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Abstract
An acousto-optic modulation (AOM) detection method is demonstrated to detect the atomic Larmor precession frequency in an all-optical K-Rb atomic magnetometer operated in Spin-Exchange Relaxation Free (SERF) regime. Magnetic field sensitivity of 14 fT/Hz1/2 was achieved by employing the uniform design (UD) [Acta Math Appl Sin. 3, 363 (1980)] and subsequently optimizing the AOM modulation conditions. Results were compared to those of Faraday and the balanced polarimetry method in the same magnetometer. The AOM detection method has several advantages, such as small volume, no extra magnetic shielding for the modulator, high measurement signal-to-noise ratio and stability. It has a good prospect for compact and multi-channel atomic magnetometers.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
All-optical atomic magnetometer operated in Spin-Exchange Relaxation Free (SERF) regime has been recognized as the most sensitive known detector of static and quasi-static magnetic fields after a series of remarkable developments in recent years [1–3]. It has enormous application value in plenty of fields including geophysics, fundamental physics and space technology [4,5], and is particularly well suited to non-invasive biomagnetic measurements [6–8]. For instance, a wearable system with an array of SERF atomic magnetometers has proved to be a suitable replacement of traditional cryogenic magnetoencephalograhy (MEG) instrument, i.e., superconducting quantum interference devices (SQUIDs) [9]. Thus, there is a tendency to develop miniaturized and multi-channel SERF atomic magnetometer with high sensitivity and stability.
Practical atomic magnetometers are limited not only by the atomic spin-projection noise and the photon shot noise, but also by diverse kinds of technical noise in the process of detecting atomic spin precession. From the phenomenological standpoint, the magnetometer sensitivity is determined mainly by the signal-to-noise ratio (SNR) of the Zeeman resonance signal and the linewidth of the resonance. Thus, it is critical to find a detection method capable of increasing SNR and serving for compact magnetometer implementation. Based on the magneto-optical rotation of a linearly polarized light, balanced polarimetry method, Faraday modulation method and photoelastic modulator method (PEM) are the three most commonly used detection methods [10–12]. Due to the simple structure and no extra power consumption, the balanced polarimetry method is the most popular detection method in atomic magnetometers arrays, while its SNR is relatively low in the low-frequency domain for lacking in effective suppression of flicker noise [13]. The Faraday modulation method performs better in sensitivity at the cost of large volume and more complicated inner structure. Since the surface temperature of magneto-optic glass will increase dramatically when the coil current in Faraday modulator generates and accumulates a large amount of heat, cooling unit and feedback system are necessary to suppress the thermal drift. Extra magnetic shield outside the coils takes considerable space as well. The PEM method holds the record of highest magnetometric sensitivity for its high modulation purity and large useful aperture, but its complex mechanical structure and an external controller are not well suited for compact magnetometers [11].
The present paper demonstrated an acousto-optic modulation (AOM) spin precession detection method applied in an all-optical K-Rb hybrid SERF atomic magnetometer. Acousto-optic modulation (AOM) technology has relatively high extinction ratio (generally greater than 1000:1), superior temperature stability and industrial maturity and has been commonly used in laser Q-switch and laser external modulation communication, etc [14]. The Bell-Bloom magnetometer has used AOM to modulate the optical pumping efficiency to realize Lorentzian-shaped phase resonances [15,16]. Its properties of low driving power, small volume and relatively low price would be advantageous in the development of sensitive and miniaturized atomic magnetometers. Arranging multiple-factor and multiple-level experiment using uniform design (UD) [17], the AOM modulation detection configuration was studied to enhance the efficiency of finding the major factors affecting the modulation effect. According to this, we optimized the magnetometer sensitivity influenced by different modulator positions, polarization directions of the incident light into acousto-optic medium, modulation frequency levels and duty cycle levels. A highest sensitivity of 14 fT/Hz1/2 @30 Hz was achieved, which was compared with the Faraday modulation method. In addition, a long-term stability test of the atomic magnetometer sensitivity was conducted with AOM detection method and Faraday modulation method separately.
