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Journal of Applied Physics

Derivation of bandwidth and filter characteristics of various types of optically pumped magnetometers

Thomas Schönau, Theo Scholtes, Ronny Stolz

Published Mar 3, 2026• 0 citations
Publisher

Abstract

We present a unified and easy-to-follow analytical framework based on the Bloch equations for deriving the small-signal frequency response of several common types of optically pumped magnetometers (OPMs). These include the Mx, light-shift dispersed Mz, Bell–Bloom, and RF (radio-frequency) types, as well as the class of unmodulated zero-field OPMs. It is shown that, depending on the operating regime, the frequency response of some of these magnetometers deviates significantly from the commonly assumed first-order filter behavior.

DOI
10.1063/5.0311659

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We present a unified and easy-to-follow analytical framework based on the Bloch equations for deriving the small-signal frequency response of several common types of optically pumped magnetometers (OPMs). These include the Mx, light-shift dispersed Mz, Bell–Bloom, and RF (radio-frequency) types, as well as the class of unmodulated zero-field OPMs. It is shown that, depending on the operating regime, the frequency response of some of these magnetometers deviates significantly from the commonly assumed first-order filter behavior.
Abstract We investigate the phase relationship between the oscillating (rf) excitation field and the detected (light) power modulation in scalar rf-driven optically pumped magnetometers (OPMs), in particular in the MxM_{x}Mx​ M x configuration. While the static dependence of the demodulation phase on the direction of the external static magnetic field vector can be largely mitigated by aligning the oscillating rf field along the light propagation direction, we demonstrate that a dynamic (transient) phase response arises under magnetic field tilts. We analytically solve the corresponding modified Bloch equation and confirm agreement with experimental observations obtained using an MxM_{x}Mx​ M x magnetometer incorporating a paraffin-coated Cs vapor cell. The results reveal fundamental limitations of MxM_{x}Mx​ M x magnetometers regarding response time and accuracy, in particular when employed with active electronic feedback, such as a phase-locked loop. Therefore, this work is highly relevant to important magnetometry applications where the direction of the quasi-static magnetic field of interest is unknown a priori or varies over time, or in measurements requiring a large detection bandwidth. Such conditions are encountered in applications such as geomagnetic surveying, particularly with mobile platforms.
Abstract We experimentally investigate the influence of the orientation of optically pumped magnetometers in Earth’s magnetic field. We focus our analysis to an operational mode that promises femtotesla field resolutions at such field strengths. For this so-called light-shift dispersed MzM_{z}Mz​ Mz (LSD-Mz) regime, we focus on the key parameters defining its performance. That are the reconstructed Larmor frequency, the transfer function between output signal and magnetic field amplitude as well as the shot noise limited field resolution. We demonstrate that due to the use of two well balanced laser beams for optical pumping with different helicities the heading error as well as the field sensitivity of a detector both are only weakly influenced by the heading in a large orientation angle range.
The optically pumped magnetometer (OPM) is a class of atomic devices that rely on the measurement of Larmor precession of an atomic spin ensemble in a magnetic field. They need the specific frequency light to complete the pumping and detection process. OPMs typically work under the Earth's magnetic field or a limited field. When operating in near-zero field, they can realize the spin-exchange relaxation-free (SERF) regime, thereby promoting a substantial increase in sensitivity. At present, OPMs have been widely used in magnetoencephalography, magnetocardiography, geomagnetic detection, and inertia measurement (comagnetometer). There are a large number of researchers engaged in the study of relevant mechanisms, devices, technologies, and applications. More importantly, supported by MEMS technology and micro/nano optics, OPMs have the potential to move toward chip-scale sensors. This special issue contains some latest developments in OPMs and related areas. We hope the reprint can provide valuable references for researchers in the related field.
Abstract Optically-pumped magnetometers (OPM) based on parametric resonance allow real-time tri-axial measurement of very small magnetic fields with a single optical access to the gas cell. Most of these magnetometers rely on circularly polarized pumping light. We focus here on the ones relying on linearly polarized light, yielding atomic alignment. For these magnetometers we investigate three second order effects which appear in the usual regimes of operation, so to clarify if they translate to metrological problems like systematic errors or increased noise. The first of these effects is the breakdown of the three-step approach when the optical beam has a large intensity. The second one is the breakdown of the rotating wave approximation when the frequencies of the RF fields are not much larger than the rates of other atomic processes. The third one is the tensor light-shift which appears when the light is slightly detuned from resonance. This work should help to clarify the accuracy reachable with OPM, which is an important question notably for medical imaging applications.
We present an optically pumped magnetometer working in a new operational mode-the light-shift dispersed Mz (LSD-Mz) mode. It is realized combining various features; (1) high power off-resonant optical pumping; (2) Mz configuration, where pumping light and magnetic field of interest are oriented parallel to each other; (3) use of small alkali metal vapor cells of identical properties in integrated array structures, where two such cells are pumped by circularly polarized light of opposite helicity; and (4) subtraction of the Mz signals of these two cells. The LSD-Mz magnetometer's performance depends on the inherent and very complex interplay of input parameters. In order to find the configuration of optimal magnetometer resolution, a sensitivity analysis of the input parameters by means of Latin Hypercube Sampling was carried out. The resulting datasets of the multi-dimensional parameter space exploration were assessed by a subsequent physically reasonable interpretation. Finally, the best shot-noise limited magnetic field resolution was determined within that parameter space. As the result, using two 50 mm3 integrated vapor cells a magnetic field resolution below 10 fT/√Hz at Earth's magnetic field strength is possible.