Compact magnetic field sensor based on plasmonic fiber-tip

Yin Liu; Qiming Liao; Zhipeng Wang; Yu Bi; Lingling Huang; Yongtian Wang; Xiaowei Li

doi:10.1364/OE.443104

1. Introduction

Magnetic field sensors are widely used in navigation, power system, space, and geophysical research. Many devices have been developed for magnetic field measurement, such as fluxgates sensors [1], spin exchange relaxation-free (SERF) atomic magnetometers [2,3], and optically pumped magnetometers [4]. However, these devices are bulky, lack of flexibility, and low integration. Optical fiber opens up the possibility of solving the above problems [5]. Fiber-optic sensors not only have the advantages of tiny size, high integration, good compactness, and strong survivability in challenging environment, but also have good compatibility with nanomaterials [6,7]. Magnetic fluid is a kind of stable colloid which is composed of magnetic nanoparticles coated with surfactant and carrier liquid. Its unique optical properties, such as dichroism, birefringence, Faraday effect, and refractive index (RI) changing with magnetic field, make it widely used in magnetic field detection. Therefore, based on magnetic fluid and different fiber-based sensing structures, a variety of fiber-optic magnetic field sensors are proposed [8–12].

Generally, most fiber-optic magnetic field sensors are based on evanescent field with the fiber wall functionalized by magnetic field sensing materials [13]. In order to increase the interaction between the evanescent field and the magnetic field sensitizer, it is necessary to artificially enhance the evanescent field strength [14–17]. Usually, these evanescent field enhanced structures and methods will increase the complexity of manufacturing and processing costs. In addition, most of the machining methods will make the fiber more vulnerable and increase the uncertainty in the manufacturing process. The fiber side wall functionalized sensor will become an obstacle to the miniaturization, and will lead to low spatial resolution. Therefore, in order to overcome these limitations, the route of sensing structure and preparation method induced diminutive size is quite important. In recent years, fabrication and integration of fiber-tip devices within limited area has become a research hotspot [18–21]. The fiber end coated with nano structure can modulate the incident light, which has attracted extensive attention [22–24]. LSPR in metallic plasmonic structures can be excited under normal incidence and various polarization conditions [25,26], which makes LSPR have unique advantages in multi-function and integration of the fiber tips.

In this paper, we propose a LSPR fiber-tip combined with magnetic fluid for magnetic field measurement. Based on the RI tunability of the magnetic fluid caused by magnetic field variation and the RI sensing characteristics of the plasmonic fiber-tip, the sensing reflection spectrum varied with the change of the external magnetic field. Compared with other magnetic field sensors, the proposed scheme elegantly avoids the damage to the integrity of the fiber mechanical structure, and the single-ended operation mode is more suitable for practical application. As a supplement to the available tool library of fiber-optic sensor, the proposed fiber-optic magnetic field sensor has potential attraction for real-time monitoring of magnetic field in scientific research.

2. Working principle and fabrication

The schematic diagram of the magnetic field fiber-optic sensor is shown in Fig. 1(a). The magnetic field sensor consists of plasmonic fiber-tip and magnetic fluid. The plasmonic fiber-tip is mainly composed of metasurface based on periodic square hole array in the Au film and MMF. The metasurface is transferred to the MMF end face by “contact and separate” method [27,28]. The incident light transmitted in the MMF core couples with the surface plasmon polaritons (SPPs) on the metasurface, resulting in resonance dips in the reflection spectrum. The scattering mechanism and momentum matching conditions provided by metasurface makes the excitation of LSPR possible, which leads to high field localization near the hole wall. The change of magnetic field leads to the variation of optical parameters of magnetic fluid, especially the change of RI. The interaction between the resonance light field and magnetic fluid lead to the change of resonance characteristics of reflection spectrum.

Fig. 1. (a) Schematic diagram of magnetic strength measuring system. (b) Schematic of the fabrication process of the proposed fiber-optic magnetic field sensor. (c) Optical image of a metallic metasurface on the SiO₂ substrate. (d) Scanning electronic microscopy (SEM) image of the air hole array on the Au film. (e) Overview of the plasmonic fiber-tip. (f) Far-field diffraction pattern of the plasmonic fiber-tip.