2. Principle
The electron spins of alkali-metal atoms are polarized along the Z-axis through depopulation pumping technique. To obtain more uniform spin polarization in the cell, K-Rb hybrid alkali metal vapor is used in this paper [18]. K atoms with lower density are directly pumped and their spin polarization is transferred to Rb atoms with higher density through spin-exchange collisions [19]. When the atomic magnetometer operates with high alkali metal density in very weak magnetic fields, spin-exchange relaxation is suppressed and the magnetometer works in the SERF regime. A small field along the Y-axis By results in a steady-state equilibrium with the average atomic spin deviating a small angle from the pumping direction. Rb atoms interacts with the transmitted linearly-polarized probe beam and results in a polarization plane rotation θ of the probe laser [10]:
where n is the alkali-metal atomic density number, c is the light velocity, re is the classical electron radius, l is the length of the cell along the probe axis, νprobe is the frequency of the probe laser, ν0 is the D1 line resonance frequency of Rb, f ≈1/3 is the oscillator strength, Γ is the pressure broadening of buffer gas and quenching gas, γe is the geomagnetic ratio of a bare electron, S0 is the equilibrium electronic spin polarization, ROP is the optical pumping rate and Rrel is the relaxation rate. As can be seen from Eq. (1), the rotation angle θ reflects the intensity of the applied field By and can be given in the proposed AOM detection method.Figure 1 shows the schematic of the AOM optical detection system, in which Fig. 1(a) shows the schematic with AOM modulator before the cell and Fig. 1(b) shows the schematic with AOM modulator after the cell. According to the theoretical calculation, the modulation effect of AOM method seems to be the same, no matter the modulator is installed before or after the cell, as were shown in the PEM and Faraday modulation method [11]. However, Both locations have their benefits from the actual operation point of view. Placing the modulator after the cell could be reasonable when considering θ emerges after the probe laser passing through the polarized atoms. But modulation before the cell can help isolate technical noise of the light in advances. Thus, the two locations were compared experimentally in the next section.
Fig. 1 Schematics of the AOM optical detection system. (a) AOM modulator is located before the cell. (b) AOM modulator is placed after the cell. (c) The square-wave modulation function with the repetition period Tmod and the duty cycle D.
The probe laser becomes linearly-polarized light by passing through the first polarization beam splitter (PBS1), whose p polarized light intensity at position ① are adjusted by rotating the first half-wave plate (HWP1). To study influences of the linear polarization state on SNR of the magnetometer, the transmission axis of polarizer is adjusted and the second half-wave plate (HWP2) is correspondingly rotated to align the polarization axis at position ② and ③ parallel and maintain the light intensity I0 entering the alkali-metal vapor cell. Each time the polarization state is altered, the last half-wave plate in the light path (HWP3) is rotated to balance the intensity entering the balanced photodetector in the absence of optical pumping.
Before entering HWP3, the beam travels through the AOM, whose Bragg-diffraction efficiency η at Bragg angle [20] is
where Id and Ii are the intensities of incident and diffracted light respectively, λ is the light wavelength, L and H are the length and width of the AOM electroacoustic transducer, M2 is the acousto-optic figure-of-merit determined by the material attributes, and Pad is the acoustic drive power. A high-frequency electrical signal drives the transducer to generate varying ultrasonic waves getting into the AOM modulator. The amplitude of the light beam can be manipulated by controlling the drive voltage. As is illustrated in Fig. 1(c), it is a square-wave modulation function f(t) with the frequency ωmod, corresponding to the period , and the duty cycle D, which can be described in the form of Fourier series as [21,22]:The zero-order diffraction light is blocked and the first-order light after modulation is analyzed by a PBS (PBS2) set at 45° to the incident polarization direction, resulting in two separate beams with individual intensities [10],
These two beams are finally detected by the balanced photodetector. The intensities are balanced when θ = 0 and unbalanced otherwise:
Its output electrical signal can be demodulated by the digital lock-in amplifier at the modulation frequency ωmod. Considering the small optical rotation , the first harmonic component of the differential signal is
Therefore, the atomic spin precession and hence the applied magnetic field can be attained by AOM detection method with suppression of low frequency noise.
3. Experimental setup
Figure 2 shows the K-Rb hybrid SERF atomic magnetometer with the AOM detection method, where the modulator is placed after the cell just to give an illustration. Both positions will be tested afterwards. This magnetometer was composed of an alkali-metal vapor cell, a magnetic field shielding and compensating system, an electrical heating system, and a light source system including the pump and probe lasers.
Fig. 2 Schematic of the SERF atomic magnetometer using AOM detection method. The modulator is placed after the cell in this picture just to make an illustration. Both positions will be tested.
