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Improved temperature stability of a fiber Sagnac-like detection system for atomic magnetometers

Jingxin Zhang, Xuejing Liu, Yue Niu, Lianjun Ma, Kun Wang, and Ming Ding

Open Access Open Access

Abstract

A novel fiber Sagnac-like detection system has unique competitive advantages for detecting atomic spin precession in atomic magnetometers. Unfortunately, its operating stability is severely limited by temperature fluctuations. In this paper, we describe a new approach to improve the temperature stability by using the ratio signal as the output instead of the conventional fundamental component. This method can effectively counteract the temperature-caused fluctuations in both light intensity and scale factor of photodetector. For a temperature range from 20°C to 40°C, a relative fluctuation of the ratio output signal of 0.97% was achieved, which was 17.4 times better than the fundamental component output. Moreover, no additional equipment and complex compensation algorithms are required during this process. It is a generic method that can also be applied to improve the stability of other detection schemes used in atomic magnetometers.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Ultra-sensitive atomic magnetometers find its applications in a wide range of areas such as space exploration [1], fundamental physics experiments [2], and, in particular, magnetoencephalography (MEG) [3]. MEG is a research hotspot that guides the path for progress in neurosurgery in the 21st century [4]. Much work has been done to accelerate the development of MEGs [5–7]. To map the brain’s magnetic field, typically, many small sensors need to be installed in a helmet [8], which makes it desirable to reduce the size (volume) of the sensors. Therefore, several miniaturized methods were designed, especially the fiber Sagnac-like interferometer for the detection of atomic spin precession in atomic magnetometers [9]. Based on the Sagnac interference principle, the system measures the spin precession of atoms using the interference of reflected light in fiber. Due to the excellent flexibility of the optical fiber, the alkali-vapor cell can be easily separated from other optoelectronic elements, minimizing the volume of bulky optical components, achieving remote detection, and enhancing the spatial resolution of the MEG probe header [9]. The use of optical fiber-based technologies can also enable magnetometers to be more compact and easier to assemble [10]. Furthermore, the device has a reciprocal optical structure that counteracts phase drift during fiber transmission, thereby greatly improving the stability of the detection system. Compared with the common detection schemes in atomic magnetometers such as Faraday modulation and Photoelastic modulation, fiber Sagnac-like detection system has a lower drift rate [9]. In short, the system provides a new approach for the development of magnetoencephalography with its unique flexibility, miniaturization and stability advantages.

However, the light source and several fiber devices are sensitive to ambient temperature, which results in poor thermal stability of fiber Sagnac-like detection system [11–14]. The experimental results show that the output-signal amplitude of the system drifts significantly with temperature. In other words, the problem of temperature stability is a key obstacle to its application, and needs to be solved urgently. There are various studies that focus on improving the stability of the fiber detection system. Dong et al. used a ultralow thermal sensitivity material Photonic Crystal Fiber (PCF) to improve the temperature performance of the optical fiber [15]. Although this approach has enabled some improvement, the use of PCF will increase the cost significantly, and it will cause a large transmission loss when splicing with ordinary optical fiber. In addition, Chen et al. designed and optimized a multi-function integrated circuit to improve the temperature stability of Superluminescent Diodes (SLDs) and other fiber devices [16]. However, the required control algorithm and circuit design is complex. Other approaches like modification of Radial Basis Function Artificial Neural Network (RBF ANN)-based compensation models also contribute to the improvement in temperature stability [17]. In most cases, these stabilization methods require additional devices and complex programming algorithms.

In this paper, we propose a novel method to improve the temperature stability, which is based on the specificity of the output signal of the fiber Sagnac-like detection system. According to fiber Sagnac interference theory, by performing ratio processing on the fundamental component and the second harmonic component of the output signal, the temperature-caused variation of both the light intensity and the scale factor of photodetector (PD) can be offset. This approach can significantly improve the temperature stability of the fiber Sagnac-like detection system without using costly materials and complex control algorithms.

2. Principle

For atomic magnetometer, external magnetic field is obtained by detecting the orientation of the atomic spin polarization [18–20]. The conventional detection method is to calculate the atomic spin precession angle by measuring the optical rotation angle of the linearly polarized probe beam [21–23]. The fiber Sagnac-like interferometer uses a novel detection method [9], and the optical schematic of that is illustrated as Fig. 1.

 figure: Fig. 1.

