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Abstract
Magnetic field detection exploiting nitrogen-vacancy (NV) centers in diamond has gained increasing attention and development in recent years. Combining diamond NV centers to optical fibers provides a way for achieving magnetic sensors with high integration and portability. Meanwhile, new methods or techniques are urgently desired to improve the detection sensitivity of such sensors. In this paper, we present an optical-fiber magnetic sensor based on the NV ensemble in diamond, and employ the well-designed magnetic flux concentrators to enhance the sensitivity up to 12 pT/Hz1/2, an outstanding level among the diamond-integrated optical-fiber magnetic sensors. The dependence of sensitivity on the key parameters including the size and gap width of the concentrators are investigated by simulations and experiments, based on which the predictions on the further enhancement of sensitivity to fT level are presented.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Benefiting from the unique quantum properties of nitrogen-vacancy (NV) centers in diamond, diamond-based quantum sensors have gained great attentions and rapid development in recent years [1,2]. Taking advantage of the optically detected magnetic resonance (ODMR) method, the detection to various physical parameters such as temperature, magnetic field, and pressure that can affect the quantum state of NV centers can be easily implemented [3,4]. Among them, the magnetic detection has received the most research, and numerous sensors with various schemes have been proposed [5]. For the most of previously-reported sensors, the excitation light was focused on diamonds by free light coupling through microscopes or lenses, and the fluorescence emitted from diamonds was collected through the same optical elements [6], which results in a poor integration and thus portability.
Recent works have demonstrated significant progress in portability through integrating diamond with optical fibers [7–12], and different integration forms have been proposed accordingly. For the nanoscale diamonds (termed as nanodiamonds), they were physically deposited on the surface of a tapered single-mode fiber [13] or the end face of a multi-mode fiber [14], or directly-doped in a glass rod to be drawn as magnetically-sensitive optical fiber [15]. However, due to the limited number of NV centers in nanodiamonds and low fluorescence collection rate, the sensitivity of this type of sensors is always limited at the level of µT/Hz1/2. Micro or millimeter size diamonds, which contain a high density of NV centers (termed as NV ensemble) and are usually adhered on the end face of fiber using optical glue, can provide a stronger fluorescence signal thus an improvement of sensitivity to nT/Hz1/2 [16,17]. Moreover, R. Patel et.al employed lenses to reduce the optical coupling loss between fiber and diamond, enhancing the sensitivity for a fiber-coupled diamond magnetometer to the sub-nanotesla level (310 pT/Hz1/2) for the first time [18]. S. Zhang et.al recently used the pulsed ODMR scheme and coated reflective film on the diamond surfaces to improve the fluorescence collection, achieving the sensitivity of 50 pT/Hz1/2, the best one among the reported fiber-based diamond magnetometers so far [19]. Though the sensitivity at sub-pT level had been obtained by using flux concentrators [20,21], the sensors still perform as a poor integration and portability due to the employed free light coupling method. Therefore, new methods or techniques are still needed to improve the sensitivity of fiber-based sensors to detect a weaker magnetic field, which plays a key role in the application fields such as ocean monitoring, resource exploration, and magnetocardiogram acquisition.
In this paper, we present a sensitivity-enhanced fiber-coupled diamond magnetic sensor by introducing a pair of high permeability cone-shaped flux concentrators. The sensor is constructed by adhering a micron-size diamond containing NV ensemble on the end face of a tapered multi-mode fiber, and clamping the diamond by the concentrators. The structural parameters of the concentrators on the detection sensitivity were well studied by simulations and experiments, and a high sensitivity of 12 pT/Hz1/2 @ 1 Hz was achieved experimentally. The discussions on the sensor optimization and the consequent sensitivity improvement were also presented.
