundation China (Grant Specialty Fiber Optics and Optical Access Networks (Grant No. SKLSFO2014-05), and Hujiang Foundation of No. B14004). China (Grant No. B14004). Author Contributions: Jie Rao conceived, designed and performed the experiments; Jie Rao and Shengli Pu analyzed the data, and co-wrote the manuscript; Shengli Pu planned and supervised the research, and gave suggestions at all stages. Tianjun Yao and Delong Su contributed to the simulations. All authors contributed to the discussions and reviewed the manuscript. Conflicts of Interest: The authors declare no conflict of interest.
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Lee, C.-L.; Lin, K.-H.; Lin, Y.Y.; Hsu, J.-M. Widely tunable and ultrasensitive leaky-guided multimode fiber interferometer based on refractive-index-matched coupling. Opt. Lett. 2012, 37, 302–305. [CrossRef] [PubMed] Bhowmik, T.; Maity, A. Design and analysis of broadband single-mode photonic crystal fiber for transmission windows of the telecom wavelengths. Opt.-Int. J. Light Electron Opt. 2017, 139, 366–372. [CrossRef] Hou, Y.; Fan, F.; Zhang, H.; Wang, X.-H.; Chang, S.-J. Terahertz single-polarization single-mode hollow-core fiber based on index-matching coupling. IEEE Photonics Technol. Lett. 2012, 24, 637–639. [CrossRef] Sun, B.; Chen, M.-Y.; Zhang, Y.-K.; Yang, J.-C. Design of refractive index sensors based on the wavelength-selective resonant coupling phenomenon in dual-core photonic crystal fibers. J. Biomed. Opt. 2012, 17, 037002. [CrossRef] [PubMed] Hong, C.-Y.; Chieh, J.-J.; Yang, S.-Y.; Yang, H.-C.; Horng, H.-E. Simultaneous identification of the low-field-induced tiny variation of complex refractive index for anisotropic and opaque magnetic-fluid thin film by a stable heterodyne Mach–Zehnder interferometer. Appl. Opt. 2009, 48, 5604–5611. [CrossRef] [PubMed] © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Ultrasensitive Magnetic Field Sensing Based on Refractive-Index-Matched Coupling Jie Rao 1 , Shengli Pu 1,2, * 1 2
*
, Tianjun Yao 1 and Delong Su 1
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China; [email protected] (J.R.); [email protected] (T.Y.); [email protected] (D.S.) Shanghai Key Laboratory of Modern Optical System, University of Shanghai for Science and Technology, Shanghai 200093, China Correspondence: [email protected]; Tel.: +86-21-6566-6454
Received: 22 May 2017; Accepted: 3 July 2017; Published: 7 July 2017
Abstract: An ultrasensitive magnetic field sensor is proposed and investigated experimentally. The no-core fiber is fusion-spliced between two pieces of single-mode fibers and then immersed in magnetic fluid with an appropriate value of refractive index. Under the refractive-index-matched coupling condition, the guided mode becomes leaky and a coupling wavelength dip in the transmission spectrum of the structure is observed. The coupling wavelength dip is extremely sensitive to the ambient environment. The excellent sensitivity to the refractive index is measured to be 116.681 µm/RIU (refractive index unit) in the refractive index range of 1.45691–1.45926. For the as-fabricated sensors, the highest magnetic field sensing sensitivities of 6.33 and 1.83 nm/mT are achieved at low and high fields, respectively. The sensitivity is considerably enhanced compared with those of previously designed, similar structures. Keywords: magnetic field sensor; magnetic fluid; singlemode-no-core-singlemode fiber structures; refractive-index-matched coupling
1. Introduction Magnetic fluid (MF) is a novel kind of functional material, which presents solid-magneticmaterial-like magnetism and liquid-like fluidity. It consists of magnetic nanoparticles dispersed in a suitable liquid carrier. The magnetic nanoparticles are coated with surfactant to form a stable colloidal system [1]. The microstructures within MF are diverse under the external applied magnetic field. This will lead to many unique optical properties of MF under an applied magnetic field, such as tunable refractive index (RI), tunable birefringence, and tunable transmittance [2]. Until now, many optical devices and applications based on MF have been proposed and demonstrated, for example, optical