Fig. 1. Schematic of the fiber Sagnac-like detection system in the atomic magnetometer. Pump laser: external cavity diode laser; Col: collimator; P: linear polarizer; λ/4: quarter waveplate; Cell: K atomic vapor cell; R: reflector; Shields: magnetic shielding cylinder; Oven: atomic vapor cell oven; SLD: superluminescent diode; Cir: circulator; Polarizer: fiber linear polarizer; PM: phase modulator; PMF Coil: polarization-maintaining fiber coil; PD: photodetector; Lock-in Amp: lock-in amplifier; DAQ: data acquisition system. The dashed box marks the thermostat for temperature tests of the internal fiber components.

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Pump laser is required to polarize atomic alkali-vapor in the cell to spin exchange relaxation free (SERF) state before the detection system operates [18,24]. After the collimator (Col), the pump light becomes a spatial beam, which is then circularly polarized by the linear polarizer (P) and the quarter wave plate (λ/4) to pump the Potassium (K) atomic vapor in the cell (Cell). The superluminescent diode (SLD) light source is directed by a circulator (Cir) to fiber linear polarizer (Polarizer), which produces 45-degree linear-polarized light E with respect to the principal axes of the phase modulator (PM). Thus, the linear-polarized light could be decomposed into the principal axes of the PM with the same intensity component. These two orthogonal polarized lights, after decomposition, are defined as E1 and E2, which are modulated by the phase modulations ϕ1(t$\textrm{ - }$τ) and ϕ2(t$\textrm{ - }$τ), respectively, through PM at time t$\textrm{ - }$τ, where τ represents the transmission time of the light throughout the optical path. Then, the two beams transmit along the fast and slow axes of a polarization-maintaining fiber (PMF), which produces the phase delays ϕf and ϕs, respectively. After the collimator, they are converted to left-circularly-polarized light and right-circularly-polarized light, by the quarter waveplate. After passing through the K atomic vapor cell, the left- and right-circularly-polarized light generate a phase difference Δϕ, which can be denoted as spin precession angle θ according to Δϕ=2θ [19]. After being reflected by the reflector (R), two circularly-polarized lights switch the polarization between left and right, and transform into linear-polarized lights again, after passing through the quarter waveplate. After that, two orthogonal polarized lights propagate back along the same optical path, to produce the phase delays ϕf and ϕs that simply cancel out with the phase delays of the forward-light path in the PMF and the phase modulation of ϕ1(t) and ϕ2(t) through PM at time t. The E1 and E2 of the reverse optical path interfere in front of the linear polarizer, and the interference light is finally detected by PD after the circulator. Through demodulation of the lock-in amplifier, the spin-precession angle θ can be obtained.

As the ambient temperature fluctuates, both the output light intensity of the light source and the transmission loss of some fiber-optic components may change, which leads to instability of the output signal [11–14]. This means the temperature stability of fiber Sagnac-like detection system is unsatisfactory.

The output of the detection system as detected by PD can be expressed as [9]:

$${I_{out}} = \frac{{K{I_0}}}{2}\{{1 + \cos [4\theta - \Delta \phi (t) + \Delta \phi (t - \tau )]} \}$$
Where I0 is the intensity of input probe light, K is the scale factor of PD and Δϕ(t)$\textrm{ = }$ϕ1(t)$\textrm{ - }$ϕ2(t), Δϕ(t$\textrm{ - }$τ)$\textrm{ = }$ϕ1(t$\textrm{ - }$τ)$\textrm{ - }$ϕ2(t$\textrm{ - }$τ). Among them, Δϕ(t) and Δϕ(t$\textrm{ - }$τ) are the phase delays between E1 and E2 produced by PM at different moments. By using the small angle approximation, Eq. (1) can be simplified to
$${I_{out}} = K{I_0}\left[ {1 - {{\sin }^2}\left( {\frac{{4\theta - \Delta \phi (t) + \Delta \phi (t - \tau )}}{2}} \right)} \right] = K{I_0} - \frac{{K{I_0}}}{4}{[{4\theta - \Delta \phi (t) + \Delta \phi (t - \tau )} ]^2}$$
Where Δϕ(t)$= $asinωt, Δϕ(t$\textrm{ - }$τ)$= $asinω(t$\textrm{ - }$τ), and a is the amplitude of the differential phase modulation of PM. It can be written as:
$$\begin{array}{l} {I_{out}} = K{I_0} - \frac{{K{I_0}}}{4}\left[ {16{\theta^2} + 2{a^2}{{\sin }^2}\left( {\frac{{\omega \tau }}{2}} \right) + 16\theta a\sin \left( {\frac{{\omega \tau }}{2}} \right)\sin \omega \left( {t - \frac{\tau }{2}} \right)} \right.\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} - \left. {2{a^2}{{\sin }^2}\left( {\frac{{\omega \tau }}{2}} \right)\cos 2\omega \left( {t - \frac{\tau }{2}} \right)} \right]{\kern 1pt} \end{array}$$
To reduce the influence of backscatter in the optical fiber [25], when the phase modulator works at the eigenfrequency ω$= $π/τ of the fiber coil, the backscatter light passes through the phase modulator twice, and is modulated by two phases with the same amplitude and opposite direction, so that the backscattering noise can be suppressed. Then the fundamental component of the output signal can be derived as:
$${I_\omega } = 4K{I_0}a\theta$$
The second harmonic component is
$${I_{2\omega }} = \frac{1}{2}K{I_0}{a^2}$$

