Design of Micro-Integrated Self-Shielded Biplanar Coils Based on Multipole Moment Expansion

Emerging optically pumped magnetometers (OPMs) rely heavily on uniform-field coils that enable precise generation of magnetic field for either compensation or modulation, while conventional uniform-field coils suffer from stray fields between adjacent devices, which has become the major drawback for applications where magnetometer array are needed including magnetoencephalography (MEG) and magnetocardiography (MCG). In this article, a novel uniform-field coil that enables stray field reduction and uniform magnetic field generation is proposed. Multipolar expansion of the magnetic vector potential is applied to the target field method (TFM), where the relative magnitude of the stray fields is estimated through Fourier coefficients of the stream function. Results demonstrate that the maximum absolute value of the field relative inhomogeneity error of B_x is 9.4%, and the maximum absolute value of the external relative magnetic field at 16.3 mm from the origin is approximately 1%. The device is fabricated through a CMOS-compatible microfabrication method and is characterized in a multilayer magnetic shield with a residual magnetic field of less than 10 nT, which exhibits an open-loop sensitivity of 16 fT/Hz^1/2 in magnetometer experiments. This work paves the way for the integration of atomic magnetometers on the chip.