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The metasurface can effectively convert the incident light into surface plasmon modes based on momentum conservation condition [29]. For the metasurface coated with magnetic fluid, the wavelength of transmission peak ${\lambda _{\max }}$ under normal incidence can be calculated approximately from the dispersion relation of surface plasma [14,30]

(1)$${\lambda _{\max }} \cong \frac{P}{{\sqrt {{i^2} + {j^2}} }}\sqrt {\frac{{ - {\varepsilon _m}\left\{ {{\varepsilon_{\textrm{col}}} + {\varepsilon_{\textrm{liq}}} - \frac{{\sqrt {{{[{{\varepsilon_{\textrm{col}}}({1 - f} )+ {\varepsilon_{\textrm{liq}}}({f - 1} )} ]}^2} + 4{{({1 + f} )}^2}{\varepsilon_{\textrm{col}}}{\varepsilon_{\textrm{liq}}}} }}{{2({1 + f} )}}} \right\}}}{{{\varepsilon _\textrm{m}} - {\varepsilon _{\textrm{col}}} - {\varepsilon _{\textrm{liq}}} + \frac{{\sqrt {{{[{{\varepsilon_{\textrm{col}}}({1 - f} )+ {\varepsilon_{\textrm{liq}}}({f - 1} )} ]}^2} + 4{{({1 + f} )}^2}{\varepsilon _{\textrm{col}}}{\varepsilon _{\textrm{liq}}}} }}{{2({1 + f} )}}}}},$$

where $P$ is the square-lattice constant. $i$ and $j$ are the diffraction orders from the hole arrays. ${\varepsilon _\textrm{m}}$, ${\varepsilon _{\textrm{col}}}$, and ${\varepsilon _{\textrm{liq}}}$ are the permittivity for the Au film, magnetic column, and liquid phase, respectively. ${\varepsilon _{\textrm{liq}}}$ varies with the magnitude of the magnetic field. $f = {r_{col}}/({1 - {r_{col}}} )$, where ${r_{col}}$ represents the ratio of the area occupied by the magnetic columns to the total area. This equation does not consider the existence of holes and the related scattering loss, and ignores the Fano-type interaction, which leads to the resonance redshift, so the predicted peak wavelength is slightly smaller than the actual value [31].

As a key optical property of magnetic fluid, RI can be determined by the applied magnetic field intensity $H$ and the relative direction between the electric field of the LSPR ${E_{\textrm{LSPR}}}$. The RI of the magnetic fluid ${n_{\textrm{MF}}}$ can be given by [32,33]

(2)$$\begin{aligned} {n_{\textrm{MF}}} &=\sqrt {1 + {\chi _{\textrm{MF}}}} \\ &=\left\{ \begin{array}{ll} \sqrt {1 + \frac{{({1 - \nu } ){\chi_\textrm{C}} + \nu ({{\varepsilon_0} + {\chi_C}/3} )\left[ {\frac{1}{{{A_1}}} - \frac{{2kT}}{{mH}}\left( {\frac{1}{{{A_1}}} - \frac{1}{{{A_2}}}} \right)L\left( {\frac{{mH}}{{kT}}} \right)} \right]}}{{1 + \frac{{\nu {\chi_C}}}{{3{\varepsilon_0}}} - \nu \left[ {\frac{1}{{{A_1}}} - \frac{{2kT}}{{mH}}\left( {\frac{1}{{{A_1}}} - \frac{1}{{{A_2}}}} \right)L\left( {\frac{{mH}}{{kT}}} \right)} \right]\left( {3 + \frac{{{\chi_C}}}{{{\varepsilon_0}}}} \right)}}} & {E_{\textrm{LSPR}}}{\parallel }H\\ \sqrt {1 + \frac{{({1 - \nu } ){\chi_\textrm{C}} + \nu ({{\varepsilon_0} + {\chi_C}/3} )\left[ {\frac{1}{{{A_2}}} - \frac{{2kT}}{{mH}}\left( {\frac{1}{{{A_1}}} - \frac{1}{{{A_2}}}} \right)L\left( {\frac{{mH}}{{kT}}} \right)} \right]}}{{1 + \frac{{\nu {\chi_C}}}{{3{\varepsilon_0}}} - \nu \left[ {\frac{1}{{{A_2}}} - \frac{{2kT}}{{mH}}\left( {\frac{1}{{{A_2}}} - \frac{1}{{{A_2}}}} \right)L\left( {\frac{{mH}}{{kT}}} \right)} \right]\left( {3 + \frac{{{\chi_C}}}{{{\varepsilon_0}}}} \right)}}} & {E_{\textrm{LSPR}}} \bot H \end{array} \right. \end{aligned}$$