gratings [3,4], optical switches [5], magnetic field sensors [1,6–16], tunable filters [17], tunable slow light [18], and couplers [19]. Recently, the singlemode-multimode-singlemode (SMS) or singlemode-no-core-singlemode (SNS) fiber structures have been designed to sense temperature, RI, chemical concentration, strain and magnetic field [1,6,20–23]. They are low-cost and easy to fabricate. The fundamental sensing principle is the multimode interference within the multimode fiber or no-core fiber (NCF). The sensitivity of these structures depends on the difference of response to ambient variation between the involved modes. On the other hand, refractive-index-matched coupling (RIMC) is attractive for widely tunable filtering and ultrasensitive sensing applications [24–27]. The fundamental principle is based on the material dispersion effect. In this work, an MF with an appropriate RI value is utilized to cover the SNS fiber structure to realize magnetic field sensing with ultrahigh sensitivity. Different from the conventional SMS/SNS
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placed in a capillary tube, which is filled with MF. Both ends of the capillary tube are sealed with UV glue to prevent the MF from leaking and evaporating. Therefore, the cladding of the NCF is actually the ambient MF. The as-fabricated sensor is shown in Figure 1b. When the incident light is broadband and propagates within the NCF, there are three possible cases depending Sensors 2017, 17, 1590 on the relative relationship between the RI of NCF and that of MF: guided, index2 of 9 matched, and leaky (see Figure 1a). Due to the different dispersion properties of NCF and MF, their dispersion profiles may intersect at a certain wavelength range. The guided condition means that the fiber structures, the sensing of this work isnbased on RIMC. At RIMC, the guided modes nNCF (1 ) internal total reflection (ITR) principle happens, i.e., S (1 ) , where nNCF (1 ) and nS (1 ) are the RIs within the NCF become leaky, which yield a coupling wavelength dip (CWD) in the transmission of NCF and MF at , respectively. At a specific wavelength (for example 2 ), nNCF (2 ) nS (2 ) spectrum. The CWD 1will shift significantly, and even the ambient environment changes slightly. and the index-matched is satisfied. This field is thesensor RIMC, which can cause a high loss at this Therefore, the sensitivitycondition of the proposed magnetic can be markedly enhanced. specific wavelength. The leaky case implies nNCF (3 ) nS (3 ) and the Fresnel reflection (FR) will 2. SensoratStructure and Sensing Principle happen this wavelength. Figure 1c–e) displays the simulations of energy distribution within the NCF for the three cases, respectively. It is clear from Figure 1c–e that the light is effectively confined Figure 1a shows the schematic diagram of the proposed sensor. A section of NCF with a diameter within the NCF when nNCF (1 ) nS (1 ) . Strong interference is obvious. Under the index-matched of 125 µm is fusion spliced between two pieces of singlemode fibers. The whole structure is placed n ( ) n ( ), thewith energy leaksends out of ofthe NCF along tube withare thesealed light with propagation. condition ( NCF 2 S 2 in a capillary tube, which is)filled MF. Both capillary UV glue (3 )evaporating. nS (3 ) ), partTherefore, Meanwhile, forMF thefrom FR case ( nNCFand of energythe returns to theoffiber. Then,isweak light is to prevent the leaking cladding the NCF actually the ambient The the as-fabricated sensorinisFigure shown1e. in Figure 1b. observedMF. within NCF as shown
Figure 1. (a) Schematic of the proposed sensor; (b) picture of the as-fabricated sensor; (c) simulation Figure 1. (a) Schematic of the proposed sensor; (b) picture of the as-fabricated sensor; (c) simulation of energy distribution within the no-core fiber (NCF) for the guided ( nNCF (1 ) nS (1 ) ); (d) indexof energy distribution within the no-core fiber (NCF) for the guided (n NCF (λ1 ) > nS (λ1 )); (d) 2 ) (nλS ()2=) )nand matched ( nNCF ((n (e) leaky ( nNCF (3 ) nS (3 ) ) cases, respectively. index-matched NCF 2 S ( λ2 )) and (e) leaky (n NCF ( λ3 ) < nS ( λ3 )) cases, respectively.