A 25 cm diameter spherical GE180 glass cell contained K and Rb hybrid vapor with the density ratio of approximately 1:180, 50 torr N2 as quenching gas and 2.5 atm 4He as buffer gas. The typical experimental temperature of 473 K was obtained using 99 kHz AC heating currents. The corresponding density of Rb vapor was about 9.23 × 1014 cm−3, estimated via the saturated vapor pressure curve [23]. As the sensitive unit, the alkali metal vapor cell was placed in an evacuated chamber in the center of three-dimensional Helmholtz coils. The residual magnetic fields were compensated by coils after zeroing procedures [24], with compensation values of 6.984 ± 0.002 nT, 0.946 ± 0.002 nT and 2.342 ± 0.002 nT on the X, Y and Z axis respectively. Laying outside was a set of five-layer cylindrical magnetic shielding, which was made of permalloy with high relative permeability. The innermost layer of the magnetic shielding is about φ 240 mm × 480 mm, and the outermost layer is about φ 350 mm × 700 mm. The magnetic shielding and the triaxial magnetic coil system can provide a weak magnetic field environment for the atomic magnetometer together. During the whole experiment, a reference signal applied through Y-axis coil was set as 5 mVpp @30 Hz, corresponding to an oscillating magnetic field of 25.8 pTrms.
An external-cavity diode laser (ECDL) (model 6910, New Focus, USA) was used as the pump laser, whose power was 208 mW and beam diameter was 13 mm. The pump beam wavelength was stabilized at the D1 line (770.108 nm) of K with a wavelength meter (model WS7, Highfiness, Germany). An distributed-feedback (DFB) laser (model DL100 DFB-L, Toptica, Germany) with 3.8 mW output power was chosen as the probe light, whose wavelength was tuned to 795.475 nm, close to the D1 line of Rb (795 nm). The beam diameter of the probe beam was restricted to 2.5 mm with an aperture. To optimize the magnetometer’s sensitivity, the pumping light power, the probe light power and the detuning of the wavelength of the probe laser were adjusted to the points with maximum response signal. Additionally, the probe light was carefully directed through the center of the cell in order to reduce the refraction on the spherical glass cell and the subsequent depolarization effects of electron spins.
The acousto-optic figure-of-merit M2 of the AOM modulator (AOMO model 3200-124, AODR model 1200AF-DIF0-2.0, GOOCH& HOUSEGO, UK) used in this experiment was about 845 × 10−15s3/kg, determined by the acousto-optic medium of TeO2 and the work pattern of abnormal AOM diffraction. Its Bragg angle was 19.8 mrad and the beam separation was 39.6 mrad. We set the radiofrequency power on the electroacoustic transducer to 2 W and adjusted the incident angle to the surface of acousto-optic crystal to maximize the diffraction efficiency. Modulation input on the transducer is generated by a waveform generator (model 33522A, Agilent, USA). The probe beam carrying the rotation information was finally analyzed by a PBS and detected by the balanced photodetector (model 2307, New Focus, USA).
The first harmonic component of the output signal was extracted by a lock-in amplifier (model SR830 DSP, Stanford research systems, USA) with the time constant of 30 μs and acquired by a data acquisition card (model PXI6366, 24 bits, NI, USA) based on LabVIEW program with a sampling rate of 1 kHz and a typical single measurement time of 100 s. The scale factor was measured to be approximately 23.52 V/nT @30 Hz. The acquired data in the time domain were transferred to frequency domain by fast Fourier transform (FFT) [2].
To acquire the best performance of the AOM modulation detection system, four operational factors influencing the effect of AOM detection method were investigated in this paper, including modulator positions, polarization directions of the incident light into acousto-optic medium, modulation frequency levels and duty cycle levels. Each of them has different numbers of factor-level. We chose 2 modulator positions, 6 polarization directions on the AOM surface, 12 modulation frequency levels and 6 different duty cycles of square-wave modulation function. In order to go through various combinations of these components, at least 864 groups of experiment were expected to find the optimal operation conditions without considering repetition to reduce measurement error. Therefore, to dramatically reduce the complexity of the experiment, UD experimental method was employed by selecting several representative experimental conditions with specific SNR measured on K-Rb hybrid atomic magnetometer [25]. UD is assumed as an applicable experimental design method since it distributes experimental points uniformly on the experimental domain to significantly reduce the number of experiments while rationally depicting the nature of the measurement system [26,27]. UD in this paper was planned based on the first, the sixth, the seventh and the ninth column of the basic uniform table U12(1210) according to [25] and experiments were carried out correspondingly. To make a comparison, the sensitivity measurement experiments with the Faraday modulation method were carried out. Finally, sensitivity fluctuations were measured for 2 hours with an interval of 15 minutes after the AOM factor combination optimization.
