Unified Stokes-Mueller polarimetry for multi-photon processes at varying wavelengths

Existing polarimetry, mainly focusing on harmonic generations, overlooks the differences in retardance (DRs) caused by illuminations with different wavelengths in nonlinear processes, consequently falling short in accuracy beyond frequency doubling. In this Letter, with DRs considered, we propose a universal nonlinear Stokes-Mueller (NSM) polarimetry design involving illuminations with different wavelengths. Then, we optimize the NSM measurement model, applied to sum-frequency generation (SFG) and difference frequency generation. To demonstrate the necessity of consideration of DRs, the processes of polarization measurement for SFG are simulated, where the condition number decreases by 51.2%, and the root mean square error of the nonlinear Mueller matrix decreases by 20.48%.