When the incident light is broadband and propagates within the NCF, there are three possible cases depending on the relative relationship between the RI of NCF and that of MF: guided, index-matched, and leaky (see Figure 1a). Due to the different dispersion properties of NCF and MF, their dispersion profiles may intersect at a certain wavelength range. The guided condition means that the internal total reflection (ITR) happens, i.e., n NCF (λ1 ) > nS (λ1 ), where n NCF (λ1 ) and nS (λ1 ) are the RIs of NCF and MF at λ1 , respectively. At a specific wavelength (for example λ2 ), n NCF (λ2 ) = nS (λ2 ) and the index-matched condition is satisfied. This is the RIMC, which can cause a high loss at this specific wavelength. The leaky case implies n NCF (λ3 ) < nS (λ3 ) and the Fresnel reflection (FR) will happen at this wavelength. Figure 1c–e) displays the simulations of energy distribution within the NCF for the three cases, respectively. It is clear from Figure 1c–e that the light is effectively confined within the NCF when n NCF (λ1 ) > nS (λ1 ). Strong interference is obvious. Under the index-matched condition (n NCF (λ2 ) = nS (λ2 )), the energy leaks out of NCF along with the light propagation. Meanwhile, for
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the FR case (n NCF (λ3 ) < nS (λ3 )), part of energy returns to the fiber. Then, weak light is observed Sensors 2017, 17, 1590 3 of 9 within the NCF as shown in Figure 1e. The with the the index-match index-matchbetween betweenthe theNCF NCFand andthe thesurrounding surrounding media (MF) The CWD CWD is is related related with media (MF) at at a specific wavelength. The RI of the MF changes with the external magnetic field, but that of the a specific wavelength. The RI of the MF changes with the external magnetic field, but that of the NCF NCF is independent of magnetic So,index-matched the index-matched wavelength will with shift the withmagnetic the magnetic is independent of magnetic field.field. So, the wavelength will shift field. field. Due to the low dispersion of the NCF and MF, i.e., small slopes of the dispersion profiles, the Due to the low dispersion of the NCF and MF, i.e., small slopes of the dispersion profiles, the indexindex-matched wavelength will shift significantly, and even the ambient environment varies slightly. matched wavelength will shift significantly, and even the ambient environment varies slightly. Thus, Thus, the magnetic sensing ultrahigh sensitivity be realized through observing shift the magnetic field field sensing withwith ultrahigh sensitivity can can be realized through observing thethe shift of of the CWD. the CWD. 3. Experimental Results and Discussion 3. Experimental Results and Discussion The schematic of the experimental setup for investing the sensing properties is shown in Figure 2. The schematic of the experimental setup for investing the sensing properties is shown in Figure Light from the supercontinuum broadband source (SBS, Wuhan Yangtze Soton Laser Co., Ltd., Wuhan, 2. Light from the supercontinuum broadband source (SBS, Wuhan Yangtze Soton Laser Co., Ltd., China) is launched into the sensing structure and the output light is monitored and analyzed by an Wuhan, China) is launched into the sensing structure and the output light is monitored and analyzed optical spectrum analyzer (OSA, Yokogawa AQ6370C, Tokyo, Japan). The magnetic field strength by an optical spectrum analyzer (OSA, Yokogawa AQ6370C, Tokyo, Japan). The magnetic field is adjusted by changing the magnitude of the supply current and calibrated by a gauss meter. The strength is adjusted by changing the magnitude of the supply current and calibrated by a gauss meter. magnetic field direction is perpendicular to the optical fiber axis. During our experiments, the ambient The magnetic field direction is perpendicular to the optical fiber axis. During our experiments, the temperature is kept constant. ambient temperature is kept constant.