where ${\chi _{\textrm{MF}}}$ and ${\chi _\textrm{C}}$ are the electric susceptibility of the magnetic fluid and the carrier fluid, respectively. $\nu$, ${\varepsilon _0}$, $k$, $T$, and $m$ are the volume of the magnetic particles, the electrical permittivity of vacuum, Boltzmann’s constant, absolute temperature, and dipolar magnetic moment of each particle, respectively. ${A_1} = \frac{{{b^2}}}{{2a\sqrt {{a^2} - {b^2}} }}\left( { - 2\sqrt {1 - \frac{{{b^2}}}{{{a^2}}}} + \ln \frac{{a + \sqrt {{a^2} - {b^2}} }}{{a - \sqrt {{a^2} - {b^2}} }}} \right)$ and ${A_2} = \frac{{1 - {A_1}}}{2}$, where $a$ and $b$ are half the length in the long axis of the ellipsoidal magnetic particles and radius of the major circular cross section. When ${E_{\textrm{SPW}}}$ is parallel/ perpendicular to $H$, ${\chi _{\textrm{MF}}}$ increases/decreases with the increasing $H$.

Figure 1(a) shows the schematic diagram of the experimental device of the magnetic strength monitoring system. A broadband super-continuum laser source (BBS) is used to provide input spectrum with a wavelength range of 450-2400 nm. The reflection spectrum is measured in real time by optical spectrum analyzer (OSA). The fiber-optic magnetic field sensor is placed in the center of the electromagnet and as close as possible to the sensing probe of the Gauss meter. The magnetic strength is adjusted by the supply current and calibrated by Gauss meter.

The preparation process of the fiber-optic magnetic field sensor is shown in Fig. 1(b). The first is the preparation of metallic metasurface based on periodic square hole array. A layer of Au film was evaporated on a double-sided polished SiO₂ substrate. The electron beam lithography (EBL) method was used to prepare a metasurface on the Au film. The thickness of Au film obtained by the film thickness monitor is about 100 nm. The period and the side length of the square hole were set about 700 nm and 200 nm, respectively. A picture of the SiO₂ substrate on which the metasurface has been prepared on the Au film and a scanning electronic microscopy (SEM) image of the metasurface is shown in Fig. 1(c) and 1(d). The next step is to transfer the metasurface to the end face of the fiber. The epoxy coated on the end face of the MMF was pre-cured, the MMF core was aligned to the metasurface through an alignment system. The alignment system consists of 3D displacement platform and top&side view imaging monitoring system. The top view imaging system mainly monitors the central position of the MMF core and the metasurface, and the side view imaging system mainly monitors the distance between the MMF facet and the metasurface. After the epoxy was cured, the metasurface was firmly attached to the epoxy. By lifting the SiO₂ substrate, the metasurface remains on the epoxy. In this way, the transfer of the metasurface on the end face of the MMF is completed. The photographs of the plasmonic fiber-tip prepared and the diffraction patterns produced by the plasmonic fiber-tip are shown in Fig. 1(e) and 1(f). We inserted the plasmonic fiber-tip into a glass capillary filled with magnetic fluid, and sealed both ends of the capillary with glue to prevent the outflow and evaporation of magnetic fluid. The magnetic fluid (MFW, Shenran ferrofluid technological Co., Ltd) is water-based Fe₃O₄ nanoparticles.

We calculated the reflection spectra and the electric field distributions of the plasmonic fiber-tip in air by finite difference time domain (FDTD) method with the period@700 nm, Au thickness@100 nm, and filling factor@ 0.286. The simulated reflection spectrum is in good agreement with the experimental data, as can be seen in Fig. 2. This mismatch can be explained by considering the inevitable manufacturing defects of ideal structure, inclination of MMF facet and metasurface, and deviation of permittivity of the components between in numerical analysis and practical experiments.