The conventional approach generally used the fundamental component of the demodulated signal as the output signal. Equation (4) shows that the fundamental component is affected by the scale factor K of PD, the light intensity I0, and the modulation amplitude a of the PM. Because both of them fluctuate with ambient temperature, these leads to poor temperature stability of the system. The ratio of the fundamental component to the second harmonic component can be expressed as:

$$\frac{{{I_\omega }}}{{{I_{2\omega }}}} = \frac{{8\theta }}{a}$$
Where the atomic spin precession angle θ still remains. If the Eq. (6) is used as the output of the fiber Sagnac-like detection system, the effect of I0 and K on the output signal is cancelled out, which improves the temperature stability of this system significantly. In addition, the above expressions of the demodulated signal are similar in other modulation detection schemes in atomic magnetometers [19], such as Faraday modulation detection and Photoelastic Modulator (PEM) detection. Therefore, this method may be applicable for these detection systems to improve their performance.

3. Experimental setup

The experimental setup is shown in Fig. 1. The method to improve the temperature stability of the detection system is realized by demodulating the reverse optical signal and processing the ratio of the fundamental component and the second harmonic component.

The external cavity diode laser (ECDL) (6910, New Focus, USA), with a center wavelength of 770 nm (D1 line of K atom) and output power of 9 mW, was used as pump light. After passing through the collimator (PAF-X-15-PC-B, Thorlabs), linear polarizer (GT10-B, Thorlabs) and quarter waveplate (WPQ05M-780, Thorlabs), the output light was circularly polarized to pump K atomic vapor in the glass cell to the SERF state. The glass cell contained a droplet of Potassium metal, 3 atm buffer-gas 4He and 60 Torr quenching-gas N2, and an AC current heater pasted outside the oven heated the cell to 473 K.

To reduce backscattering noise in the optical fiber, a Superluminescent Diode (SLD-331, Superlum) was selected as probe-light source [9,14], which has the output power of 22 mW, a wavelength range from 753 nm to 855 nm, and a frequency bandwidth of 43 THz. The light beam traveled through the fiber, passed through a circulator (VCIR-3-766-L-10-FA, Ascentta) with an isolation of 28 dB, before it was linearly-polarized by a fiber polarizer (LPT-780) with an extinction ratio of 28 dB. The polarization state of the probe light was modulated by the fiber lithium niobate electro-optic phase modulator (PM-0S5-10-PFU- 766/795, EOSpace Inc, USA), with 7.8 V @106 kHz half-wave voltage. The modulation signal was provided by the sinusoidal signal output at 106 kHz of the Lock-in Amplifier (MFLI, Zurich Instruments). Subsequently, the probe light was transmitted via a 500-meter-long polarization-maintaining fiber (PM630-HP, Nufern) coil, with a high birefringence of 3.5 × 10−4@630 nm. The collimator (PAF-X-15-PC-B, Thorlabs) converted the optical light from the fiber into spatial parallel light, with a diameter of 3 mm. After passing through the glass cell, the probe beam was reflected by the reflector (BB1-E03, Thorlabs) and passed through the cell again. As a result, the signal of the atomic polarization state doubled, and the reflected light returned along the original light-path. Finally, the output from the circulator was detected by the PD (DET025A, Thorlabs) with a peak response of 0.46 A/W @740 nm. Using the lock-in amplifier, both the fundamental component and the second harmonic component of the atomic spin precession signal were obtained, simultaneously, by demodulation at 106kHz, and both of them were collected by the DAQ system (USB-6366, National Instruments) and fed into the computer for ratio processing.

