Suppression of probe laser power errors based on normalized power splitting model in NMR co-magnetometers

The nuclear magnetic resonance (NMR) co-magnetometer enables high-precision magnetic field measurement through the balanced polarimetry detection technique. The probe laser power is a critical parameter in this technique, directly affecting the magnetic field signal scale factor. Although probe laser power stabilization via power splitting detection has been widely adopted, inherent limitations persist due to power splitting ratio variations induced by phase retardation fluctuations in half-wave plates, which degrade power stability. To mitigate these errors, a normalized power splitting model has been implemented, considering the power stabilization characteristic. The impact of phase retardation in the half-wave plate on probe laser power is developed using the Jones matrix formalism, leading to the proposal of a phase retardation suppression point that minimizes sensitivity to half-wave plate errors. This approach directly mitigates probe laser power instability without hardware modifications or component replacement. Triplicate experimental validations demonstrate that the peak-to-peak power fluctuations are reduced by 14.5 % during the 3-hour continuous operation, while Allan deviation analysis reveals a 17.9 % decrease in bias instability. This stability enhancement significantly improves the error suppression capability of magnetic field measurements, thereby advancing the performance of NMR co-magnetometer systems.