Fig. 2. Reflection spectrum of the plasmonic fiber-tip based on numerical simulation and experiment.

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To understand the physical properties related to the spectral characteristics of plasmonic nanostructures in details, a near-field profile is needed. The simulated electric field distributions of the simulated reflection spectrum in Fig. 2 are extracted at the wavelengths of 621 nm, 638 nm, 713 nm, 730 nm, 765 nm, and 800 nm of the X -Z plane, the air/Au interface, and Au/epoxy interface from the Fig. 2, as shown in Figs. 3(a)–3(f). The mode of electric field distribution at 621 nm and 638 nm indicates that the Peak 1 and Dip 1 are caused by the coupling oscillation between the air / Au interface and Au / epoxy interface, as shown in Figs. 3(a) and 3(b), respectively. The extension of the electric field beyond the hole boundary of the Au / epoxy interface implies the out of plane characteristics of the oscillation. The in and out of plane oscillations at 713 nm, 730 nm, and 800 nm shows the localized surface plasmon excitation in Figs. 3(c), 3(d), and 3(f). At the wavelength of 765 nm, the strong intensity at the center of the hole confirms the direct transmission, as can be seen in Fig. 3(e).

Fig. 3. Electric field profiles at the central wavelengths of about (a) 621 nm, (b) 638 nm, (c) 713 nm, (d) 730 nm, (e) 765 nm, and (f) 800 nm of the simulated reflection spectrum (Fig. 2) in the X-Z plane, in up interface (air/Au), and in down interface (Au/epoxy), respectively.

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3. Experimental results and analysis

The RI of the magnetic fluid changes with the variation of the magnetic field. The wavelength of the resonance peaks/dips varies with the change of the RI of the magnetic fluid. Therefore, the RI sensitivity of the plasmonic fiber-tip ultimately determines the magnetic field measurement sensitivity. Firstly, we study the RI response of the plasmonic fiber-tip using different concentrations of NaCl solution. The reflection spectra of the plasmonic fiber-tip in air and NaCl solution@RI = 1.336 are shown in Fig. 4(a) inset. The resonance peaks/dips with central wavelengths of about 616 nm, 646nm, 756 nm, 770 nm, 793 nm, 811 nm, 833 nm, 855 nm, and 880 nm were selected as P1, D1, D2, P2, D3, P3, D4, P4, D5, respectively. The relationship between the central wavelength of these resonance peaks/dips and the environmental RI is shown in Fig. 4(b). It can be seen from the Fig. 4(b) that with the increase of the environmental RI, the central wavelength of these monitored resonance peaks/dips moves to a longer wavelength proportionally. Accordingly, the RI sensitivities of P1, D1, D2, P2, D3, P3, D4, P4, and D5 were determined to be 443 nm/RIU, 712 nm/RIU, 384 nm/RIU, 708 nm/RIU, 255 nm/RIU, 169 nm/RIU, 119 nm/RIU, 88 nm/RIU, and 199 nm/RIU, respectively. In the RI range of 1.336-1.351, compared with other types of fiber-optic sensors [34–37], the RI sensitivities of some resonance peaks or dips, such as D1 and P2, are satisfactory. The reason why the sensitivity of the D1 and P2 are much higher than others may be that the RI sensitivity of the fiber-optic SPR sensor based on the nanohole array depends not only on the period but also on the order of excited surface plasmon polariton modes [38].

Fig. 4. (a) Reflection spectra of the plasmonic fiber-tip under air and NaCl solution. (b) Wavelength response to the surrounding RI.

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In the absence of an external magnetic field, the magnetic particles are randomly distributed in the magnetic fluid, and the particles move due to Brownian motion and separate from each other due to repulsive force. In the case of the applied magnetic field intensity $H\textrm{ = }{H_c}$, where ${H_c}$ is the magnetic field intensity when magnetic chains are just formed, the magnetic particles tend to arrange along the direction of the applied magnetic field to form a magnetic chain. With the further increase of the magnetic field intensity, in the case of the magnetic field intensity ${H_s} > H > {H_c}$, where ${H_s}$ is the saturation magnetic field intensity, most of the particles form magnetic columns, and a small number of magnetic particles are still suspended in the magnetic fluid. When the external magnetic field intensity exceeds ${H_s}$, the suspended particles disappear and the solid-liquid separation occurs due to the aggregation of magnetic particles. The reversible change of magnetic fluid in the process of increasing and decreasing the magnetic field intensity leads to the change of its optical properties, especially the RI. The magnetic strength can be detected by monitoring the change of the center wavelength of the plasmonic fiber-tip resonant peaks/dips.