In the experiment, independent temperature tests were done for each part of the fiber Sganac-like detection system. Then the whole detection system was placed inside a thermostat to perform the overall test as shown in Fig. 1. To verify the temperature-stability improvement method, a normal operating temperature range for the detection system was selected for testing. As the temperature increased slowly from 20°C to 40°C, we observed the attenuation trends of both the fundamental component and the second harmonic component, and then compared the temperature stability of the fundamental-frequency output signal and the ratio output signal.

4. Results and discussion

In the independent temperature test, the output of each experimental device in the dashed box in Fig. 1 was tested separately, with ambient temperature ranging from 20°C to 40°C. The experimental data were normalized by average value as shown in Fig. 2. The birefringence and thermal expansion coefficient of the lithium niobate crystal in the phase modulator (PM) were both affected by temperature [26], and experimental data indicate that the modulation amplitude has a slight upward-trend (a). Besides, due to the temperature sensitivity of the SLD light source [13,16], the output-light intensity decreased with increased temperature (b). This indicates that the temperature control module of SLD is inefficient. In addition, the output of the PD also damped with increasing temperature (c), as the output-wavelength range of the SLD light source drifted with temperature, deviating from the maximum spectral response curve of the PD. Additionally, as temperature affected the loss of fiber transmission, the output of the fiber coil was affected by the ambient temperature (d). Especially, in the temperature test of the fiber polarizer, the output light power decayed significantly by 37.8% (e). The SLD light source emitted partial linearly-polarized light, which was transmitted to the polarizer through the PMF. The birefringence of the PMF changed with temperature [15], which gave rise to the drift of polarization state and the coupling-loss of the fiber polarizer. Comparatively speaking, the coupling loss of the fiber polarizer is a major contributor to the poor temperature stability of the fiber Sagnac-like detection system.

 figure: Fig. 2.

Fig. 2. Independent temperature-stability test for each component of the fiber Sagnac-like detection system. These curves reflect the variation trends with temperature of the modulation amplitude of the PM (a), the output-light intensity of the SLD source (b), the scale factor of PD (c), the output power of the fiber coil (d), and the coupling loss of the fiber polarizer (e), respectively. All experimental data were normalized by average value. The error bars are defined by one standard deviation of uncertainty.

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In the temperature test of the entire detection system, the tendencies of the fundamental component and the second harmonic component to change with temperature, from 20°C to 40°C, are shown in Fig. 3. Their amplitudes drifted drastically, and the relative fluctuations (defined as the percentage of the standard deviation divided by the mean value) were 16.86% (the fundamental component) and 14.12% (the second harmonic component) respectively. These indicate that the output signals were clearly affected by temperature. In addition, the decay trends of both the fundamental component (from 43 mV to 24.6 mV, attenuation of 42.8%) and the second harmonic component (from 1.8 V to 1.05 V, attenuation of 41.7%) were very similar. However, it can be seen from Eq. (4) and Eq. (5) that the fundamental component is proportional to a, and the second harmonic component is proportional to the square of a. Thus, we can draw the conclusion that it was mainly the change of I0 and K that caused the attenuation of the signal, rather than a. By the ratio of the fundamental component to the second harmonic component, the I0 and K can be cancelled out as the Eq. (6), which can improve the temperature stability of the output signal substantially.

 figure: Fig. 3.

Fig. 3. The attenuation trend of the fundamental component and the second harmonic component as a function of ambient temperature from 20°C to 40°C. The black line and the red line denote the fundamental component and the second harmonic component, respectively. The error bars are defined by one standard deviation of uncertainty.

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As shown in Fig. 4, compared with the conventional output signal of a fiber Sagnac-like detection system, i.e. the fundamental component from Eq. (4), the temperature stability of the ratio output signal improved significantly. The ratio signal shows no obvious attenuation trend (from 22.9 to 22), and the relative fluctuation was 0.97%, which is 17.4 times better than the fundamental component signal (16.86%). By using the ratio signal as the output, the temperature stability of fiber Sagnac-like detection system can be improved substantially.

 figure: Fig. 4.

