Simultaneous measurement of magnetic field and temperature based on magnetic fluid-clad long period fiber grating

Simultaneous measurement of magnetic ﬁeld and temperature is proposed and experimentalized with a magnetic ﬂuid-clad long period ﬁber grating structure. Magnetic ﬂuid is used as the surrounding material of the long period ﬁber grating. Both of the wavelength and intensity of the spectral resonance valley of the proposed structure can be inﬂuenced by the applied magnetic ﬁeld and ambient temperature variation. A two-parameter matrix method is proposed and utilized to measure the magnetic ﬁeld and temperature simultaneously. The linear relationship between the corresponding wavelength shift/intensity variation and magnetic ﬁeld/temperature change is obtained at certain ranges of magnetic ﬁeld and temperature, which is favorable for sensing applications.


INTRODUCTION
Optical fiber sensors have attracted extensive interest over the past decades, which are due to their particular characteristics, such as high sensitivity, low cost and ease of fabrication.Versatile structures have been employed, for example, single-mode-multimode-multimode fiber structure [1], up-tapered joints fiber-optic structure [2].On the other hand, magnetic fluid (MF) is a kind of intriguing material with the fluidity of liquids and magnetic property of solid magnetic materials, which consists of surfactant-coated ∼10 nm magnetic nanoparticles dispersed in a suitable liquid carrier and has various applications in optical and sensing fields because of its unique magneto-optical effects such as linear birefringence, linear dichroism, Faraday ellipticity and Faraday rotation.Recently, many potential optical and fiber-optic magnetic field sensing applications based on MFs have been proposed.The designed structures including Sagnac interferometer [3], Fabry-Perot Interferometer [4], singlemode-multimode-singlemode fiber structure [5,6], multimode-singlemode-multimode fiber structure [7], coreoffset fiber structure [8,9], tapered fiber structure [10]- [12], thin-core fiber mode interferometer [13,14], hollow-core fiber [15] and photonic crystal fiber/waveguide [16]- [18].Most of the magnetic field sensing structures are based on the interferometric configurations.Due to the large thermooptical coefficient of MF, the corresponding sensing structures may be sensitive to the ambient temperature variation simultaneously [19,20], which will affect the magnetic field sensing accuracy and performance.That is to say, the issue of magnetic field and temperature cross-sensitivity occurs for the MF-based fiber-optic magnetic field sensors.
Long period fiber grating (LPFG) operates through the coupling between core and cladding modes.The resonant wavelength of LPFG is highly sensitive to the external surroundings and the ambient temperature.Therefore, LPFG is very suitable for measuring the external surrounding variation (usually refractive index variation) and ambient temperature change.LPFG has been successfully utilized for temperature measurements and compensation [21]- [25].Considering these, the MF-clad LPFG is proposed to measure magnetic field and temperature simultaneously in this work.

EXPERIMENTS AND PRINCIPLES
The LPFG utilized in our experiments is provided by Nanjing π-Lightwave Information Technology Co., ltd.The LPFG period is 608 µm.The core and cladding diameters of the LPFG are around 9 and 125 µm, respectively.The LPFG is put into the capillary filled with MF.The inner diameter of the capillary is about 1 mm.Both ends of the capillary are then sealed with UV glue to avoid MF evaporating or leaking.The water-based Fe 3 O 4 MF with saturation magnetization of ∼20 mT and density of 1.18 × 10 3 kg/m 3 are provided by Beijing Sunrise Ferrofluid Technological Co.The diameter of the magnetic nanoparticles within the MF is around 10 nm.The as-fabricated structure is placed in the magnetic field for ex- perimental investigation as shown in Figure 1.The magnetic field is produced by an electrical magnet and its strength can be tuned by adjusting the supply current.The light from the broadband light source (BBS) is coupled into the sensing segment (MF-clad LPFG).The transmitted light is analyzed by an optical spectrum analyzer (OSA).For studying the temperature effect, the sensing segment is put on a heating stage.The ambient temperature around the sensing segment is controlled by the temperature controller.
Under phase matching condition, the resonant wavelength of the LPFG can be written as [26] where λ i is the i-order mode resonant wavelength, n core (λ i ) is the effective index of the core mode, n i clad (λ i ) is the effective index of the i-order cladding mode and Λ is the grating period.It is well-known that MF has unique properties of magnetic-field-dependent refractive index [27]- [29].When MF is used as the external surrounding of the LPFG, the effective index of LPFG cladding mode will vary with the magnetic field.According to Eq. ( 1), the LPFG resonant wavelength will vary with the magnetic field as well.Hence, the magnetic field sensing purpose is realized.Besides, the Λ and effective indices of the core and cladding modes will vary with ambient temperature due to the thermal expansion and thermo-optical effects of the LPFG material, respectively.This will lead to the shift of LPFG resonant wavelength with temperature.So, the issue of magnetic field and temperature cross-sensitivity occurs.To fix this issue, a two-parameter matrix method is proposed and utilized in this work.
Under the influence of magnetic field and temperature, the resonant wavelength shift (∆λ) of the MF-clad LPFG changes as follows where B and T are the applied magnetic field and ambient temperature variation, respectively.K λ, B , K λ, T are, respectively, the sensitivities of resonant wavelength shift to magnetic field and temperature.Meanwhile, the depth (viz.transmission loss) of the resonance valley in the transmitted spec-trum changes with the magnetic field and temperature.This is assigned to the coupling variation between core and cladding modes.This coupling variation is due to the influence of magnetic field and temperature on the field profiles of LPFG core and cladding modes.As a result, the transmitted intensity variation of the resonance valley (∆I) can be express as where K I,B and K I,T are, respectively, the sensitivities of intensity variation at resonant wavelength to magnetic field and temperature.Combining Eqs. ( 2) and ( 3), a well-conditioned system of two equations for ∆λ and ∆I can be given in a matrix form as follows According to Eq. ( 4), the strength of magnetic field B and the ambient temperature variation T can be obtained as where is the determinant of the coefficient matrix.Therefore, by monitoring the wavelength shift (∆λ) and intensity variation (∆I) at resonant wavelength simultaneously, the measurands (B and T) can be derived from Eq. ( 5) simultaneously.By this two-parameter matrix method, the issue of magnetic field and temperature cross-sensitivity can be solved in a simple and easy way.