Figure 2. 2. Schematic Schematic diagram diagram of of the the experimental experimental setup setupfor forinvestigating investigatingthe thesensing sensingproperties. properties. Figure
The NCF with a diameter of 125 μm was provided by Yangtze Optical Fibre and Cable Joint The NCF with a diameter of 125 µm was provided by Yangtze Optical Fibre and Cable Joint Stock Stock Limited Company (Wuhan, China). The RI of the oil-based MF (EXP08103, Ferrotec, Chiba, Limited Company (Wuhan, China). The RI of the oil-based MF (EXP08103, Ferrotec, Chiba, Japan) Japan) with volume fraction of 5.62% used in this work is measured to be 1.56403 by a refractometer with volume fraction of 5.62% used in this work is measured to be 1.56403 by a refractometer (A670, (A670, Hanon, Jinan, China). For the easy occurrence of the abovementioned three cases, the initial Hanon, Jinan, China). For the easy occurrence of the abovementioned three cases, the initial MF is MF is diluted with ethyl oleate to around 0.4% volume fraction, whose RI approaches that of the NCF. diluted with ethyl oleate to around 0.4% volume fraction, whose RI approaches that of the NCF. The The diluted MFs with RIs of 1.45468, 1.45691, 1.45786, and 1.45926 (measured by the same diluted MFs with RIs of 1.45468, 1.45691, 1.45786, and 1.45926 (measured by the same refractometer) refractometer) are obtained through finely tuning the volume fraction further, which are then utilized are obtained through finely tuning the volume fraction further, which are then utilized to fabricate to fabricate the proposed sensing structures. The corresponding transmission spectra are shown in the proposed sensing structures. The corresponding transmission spectra are shown in Figure 3a. Figure 3a. Figure 3a indicates that the spectra for the MF-covered SNS structures is much smoother Figure 3a indicates that the spectra for the MF-covered SNS structures is much smoother than that than that without the MF. This may be due to the RI of the MF approaching that of the NCF, which without the MF. This may be due to the RI of the MF approaching that of the NCF, which leads to the leads to the weakly guided case. More high-order modes radiate into the MF and become lossy, which weakly guided case. More high-order modes radiate into the MF and become lossy, which weakens the weakens the modal interference effect. For clarity, the spectra at short and long wavelength regimes modal interference effect. For clarity, the spectra at short and long wavelength regimes are replotted in are replotted in Figure 3b,c respectively. Figure 3b shows that the spectrum red-shifts with the RI of Figure 3b,c respectively. Figure 3b shows that the spectrum red-shifts with the RI of the MF (see the the MF (see the red arrow). This is qualitatively consistent with that in [6]. Therefore, the mode red arrow). This is qualitatively consistent with that in [6]. Therefore, the mode interference dominates interference dominates the spectrum at the short wavelength regime. The total wavelength shift is the spectrum at the short wavelength regime. The total wavelength shift is 40.2 nm. For the RI ranging 40.2 nm. For the RI ranging from 1.45468 to 1.45926, the obtained wavelength shift is 13.8 nm and the corresponding average RI sensing sensitivity is 3013 nm/RIU (refractive index unit).
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from 1.45468 to 1.45926, the obtained wavelength shift is 13.8 nm and the corresponding average RI is 3013 nm/RIU (refractive index unit). 4 of 9
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Figure 3. (a) Transmission spectra of the as-fabricated sensing structures, (b) the corresponding spectra Figure 3. (a) Transmission spectra of the as-fabricated sensing structures, (b) the corresponding at the short wavelength regime and (c) at the long wavelength regime. spectra at the short wavelength regime and (c) at the long wavelength regime.
