Modeling of Conical Flux Concentrator for Miniaturized Atomic Magnetometers

High-sensitivity and high-spatial-resolution magnetic field measurements are increasingly required in neuroscience, geomagnetic exploration, and other advanced scientific and technological fields. Spin-exchange relaxation-free (SERF) atomic magnetometers can achieve ultrahigh sensitivity at the level of lT/Hz"2, but their spatial resolution is limited by dimensions of vapor cell. Incorporating flux concentrators (FCs) provides an effective mean to enhance spatial resolution while preserving the probe volume of the SERF atomic magnetometer, thereby maintaining its high sensitivity. However, most existing studies primarily demonstrate the performance of FCs, with limited development of predictive models capable of accurately estimating amplification efficiency and spatial resolution. In this work, we develop an analytical relationship between the amplification factor of conical FCs, the most commonly used geometry, and their geometric parameters, based on demagnetization factor theory. Furthermore, we propose a finite element analysis (FEA)-based method to predict the achievable spatial resolution. Our method allows efficient estimation of amplification efficiency and spatial resolution for a given FC geometry, as validated by numerical simulations. This modeling framework offers important guidance for FC design and can be extended to other types of magnetic sensors, such as nitrogen-vacancy (NV) center magnetometers.