Optimal nonlinear Stokes–Mueller polarimetry for multi-photon processes

In this Letter, we present an optimization model for nonlinear Stokes–Mueller polarimetry (SMP) to improve the precision in estimating the nonlinear Mueller matrix (MM) for two- and three-photon processes. Although nonlinear polarimeters can measure the polarization properties of multi-photon processes or materials, existing methods are suboptimal, leading to low measurement precision. Based on the model and its solution, we have designed a new measurement strategy to substantially reduce the estimation variance of nonlinear MM coefficients by approximately 58.2% for second-harmonic generation polarimetry and 78.7% for third-harmonic generation polarimetry. The model and measurement method can be directly applied to multi-photon processes to improve the precision of SMP.