At the long wavelength regime, there is a newly emerging dip wavelength occurring around 1480 nm when the RI of the MF is increased to 1.45691 (see Figure 3c). When the RI of the MF further increases, the newly emerging emerging dip wavelength wavelength shifts shifts toward toward the short wavelength wavelength side side (see (see the red increases, arrow in Figure 3c), which is is opposite opposite to to the the mode mode interference interference effect effect at atthe theshort shortwavelength wavelengthregime. regime. This newly newly emerging emergingdip dipwavelength wavelengthcorresponds correspondstotothe theCWD. CWD.AtAt this specific wavelength, this specific wavelength, thethe RI RI of of the equals that NCF. illustratethe theshift shiftofofthe theCWD CWDexplicitly, explicitly, Figure Figure 44 schematically the MFMF equals that of of thethe NCF. ToToillustrate plots the dispersion profiles of the NCF and MFs with different RIs. The intersection point between dispersion profiles of the NCF and MF corresponds to the CWD. Figure 4 clearly indicates that the dispersion the intersection point shifts toward the short wavelength side as the RI of the MF increases. This is in agreement with the experimental results shown in Figure 3c.
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Figure 4. 4. Dispersion Dispersion profiles of the and magnetic with different refractive Figure profiles of the the NCFNCF and magnetic magnetic fluidsfluids (MFs) (MFs) with different different refractive indices Figure 4. Dispersion profiles of NCF and fluids (MFs) with refractive indices indices (RIs). (RIs). (RIs).
At the the long wavelength regime, the the totaltotal wavelength shift is is 274.2 nm in the the range of range 1.45691– thelong longwavelength wavelength regime, wavelength shift is nm 274.2 nmrange in the of At regime, the total wavelength shift 274.2 in of 1.45691– 1.45926, which which corresponds corresponds to an an average average RI sensing sensing sensitivity of 116.681 116.681 μm/RIU. Hence, the 1.45691–1.45926, which corresponds to an average RI sensing sensitivity of 116.681 µm/RIU. Hence, 1.45926, to RI sensitivity of μm/RIU. Hence, the sensitivity based on the thethe RIMC (leak of guided guided modes) is is around 3939times times higher than that based on the sensitivity based on RIMC (leak of guided modes) around39 timeshigher higherthan thanthat thatbased based on sensitivity based on RIMC (leak of modes) is around mode interference. Thus, the proposed structure can be employed to realize a magnetic field sensor Thus,the the proposed structure can be employed to realize a magnetic field sensor mode interference. Thus, ultrahigh sensitivity sensitivity through through interrogating interrogating the the CWD. CWD. with ultrahigh with In of the the proposed structure in in order to investigate the magnetic field sensing characteristics of proposed structure In order to investigate the magnetic field sensing characteristics detail, the the MF MF with with an an RI first employed, of NCF RI of of 1.45786 1.45786 is is first employed, and and two two structures structures consisting consisting of NCF with with detail, lengths of of 2.5 2.5 and The experimental experimental results results are are shown 5. Figure Figure 5a,b and 3.5 3.5 cm cm are are fabricated. fabricated. The shown in in Figure Figure 5. 5a,b lengths display that the CWDs (denoted as C) side field move to the short wavelength with the magnetic display that the CWDs (denoted as C) move to the short wavelength side with the magnetic field as B), B), which which is is contributed contributed to the increase of the RI of the MF with the magnetic field [28]. (denoted as contributedto tothe theincrease increaseof ofthe theRI RIof ofthe theMF MFwith withthe themagnetic magneticfield field[28]. [28]. (denoted be more more explicit, explicit, the the shift shift of of the the CWDs CWDs labeled labeled in in Figure Figure 5a,b field is To be 5a,b with with the the magnetic magnetic field is replotted replotted To in Figure Figure 5c. 5c. Figure Figure 5c 5c indicates indicates that that the the CWDs CWDs change change significantly significantly with with the the magnetic magnetic field field under under in the low field region region (≤6 mT). The corresponding sensitivities are 5.49 and 5.62 nm/mT, respectively. low field ((≤6 ≤6mT). mT).The Thecorresponding correspondingsensitivities sensitivitiesare are5.49 5.49and and5.62 5.62 nm/mT, nm/mT,respectively. respectively. the increase, shift becomes slight. This is due As the magnetic field continues to increase, the shift becomes slight. to the saturation As magnetic continues This is due to the saturation magnetization of the MF MF at at aa relatively relatively high high magnetic magnetic field. field. The The corresponding corresponding sensitivities sensitivities at at higher higher of the magnetization field regions mT) are are 1.51 1.51 and and 1.42 1.42 nm/mT, nm/mT, respectively. respectively. The experimental experimental results results indicate indicate that that regions (6–26 (6–26 mT) nm/mT, respectively. The field the length sensitivity of the SNS structure. of the NCF has a negligible effect on the sensitivity of the SNS structure. the length of the NCF
Figure 5. Cont.