Fig. 4. Temperature stability comparison of the fundamental component signal and the ratio output signal of the fiber Sagnac-like detection system. The black line denotes the fundamental component of the demodulated signal, while the red line indicates the ratio output signal of the fundamental component to the second harmonic component. The error bars are defined by one standard deviation of uncertainty.

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After stability optimization, according to Eq. (6), the remaining fluctuation of the ratio output signal with temperature may be due to both the drift of the modulation coefficient a of the PM and the phase difference of the non-reciprocity of the optical path. The stability of the fiber Sagnac-like detection system may be further improved in the future via structural design optimization of PM and fiber coil.

5. Conclusion

In this paper, we demonstrated a new method to improve temperature stability of the fiber Sagnac-like detection system. Through the ratio processing of the fundamental component to the second harmonic component, the temperature-caused fluctuations in both light intensity and scale factor of PD can be offset, thereby greatly improving the temperature stability of the detection system. Using the ratio signal instead of the fundamental component signal as the system output, the relative fluctuation was reduced from 16.86% to 0.97% significantly. This approach does not require additional equipment and complex compensation algorithms. Besides, it has a potential impact on improving the stability of other modulation detection systems such as Faraday modulation detection and Photoelastic Modulator (PEM) detection.

Funding

National Key Research and Development Program of China (2017YFB0503100); Natural Science Foundation of Beijing Municipality (4191002).

Disclosures

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

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Figures (4)
Fig. 1.
Fig. 1. Schematic of the fiber Sagnac-like detection system in the atomic magnetometer. Pump laser: external cavity diode laser; Col: collimator; P: linear polarizer; λ/4: quarter waveplate; Cell: K atomic vapor cell; R: reflector; Shields: magnetic shielding cylinder; Oven: atomic vapor cell oven; SLD: superluminescent diode; Cir: circulator; Polarizer: fiber linear polarizer; PM: phase modulator; PMF Coil: polarization-maintaining fiber coil; PD: photodetector; Lock-in Amp: lock-in amplifier; DAQ: data acquisition system. The dashed box marks the thermostat for temperature tests of the internal fiber components.

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Fig. 2.
Fig. 2. Independent temperature-stability test for each component of the fiber Sagnac-like detection system. These curves reflect the variation trends with temperature of the modulation amplitude of the PM (a), the output-light intensity of the SLD source (b), the scale factor of PD (c), the output power of the fiber coil (d), and the coupling loss of the fiber polarizer (e), respectively. All experimental data were normalized by average value. The error bars are defined by one standard deviation of uncertainty.

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Fig. 3.
Fig. 3. The attenuation trend of the fundamental component and the second harmonic component as a function of ambient temperature from 20°C to 40°C. The black line and the red line denote the fundamental component and the second harmonic component, respectively. The error bars are defined by one standard deviation of uncertainty.

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Fig. 4.
Fig. 4. Temperature stability comparison of the fundamental component signal and the ratio output signal of the fiber Sagnac-like detection system. The black line denotes the fundamental component of the demodulated signal, while the red line indicates the ratio output signal of the fundamental component to the second harmonic component. The error bars are defined by one standard deviation of uncertainty.

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Equations (6)

Equations on this page are rendered with MathJax. Learn more.

I o u t = K I 0 2 { 1 + cos ⁡ [ 4 θ − Δ ϕ ( t ) + Δ ϕ ( t − τ ) ] }
I o u t = K I 0 [ 1 − sin 2 ( 4 θ − Δ ϕ ( t ) + Δ ϕ ( t − τ ) 2 ) ] = K I 0 − K I 0 4 [ 4 θ − Δ ϕ ( t ) + Δ ϕ ( t − τ ) ] 2
I o u t = K I 0 − K I 0 4 [ 16 θ 2 + 2 a 2 sin 2 ( ω τ 2 ) + 16 θ a sin ⁡ ( ω τ 2 ) sin ⁡ ω ( t − τ 2 ) − 2 a 2 sin 2 ( ω τ 2 ) cos ⁡ 2 ω ( t − τ 2 ) ]
I ω = 4 K I 0 a θ
I 2 ω = 1 2 K I 0 a 2
I ω I 2 ω = 8 θ a
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