2. Structure and principles
The fiber magnetic sensor employed in our work is composed of a tapered fiber tip integrated with a micron-size diamond, as shown in Fig. 1(a). Compared to a normal fiber tip, the tapered tip can significantly improve the light excitation and collection efficiency to the fluorescence from diamond [12]. In experiments, a step index profile multi-mode fiber with core/cladding diameter of 105/125 µm was tapered to reduce the cladding diameter to ∼50 µm by hydrogen-oxygen flame heating method. Then, the tapered fiber was cut at the waist to obtain a fiber tip. At the same time, a micron-size diamond particle, which has a close size (75 × 120 µm) with fiber tip diameter and contains a high density of NV centers (∼10 ppm provided from the manufacturer), was adhered on the tip using optical glue. To enhance the magnetic detection sensitivity, the diamond was clamped by a pair of cone-shaped magnetic flux concentrators (MFCs), which can collect the environmental flux from a larger area and concentrate it on the diamond [21]. The concentrators are made from permalloy (1J79) with a high relative permeability at level of 104. In our experiments, the tip diameter of concentrator was fixed at 0.8 mm while the base diameter, which was equal to the height, was varied to study its influence on sensitivity.
Fig. 1. (a) Schematic diagram of the fiber magnetic sensor based on diamond clamped by a pair of concentrators having the same parameters. BD, base diameter; TD, tip diameter; GD, gap width; MFC, magnetic flux concentrator. BD = Height in this work. Inset presents the microscope image of the fabricated sensor head. (b) Spin dependent polarization and relaxation dynamics of an NV center.
Magnetic detection using an NV center is based on its unique energy-level structure and magnetic-sensitive electronic spin states as shown in Fig. 1(b). The NV centers are featured by a ground electronic spin triplet states, namely ms = 0 and ms=±1, and a simplified Hamiltonian for the ground state of an NV center under magnetic field B can read as
where the first item means the zero-field split between ms = 0 and ms=±1, and D = 2.87 GHz depending on temperature; the second item present the magnetic field related Zeeman split, and γe = 28 GHz/T is the electron spin gyromagnetic ratio, and S = (Sx, Sy, Sz) is the electron spin vector of NV center. A green laser (usually at 532 nm) can polarize NV centers to the ms = 0, and the states between ms = 0 and ms=±1 can be further manipulated by applying a microwave field. When an external magnetic field B is applied to the NV center, a split occurs between ms=+1 and ms = -1 due to the Zeeman Effect. The split degree $\Delta$υ is proportional to the magnetic field projected along the NV axis BNV, and it can be obtained by calculating the eigenvalues of Hamiltonian presented by Eq. (1), and finally:The spin-related fluorescence intensity of the NV centers allows us to accurately measure the $\Delta$υ using ODMR method thus obtaining BNV. If MFCs were additionally applied on the diamond as shown in Fig. 1(a), the magnetic field strength experienced by NV centers will be enhanced by a factor of G, whose value is determined by the MFCs properties including structure parameters, material, etc. As a result, the BNV should be replaced with G·BNV in (2), suggesting the magnetic response thus the detection sensitivity of NV centers is improved by G times.
We first theoretically study the magnetic enhancement by MFCs based on finite element method (COMSOL Multiphysics). Simulated results [ Fig. 2(a) and 2(b)] suggest that the application of concentrators results in a significant enhancement of magnetic flux density in the gap region, where the diamond is placed. As shown in Fig. 2(c), the enhancement factor G, which is calculated by the ratio of the maximum flux densities at the gap region with and without concentrators, improves as the increase of the base diameter of concentrator, and it could reach 2500 if the base diameter is increased to 200 mm for a given gap width of 100 µm. On the contrary, the enhancement factor shows the extreme decrease as the increase of gap width [Fig. 2(d)]. Therefore, choosing a larger base diameter and a smaller gap width for the concentrators is beneficial to achieve a higher sensitivity. However, a large base diameter means a big size of the magnetometer thus a poor spatial resolution, which should be taken into account in sensor design. The largest base diameter used in our experiments is 30 mm, corresponding to a magnetic enhancement of 373, which is still larger than the ∼250 reported in [21].