The reflection spectra of the plasmonic fiber-tip in air and magnetic fluid @0°, 0 mT are shown in Fig. 5(b). We selected the wavelength of the resonant dip and peak at 620 nm and 732 nm as D and P, respectively. The evolution of the reflection spectrum over a magnetic strength range of 0-20mT with a step of 2 mT at 0° and 90° are shown in Fig. 5(c). Under different magnetic field directions, the relationship between the magnetic strength and the respective wavelength D and P are approximately linear and monotonically, as can be seen in Fig. 5(d). The magnetic strength sensitivity of D/P were 0.375/0.532 nm/mT@ 0° with a linear correlation coefficient of 0.9978/0.99974 and -0.137/-0.203 nm/mT@ 90° with a linear correlation coefficient of 0.9971/0.9967, respectively. Tracking the shift of the minimum position of the central wavelength of the resonant peak/dip with high resolution is beneficial to reduce the measurement error and improve the linear correlation coefficient. The variation trend and the absolute value of the magnetic strength sensitivity for the same resonance peak or dip under different directions are obviously different. For the problem of absolute magnetic strength sensitivity inconsistency for the same peak/dip, it can be explained by the anisotropic nanoclusters around the metasurface in the magnetic field. It may be that when the magnetic field is parallel to the plane of the metasurface, the distribution of magnetic nanoparticles in the plane of the metasurface is not uniform. The distribution of these low and high concentration nanoparticles has different effect on the environmental RI of the metasurface, resulting in a relatively small change in the environmental RI [39]. Therefore, the center wavelength of the resonant peak and dip shifts slightly in a specific direction. In view of the inconsistent change trend, this may be because the variation trend of resonance peaks/dips depends on the RI variation trend of external magnetic fluid, and the RI variation trend of external magnetic fluid is related to the relative direction between the ${E_{\textrm{LSPR}}}$ and $H$, as can be seen in Eq. (2). Because the RI of the magnetic fluid is dependent on the direction of the magnetic field, the magnetic strength and magnetic field direction can be measured simultaneously [40,41]. Unfortunately, the response of the proposed magnetic field sensor in any two adjacent quadrants is mirror symmetrical with the remaining two quadrants, that is, it can only distinguish a limited axial direction and realize the pseudo-vector sensing of the magnetic field [42,43]. If two non-coaxial magnetic field sensors are installed, the two-dimensional vector measurement of magnetic field can be realized. The magnetic field sensing structure based on plasmonic fiber-tip and magnetic fluid can be used as one of the powerful candidates of pseudo-vector magnetic field sensor.

Fig. 5. (a) Microstructure of magnetic fluid under different magnetic field intensity. (b) Reflection spectra of the proposed plasmonic fiber-tip coated with either air or magnetic fluid @0°, 0 mT. (c) Reflection spectral response to magnetic strength under different magnetic strength and direction. (d) Relationship between the wavelength and magnetic strength in different magnetic field directions

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To compare and evaluate the performance of our fiber-optic magnetic field sensor, we analyzed the performance by comparison to the previously reported results based on the fiber structure of directional coupler [44], whispering-gallery modes resonance [45]^,, bitaper-based Mach-Zehnder interferometer [15], U-shaped fiber [39], asymmetric fiber taper [46], and Mach-Zehnder interferometer with microchannel [14]. The results on magnetic strength sensitivity and range are summarized in Fig. 6. Since the magnetic strength sensitivity is related to the magnetic field direction, we use the absolute value of the maximum magnetic strength sensitivity for comparison. In order to facilitate comparison, we used unified units(nm/mT).

Fig. 6. Sensitivity comparison of various types of magnetic field sensors.

