Unified Theory for Polarization Analysis in Second Harmonic and Sum Frequency Microscopy.

A unified theoretical framework for the recovery of second-order nonlinear susceptibility tensors and sample orientations from polarization-dependent second harmonic generation and sum frequency generation microscopy was developed. Jones formalism was extended to nonlinear optics and was used to bridge the experimental observables and the local-frame tensor elements. Four commonly used experimental architectures were explicitly explored, including polarization rotation with no postsample optics, polarization-in polarization-out measurement, and polarization modulation with and without postsample optics. Polarization-dependent second harmonic generation measurement was performed on Z-cut quartz and the local-frame tensor elements were calculated. The recovered tensor elements agree with the expected values dictated by symmetry.