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Figure 5. Transmission spectra of the sensing structures consisting of the NCF with lengths of (a) 2.5 cm and (b) 3.5 cm; (c) the relationship between the coupling wavelength dip (CWD) and the magnetic field intensity.
Furthermore, another two SNS structures are fabricated employing MFs with an RI of 1.45691 and 1.45926, respectively. The length of the NCF is kept at 3.5 cm. The very similar experimental results are obtained and shown in Figure 6.
Figure 5. 5. Transmission Transmissionspectra spectraofofthe thesensing sensingstructures structures consisting NCF with lengths of 2.5 (a) cm 2.5 Figure consisting of of thethe NCF with lengths of (a) cm and relationship between the couplingwavelength wavelengthdip dip(CWD) (CWD)and and the the magnetic magnetic and (b) (b) 3.5 3.5 cm;cm; (c) (c) thethe relationship between the coupling Figure 5. Transmission spectra of the sensing structures consisting of the NCF with lengths of (a) 2.5 field intensity. field intensity. cm and (b) 3.5 cm; (c) the relationship between the coupling wavelength dip (CWD) and the magnetic field intensity.
Furthermore, another two SNS structures are fabricated employing MFs with an RI of 1.45691 Furthermore, another two SNS structures are fabricated employing MFs with an RI of 1.45691 and and 1.45926, respectively. length of the NCF is kept 3.5 cm. The very similar experimental Furthermore, another two SNS structures areThe fabricated employing MFs with an RI at of 1.45691 1.45926, respectively. The length of the NCF is kept at 3.5 cm. The very similar experimental results are and 1.45926, respectively. Theobtained length of the is kept 3.5 cm.6. The very similar experimental results are andNCF shown inatFigure obtained andinshown results are obtained and shown Figure 6.in Figure 6.
6. Transmission spectra of the sensing structures with the RI of the MF of (a) 1.45691 and (b) Figure 6. Transmission spectra of theFigure sensing structures with the RI of the MF of (a) 1.45691 and (b) 1.45926. The length of the NCF is 3.5 cm. 1.45926. The length of the NCF is 3.5 cm.
According to Figures 5 and 6, the relationship between the CWDs and the magnetic field for the three structures with the same length of NCF (3.5 cm) covered with different RIs of the MF (1.45691, 1.45786, and 1.45926) is plotted in Figure 7. From Figure 7, the sensitivities of the three structures are 6.33, 5.62, and 5.50 nm/mT under the low magnetic field region (≤6 mT), respectively. Under the high magnetic field (6–26 mT), the decreased sensitivities of 1.83, 1.42, and 1.46 nm/mT are obtained, respectively. The structure covered with the lowest RI of the MF (1.45691) has the highest sensitivity. This may be due to the dispersion profile difference between the MFs with different RIs. Then, the intersection point of the dispersion profile between the NCF and MF shifts differently for different Figure 6. Transmission spectra of thethe sensing structures with the RI ofchange. the MF of (a) 1.45691 and (b) structures under same magnetic field 1.45926. The length of the NCF is 3.5 cm.
Figure 6. Transmission spectra of the sensing structures with the RI of the MF of (a) 1.45691 and (b) 1.45926. The length of the NCF is 3.5 cm.
6.33, 5.62, and 5.50 nm/mT under the low magnetic field region (≤6 mT), respectively. Under the high magnetic field (6–26 mT), the decreased sensitivities of 1.83, 1.42, and 1.46 nm/mT are obtained, respectively. The structure covered with the lowest RI of the MF (1.45691) has the highest sensitivity. This may be due to the dispersion profile difference between the MFs with different RIs. Then, the Sensors 2017, 17,point 1590 of the dispersion profile between the NCF and MF shifts differently for different 7 of 9 intersection structures under the same magnetic field change.