RESULTS AND DISCUSSION
The transmission spectra of the MF-clad LPFG structure at magnetic field strength ranging from 0 to 60 mT (at room temperature, i.e. ambient temperature kept at T=20 • C) and at ambient temperature ranging from 25 to 70 • C (without magnetic field, i.e.B=0 mT) are plotted in Figures 2 and 3, respectively.Figures 2 and 3 imply that both of the depth and wavelength of the resonance valley change with magnetic field (especially at low field regime, i.e. 0-20 mT) and the ambient temperature obviously.This is in agreement with the aforementioned theoretical speculation.
Figures 4 and 5 explicitly show the corresponding wavelength shift and transmission variation of the spectral valley with magnetic field and temperature, respectively.Figures 4 and  5 indicate that the near linear relationships exist at certain ranges of magnetic field and temperature.The magnetic field range of 5-20 mT and temperature range of 25-70 • C have been utilized for linear fitting (for the transmission variation, the lowest magnetic field for the linear range goes down to zero).The deviation of the data points from the linear fitting may be assigned to the measurement errors or the intrinsic fluctuation of out spectrum for the MF-based sample, which may be related the Brownian motion and scattering of the magnetic nanoparticles within the liquid carrier.The very slight variation (sensitivity) at low magnetic field is due to the unique magnetic-field-dependent properties of magnetic fluid.It is well-known that the response of magnetic fluid to external magnetic field satisfies the Langevin-like function [9,30,31].So, this characteristic will limit the application of the proposed sensor at very low magnetic field regime.The slopes obtained from Figures 4 and 5 give the values for K λ,B , K λ,T , K I,B and K I,T in Eqs. ( 2)-( 5).Thus, Eq. ( 5) can now be rewritten in the explicit form According to Eq. ( 6), the magnetic field and ambient temperature variation can be measured simultaneously by synchronously monitoring the wavelength shift and intensity variation of the spectral resonance valley of the as-fabricated MF-clad LPFG structure.This provides an easy and convenient means to interrogate the magnetic field and temperature simultaneously with a simple structure, which will assure the sensing accuracy and enhance the performance of the related sensors.
Figure 2 shows that the transmission spectrum of the corresponding structure varies very slightly with the magnetic field at high field regime (25-60 mT).This may be due to the unique physical properties of MF.Under relatively high magnetic field, the agglomeration of magnetic nanoparticles within MF  tends to saturate.This characteristic limits the application of the proposed MF-clad LPFG structure under relatively high magnetic field.The shift to long wavelength of the resonant for the magnetic field beyond 20 mT may be ascribed to the influence of polarization as reported in [32].

CONCLUSION
In summary, the MF-clad LPFG structure is designed.The magnetic field and temperature sensing properties of the as-designed structure are experimentalized.The variation of wavelength and intensity at spectral resonance valley with the applied magnetic field and ambient temperature is utilized to realize the sensing purpose.Considering these properties, a two-parameter matrix method is proposed to measure the magnetic field and ambient temperature simultaneously.This kind of sensing structure may not be suitable for high magnetic field application due to the saturation of magnetic nanoparticle agglomeration within the MF.On the whole, the proposed sensing structure has the advantages of low-cost, compactness and easiness of fixing the issue of magnetic field and temperature cross-sensitivity.

FIG. 1
FIG. 1 Experimental setup for investigating the magnetic field and temperature sensing properties of MF-clad LPFG sensing structure.

FIG. 2
FIG.2Transmission spectra of the MF-clad LPFG structure at magnetic field strength ranging from 0 to 60 mT.

T r a nFIG. 3
FIG. 3 Transmission spectra of the MF-clad LPFG structure at ambient temperature ranging from 25 to 70 • C.

5 ITFIG. 4
FIG.4 Resonant wavelength and intensity of the spectral valley at different magnetic field strengths.

FIG. 5
FIG. 5 Resonant wavelength and intensity of the spectral valley at different ambient temperature.