4. Results and discussion
UD arrangements and corresponding results, taking SNR @30 Hz as the aim, were given in Table 1. In the table, factor A represented AOM modulator position, with the value 1 for the AOM modulator being placed before the cell, while the value −1 represents the opposite. The other factors B, C and D represented modulation frequency levels, polarization directions of the incident light into acousto-optic medium and duty cycle levels, respectively.
Table 1. UD arrangements and results
Multiple linear regression analysis was applied to the experimental results using Statistical Product and Service Solutions (SPSS) [25]. However, the R2 and the adjusted R2 of the obtained linear model was only 0.642 and 0.437 respectively, reflecting an unsatisfactory regression fitting effect. Therefore, stepwise regression analysis was used alternatively. The four factors A, B, C and D were transferred to 10 quadratic terms AA, AB, AC and so forth. They were used as the impacting factors along with the four original factors. We used F value as the stepping method criteria. The entry and remove F value were set as 3.84 and 2.71 respectively, as suggested in the model in [25]. Quadratic polynomial model was acquired with an acceptable R2 of 0.840 and an adjusted R2 of 0.780. The factor BD was selected as the predictive component in the first step of regression, implying that the interaction of modulation frequency and duty cycle had the largest influence on the AOM modulator performance. The incident polarization direction C was introduced in the second regression equation. Last came the combination factor AB, representing the modulator position and the modulation frequency. The final regression equation of the modulation performance Y was given as
Under the given operation conditions, the maximum Y of 1817 were expected when A = 1, B = 56 kHz, C = 90° and D = 90%. It was assumed that when the AOM modulator was put before the cell, the effective low-frequency noise isolation was realized in advance of the magneto-optical rotation of the probe light. Moreover, the light beam quality would be worse inevitably after passing through the vapor cell. Diffraction efficiency reached its highest when the incident light polarization was vertical and the response signal was subsequently strengthened. However, the measured SNR of experiment number 2 and 6 were 1059 and 1095, much higher than the others. Notably, the duty cycle values in these two experiments were both 60%. Since that, we further investigated the relationship between the modulation function duty cycle and the SNR of the atomic magnetometer using AOM detection method.
Figure 3 showed the SNR of the atomic magnetometer as a function of the duty cycle of the square-wave modulation function. Experiments were performed with the AOM modulator placed before the cell, the modulation frequency of 56 kHz and the 90° polarization direction with respect to the optical table of the incident laser on the modulator surface. Experiments at each point were repeated four times respectively. A maximum point at the duty cycle of 50% can be figured out to be around 1481, corresponding to a sensitivity of 17.4 fT/Hz1/2 @30 Hz. The small duty cycle represented the short pulse duration time, so the diffraction intensity could not reach its peak before the pulse was over. When the duty cycle was set too large, the diffraction intensity does not have enough time to fall before the next high level appeared. Both of these conditions would decrease the AOM extinction ratio and resulted in the decrease of response signal intensity.
Fig. 3 SNR @30 Hz of the magnetometer varying with the duty cycle of the modulation function, ranging from 10% to 90%. The response signal reached the highest at 50% duty cycle.
Figure 4 showed the representative magnetometer response in the frequency domain to the same reference magnetic field of 25.8 pTrms @30 Hz with the AOM method, the Faraday modulation method and the balanced polarimetry method. These spectra were compared with the probe noise baseline, which was measured with the pumping light turned on. In order to converse the output electrical signal to magnetic field, we also measured the responses of the magnetometer to excitations of By with different frequencies ranging from 5 to 95 Hz with an interval of 5 Hz, except 50 Hz, the power frequency. As was illustrated in the built-in graph of Fig. 4, the experimental results were fitted with Lorentzian profile and FWHM of 11.87 Hz was obtained, indicating this magnetometer was working in SERF regime [3]. Sensitivities of 14.33 fT/Hz1/2, 21.83 fT/Hz1/2, 26.79 fT/Hz1/2 were achieved with the AOM method, the Faraday modulation method and the balanced polarimetry method respectively, under the same conditions of heating, illumination and magnetic field environment. The Faraday modulation was employed with the modulation frequency of 3.65 kHz and the modulation amplitude of 1°. The extinction ratio of the magneto-optic glass was measured to be 3412 when the surrounding coils were not electrified.