Figure Figure 7. 7. Relationship Relationship between between the the CWD CWD and and the the magnetic magnetic field field intensity intensity for for the the sensing sensing structures structures covered covered with with an an MF MF of of different different RIs. RIs. The The length length of of the the NCF NCF is is 3.5 3.5 cm. cm.
Though the the low low concentration concentration MF MF is is utilized utilized in in this this work, work, the the sensitivity sensitivity has has been been improved improved Though significantly compared with those of previously used similar structures, based on mode interference. significantly compared with those of previously used similar structures, based on mode interference. The highest highest sensitivity sensitivity of of 6.33 6.33 nm/mT nm/mT was achieved under under the the low low magnetic magnetic field field region region ((≤6 The was achieved ≤6 mT), mT), which is is around around 38 38 times times and and 77 times timeshigher higherthan thanthose thoseof ofthe thevery verysimilar similarSMS SMS(0.1686 (0.1686nm/mT) nm/mT) and and which SNS (0.905 nm/mT) structures based on the multimode interference effect [1,6]. SNS (0.905 nm/mT) structures based on the multimode interference effect [1,6]. 4. Conclusions In conclusion, conclusion, a novel novel magnetic magnetic field field sensor sensor based based on on MF MF and and RIMC RIMC is proposed. proposed. The traditional SNS fiber structure structure is employed, employed, but the sensing principle is totally different from the previously employed multimode interference. The length of the NCF has a negligible effect on the sensitivity of the SNS SNS structure. structure. For For the the as-fabricated as-fabricated structures, structures, the the highest highest sensitivities sensitivities of of6.33 6.33and and1.83 1.83nm/mT nm/mT were ≤6 mT) mT) and and high magnetic magnetic field (6–26 mT) regions, were achieved achieved under under the the low low magnetic magnetic field field ((≤6 respectively. enhanced compared with those of respectively. The Themaximum maximumsensitivity sensitivityininthis thiswork workisisconsiderably considerably enhanced compared with those the previous designed, similar structures. By choosing an MF withwith highhigh saturation magnetization and of the previous designed, similar structures. By choosing an MF saturation magnetization and designing the initial RI MF of the MF zero (under zero magnetic field) with an appropriate value, the designing the initial RI of the (under magnetic field) with an appropriate value, the sensitivity sensitivity sensing of themagnetic proposedfield magnetic sensor canimproved. be further improved. and sensingand range of therange proposed sensorfield can be further Acknowledgments: Foundation of of China China (Grant (Grant No. No. Acknowledgments: This This research research is is supported supported by by National National Natural Natural Science Science Foundation 61675132), Shanghai “Shuguang Program” (Grant No. 16SG40), Shanghai Talent Development Fund (Grant No. 61675132), Shanghai “Shuguang Program” (Grant No. 16SG40), Shanghai Talent Development Fund (Grant No. 201529), Natural Science Foundation of Shanghai (Grant No. 13ZR1427400), Shanghai Key Laboratory of Specialty 201529), Natural ScienceAccess Foundation of (Grant Shanghai No. 13ZR1427400), Shanghai KeyofLaboratory of Fiber Optics and Optical Networks No. (Grant SKLSFO2014-05), and Hujiang Foundation China (Grant Specialty Fiber Optics and Optical Access Networks (Grant No. SKLSFO2014-05), and Hujiang Foundation of No. B14004). China (Grant No. B14004). Author Contributions: Jie Rao conceived, designed and performed the experiments; Jie Rao and Shengli Pu analyzed the data, and co-wrote the manuscript; Shengli Pu planned and supervised the research, and gave suggestions at all stages. Tianjun Yao and Delong Su contributed to the simulations. All authors contributed to the discussions and reviewed the manuscript. Conflicts of Interest: The authors declare no conflict of interest.
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