Vector model for polarized second-harmonic generation microscopy under high numerical aperture

Based on the vector diffraction theory and the generalized Jones matrix formalism, a vector model for polarized second-harmonic generation (SHG) microscopy is developed, which includes the roles of the axial component P-z, the weight factor and the cross-effect between the lateral components. The numerical results show that as the relative magnitude of P-z increases, the polarization response of the second-harmonic signal will vary from linear polarization to elliptical polarization and the polarization orientation of the second-harmonic signal is different from that under the paraxial approximation. In addition, it is interesting that the polarization response of the detected second-harmonic signal can change with the value of the collimator lens NA. Therefore, it is more advantageous to adopt the vector model to investigate the property of polarized SHG microscopy for a variety of cases.