Fig. 4 Representative magnetometer responses in the frequency domain. The blue solid line denoted the frequency spectrum of the AOM detection method with the AOM modulator placed before the cell, the modulation frequency of 56 kHz, the 90° polarization direction and the duty cycle of 50%. The green dashed line represented the Faraday modulation method with the modulation frequency of 3.65 kHz and the amplitude of 1°. The red dash-dot line denoted the result of the balanced polarimetry method. These three lines were obtained when a reference signal of 25.8 pTrms@30 Hz was applied to the system. The pink dotted line was the technical noise baseline of AOM detection system observed by switching off reference signal. To get the scale factor of the magnetometer, the frequency response was measured as was shown in the inset at the upper right corner of the figure. The bandwidth of the magnetometer can be derived from the fitting curve. The fitting results were applied to the four curves in this figure.
As can be seen in Fig. 4, the noise baseline of AOM was relatively lower than those of the other two detection methods, owing to lack of effective isolation of low-frequency noise. This kind of noise usually with a 1/f power spectrum may arise from mechanical and technical sources, such as fluctuations of laser intensity and positions [10,28]. According to the step regression model of the UD experiments, the AOM modulation performance would be better if the modulation frequency could be higher. To realize this, the incident beam diameter should be narrowed to shorten the transition time of the modulator and increase the modulation speed. As long as the beam size remained larger than a certain value, which was 0.25 mm for the modulator in this paper, the diffraction efficiency would maintain near the peak.
AOM is often used to detune light frequency [29]. When the radio frequency signal is loaded on the ultrasonic transducer of the AOM modulator, an ultrasonic wave will be propagated in the acousto-optic crystal, whose frequency is determined by the source of the radio frequency signal, like 100 MHz, 120 MHz and so on. The ultrasonic wave will modulate the refractive index of the crystal and the ultrasonic frequency will be added or subtracted with respect to the incoming light frequency. The radio frequency was 200 MHz for the modulator we used throughout paper. Considering the D1 line of Rb (795nm) as the center frequency, the corresponding laser wavelength detuning was only 0.00042nm, which was acceptable in this experiment.
Figure 5 compared SNR fluctuations of the atomic magnetometer based on the AOM method and the Faraday method for every 15 minutes for 2 hours. The reference signal was fixed and the SNR was measured three times for each point. AOM experiment results had an average SNR of 1285 and a coefficient of variance (CV) of 0.122, while the Faraday method had an average SNR of 1118 and a CV of 0.150. CV is defined as the ratio of the standard deviation to the mean value, which is often used to compare the discrete degree of variables at different levels. The AOM method performed better in long-term stability and this would benefit the performance of the magnetometer.
Fig. 5 Comparison of SNR fluctuations measured with the AOM method and the Faraday method respectively, both for every 15 minutes in 2 hours. The AOM method performed more stable.
5. Conclusion
We studied the AOM detection method on a K-Rb hybrid SERF atomic magnetometer. To improve the SNR of AOM method, a series of UD experiments were designed to optimize the modulation conditions with the significantly reduced experiment number. The stepwise regression model was obtained with the R2 of 0.840 and the adjusted R2 of 0.780. The relationship between the SNR and the duty cycle of the square-wave modulation function was further investigated experimentally. By adjusting modulator position, polarization direction of the incident light into acousto-optic medium, modulation frequency level and duty cycle, a sensitivity of ~14 fT/Hz1/2 was acquired, which outperformed the Faraday modulation method and the balanced polarimetry method under the same magnetometer working conditions. The AOM method presents some additional advantages such as small size and no extra magnetic noise, which is beneficial for portable devices. The SNR of the magnetometer was measured with the AOM method and the faraday method separately for 2 hours. Experimental results showed good stability of the AOM method.
Magnetic field gradient measurement is often performed to further improve the sensitivity of magnetometers through suppression of common mode noise [30,31]. This method is carried out by expanding the probe beam size and picking out several points in the large light spot. The AOM method could be implemented in this configuration if the modulation is employed before probe beam expansion. Since AOM has been an industrially mature product and has been used in Q-switched fiber lasers, it may have a good prospect of application in compact fiber atomic magnetometers [14]. Apart from these, another AOM method based on Raman-Nath diffraction in normal mode, with symmetric multistage diffraction lights being sufficiently utilized, can also be investigated in the future for multichannel measurement.
Fundings
National Key R&D Program of China (2017YFB0503100); National Natural Science Foundation of China (NSFC) (61227902).
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