Fig. 2. (a) Simulated two-dimensional magnetic flux density distribution for a pair of magnetic flux concentrators with the identical base diameter and separated by 100 µm gap width. (b) One-dimensional data along the white dash line in (a) when the base diameter is set as 30, 20, and 10 mm, respectively. (c) Enhancement factors for the concentrators with different base diameters while keeping the gap as 100 µm. (d) Dependence of enhancement factor on the gap between two concentrators with the identical base diameters of 30, 20, and 10 mm, respectively.
3. Experiments and discussions
According to the schematic diagram shown in Fig. 3, a test system based on continuous-wave ODMR method was built. The 532 nm laser (MGL-FN-532 nm, CNI Optoelectronics Tech. Co.) is coupled to excite the diamond adhered on fiber tip through a fiber circulator (Thorlabs WMC3L1S). The red fluorescent signal is first purified by a 600 nm long-pass filter (Thorlabs FELH0600) and then collected by a photodetector (Thorlabs APD410A/M). The microwave, generated from a microwave source (Rohde Schwarz SMB 100A) and amplified through a microwave power amplifier (ZHL-16W-43, mini-circuits), is exerted on the diamond by a homemade microwave antenna. The antenna is implemented by winding a copper wire (0.1 mm diameter) around the diamond a cycle. To prevent the damage from the returned microwave, an isolator is employed before the amplifier and the antenna is terminated with a 50 ohm matched impedance. The lock-in amplification technique is used to improve the test speed and signal to noise ratio. Therefore, the output microwave is frequency modulated, and a synchronized modulation frequency signal provided by the microwave source was sent to the reference channel of a lock-in amplifier (LIA, Sine Scientific Instruments OE1022D), whose signal channel is connected to photodetector. During measurements, the same parameters, including the MW scan range (2820-2920 MHz), scan step (0.5 MHz), dwell time (500 ms), frequency modulation deviation (2 MHz), modulation frequency (500 Hz), lock-in time constant (100 ms), filter roll-off (12 dB/oct), and the gain of the photodetector, etc., were chosen for all the probes.
According to the parameters used in simulations, three pairs of MFCs, having the same tip diameter of 0.8 mm but different base diameters of 30, 20, and 10 mm, were fabricated by mechanical processing. The MFCs were applied to the sensor, and both of them were placed in a variable magnetic environment, which was provided by a Helmholtz coil. The applied magnetic field direction is along with the central axis of the MFCs, namely perpendicular to the longitudinal axis of fiber, as shown in Fig. 1(a).
Measured lock-in ODMR (LI-ODMR) spectra of the sensor under varied magnetic fields were presented in Fig. 4(a). All the spectra feature two positive and negative peaks, resulting in three zero-crossing frequencies termed as central frequency ν0 and resonant frequencies ν±, respectively. The ν0 represents the zero-field splitting and is predominantly dependent on temperature following a linear relationship of -74 kHz/K [22]. At ν±, the resonance that occurs between the applied MW and the energy transition of ms = 0↔ms=±1 reduces the fluorescence emitted from diamond. As the increase of magnetic field, ν0 remains unchanged while ν± shifting to the opposite directions, i.e. the spectra are broadened with ν0 as the center, which corresponds to the magnetic-induced energy splitting between ms=+1 and ms = -1.
Fig. 4. (a) Measured LI-ODMR spectra of the sensor under varied magnetic field change for the cases using different base diameters MFCs. (b) Frequency change of (ν+-ν-) as a function of magnetic field variation. Rνis obtained by carrying out the linearly fitting on the data within the the whole test range. (c) Magnetic field dependence of lock-in signal at a specific frequency that possesses the maximum change. Rsis obtained by carrying out the linearly fitting on the data within the whole test range. The data for the case without using MFCs are not included in (b) and (c) because the huge difference in test range.