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Obviously, the magnetic strength sensitivity of the proposed fiber-optic magnetic field sensor is 1.73, 2.26, 3.78, and 2.57 times that of the Ref. [15], Ref. [38], Ref. [39], and Ref. [40], respectively. Its magnetic strength sensitivity is 2.0% and 80.5% that of the Ref. [14] and Ref. [35], respectively. However, the Ref. [14] will not only reduce the mechanical strength of the device itself, but also bring potential risks for microcracks. It should be noted that the narrow dynamic range will further limit the application of the Ref. [14]. The Ref. [35] have large sensing size, which is difficult to meet the needs of practical applications for miniaturization with strict requirements. Increasing the concentration of magnetic fluid is beneficial to enhance the sensitivity of the proposed magnetic field sensor, but the increase of concentration will lead to the increase of spectral light loss [47,48]. The choice of magnetic fluid concentration needs compromise consideration. The proposed magnetic field sensor skillfully avoids the damage to the mechanical integrity of the optical fiber, and has a very small sensing area and satisfactory magnetic strength sensitivity. The comprehensive performance in subsequent practical application is expected.

The RI change of magnetic fluid caused by temperature fluctuation will lead to the variation of characteristic spectrum of magnetic field sensor. In order to solve the cross-sensitivity problem, multi-device methods and multi-peak methods are better solutions [49,50]. Considering the actual situation, it is a better solution to construct the binary first-order equation by using the characteristics that different resonance peaks/dips have different sensitivity to magnetic field and temperature. Reversibility and repeatability are important parameters to characterize the robustness of fiber-optic sensors. We show the relationship between the center wavelength of D/P @ 0° and the magnetic strength in three increase/decrease cycles over the magnetic strength range from 0-20 mT in the steps of 2 mT, as can be seen in Fig. 7. The slight inconsistency between the central wavelength of the D/P and the measured magnetic strength measurement curve by the Gauss meter may be caused by the measurement error. It may be improved by averaging the reflection spectrum to reduce the background noise and ameliorating the tracking accuracy of the resonance offset. In the absence of an external magnetic field, the reason for the movement of magnetic particles is Brownian motion, which is separated from each other by repulsive force. Therefore, vibration has little effect on the distribution of magnetic nanoparticles. When the external magnetic field intensity exceeds the saturation magnetic field intensity, the suspended magnetic particles disappear due to the aggregation, resulting in solid-liquid separation, and the vibration has little effect on the RI of magnetic fluid. In the case of the magnetic field intensity ${H_s} > H > {H_c}$, the effect of vibration on the distribution of magnetic nanoparticles, that is, the RI of magnetic fluid, will be the next research direction.

Fig. 7. Reversibility and repeatability of magnetic field sensor.

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It is worth emphasizing that the reduction of effective sensing size and overall device volume of magnetic field sensor will bring significant advantages in vivo, which can not only reduce the usage of magnetic field sensitizer, but also improve the combination efficiency of sensing area and sensitizer. It is worth pointed out that the sensitivity of the magnetic field sensor can be further improved by choosing the period of the nanohole arrays. The formant tracking can be designed to operate in fiber-optic telecommunication band with low-cost devices and higher sensitivity [38].

4. Conclusion

Therefore, the combination of plasmonic fiber-tip and magnetic fluid is a suitable scheme for magnetic field sensing. The spectral shape of the plasmonic fiber-tip can be controlled by adjusting the geometric parameters of the periodic nanostructure, which has excellent design flexibility. Compared with other structural sensitization-based magnetic field sensors, the proposed magnetic field fiber-optic sensor has higher robustness, most importantly, it can be extended to high-throughput manufacturing with appropriate bundle supports and equipped with high precision alignment system. As a multi-purpose plasma platform, this portable plasmonic fiber-tip has excellent miniaturization level and satisfactory RI sensitivity. These advantages make it a promising choice for nano-plasmon biological and chemical sensing applications.

Funding

National Natural Science Foundation of China (52075041, 61775019, 61861136010, 62105020, 92050117); Beijing Outstanding Young Scientist Program (BJJWZYJH01201910007022); Beijing Municipal Natural Science Foundation (JQ20015); Fok Ying Tung Education Foundation (161009); China Postdoctoral Science Foundation (2020M680371); Guangxi Key Laboratory of Optoelectroric Information Processing (GD21201).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Compact magnetic field sensor based on plasmonic fiber-tip

Abstract

1. Introduction

2. Working principle and fabrication

3. Experimental results and analysis

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (7)

Equations (2)

Optics Express