Figure 4(a) also indicates that using MFCs can significantly improve the sensor’s magnetic response, which is defined as Rν=Δ(ν+-ν-)/ΔB namely the unit magnetic field change induced change amount of resonant frequency. The frequency change of (ν+-ν-) as a function of magnetic field variation and the corresponding Rν are presented in Fig. 4(b). The Rν was improved as the increase of the base diameter of MFCs, and it reached 882, 2259 and 2840 GHz/T when the base diameter was 10, 20, and 30 mm, respectively. Compared to the Rνof 4.8 GHz/T in the case without MFCs, the magnetic responsivity of sensor showed a significant enhancement when using MFCs.
In this work, the detection sensitivity of the sensor was assessed in a full experimental manner as presented in Ref [20]. First, the magneto-electric coefficient Rs was obtained by linearly fitting the data of lock-in signal depending on magnetic field within the whole test range at a specific frequency that possesses the maximum change, and the results are presented in Fig. 4(c). As well as Rν, Rs also exhibits noticeable improvement with the increase of MFCs base diameter. The Rs increases to 21609 V/T when using 30 mm diameter MFCs. Then, the magnetic noise in time domain BN(t) was converted from electrical noise SN(t) according to BN(t)=SN(t)/Rs, where SN(t) was obtained by continuously recording the lock-in signal using the sampling rate of 1 kHz for 60 s under the off-resonance condition, and it had little variation using different base diameter MFCs. Based on Welch’s method, the magnetic noise spectral density was obtained, and the value at 1 Hz was taken as the sensitivity of the sensor. As shown in Fig. 5, the whole magnetic noise spectrum lowers as the the increase of MFCs base diameter, and the sensitivity has been significantly improved by using MFCs. A sensitivity as high as 0.012 nT/Hz1/2 has been achieved under the 30 mm diameter MFCs. This shows an improvement of two orders of magnitude when compared to the case without MFCs.
Fig. 5. Magnetic noise spectral density of the sensor with or without the applications of different sizes MFCs.
We compared the reported fiber magnetic sensors based on diamond with our work in Table 1. Employing a bulk or micro-size diamond is beneficial to obtain a higher sensitivity compared to nanodiamond, because it contains a larger amount of NV centers thus providing a stronger fluorescence signal. We significantly improved the sensitivity to an outstanding level through the magnetic flux enhancement scheme in this work as shown in Table 1. In addition, the further improvement of sensitivity can be expected when considering the following sensitivity estimation expression [20]:
Table 1. Comparisons of the reported fiber magnetic sensors integrated with diamond. (NDs, nandodiamonds; MD, micro-size diamond; BD, bulk diamond; Deposition, depositing NDs on the fiber surface; Adhesion, adhering MD or BD on the end face of fiber; Doping, doping MDs or NDs in fiber)
4. Conclusion
In this paper, an optical fiber magnetic field sensor based on diamond NV centers was studied. Moreover, a pair of cone-shaped MFCs were introduced to enhance the sensitivity by two orders of magnitude. The key parameters (including the MFC base diameter and gap width) that affect the sensitivity were investigated by simulations. Results indicate that a larger base diameter and a smaller gap are beneficial to obtain a higher sensitivity, which provides basic for sensor optimization. Corresponding sensors were fabricated and tested, and the results agreed well with the simulated ones. Employing the MFCs with tip and base diameters of 0.8 and 30 mm, a sensitivity as high as 12 pT/Hz1/2 was achieved experimentally. This sensitivity is outstanding among the diamond-based fiber magnetic sensors. The further improvement can be expected by taking the measures such as optimizing the tapered fiber and MFCs, adopting common mode rejection scheme, and exciting hyperfine split transitions. The sensor presented herein hold the promising application potentials in various fields such as ocean monitoring, resource exploration, and magnetocardiogram acquisition.
Funding
National Natural Science Foundation of China (62275109, 61805108, 61904067, 62075088, 62175094); Basic and Applied Basic Research Foundation of Guangdong Province (2020A1515011498, 2022A1515010272, 2022A1515011671, 2022A1515140055); Basic and Applied Basic Research Foundation of Guangzhou (202102020758, 202201010553).
Disclosures
The authors declare no conflicts of interest.
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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