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

Area of Science:

• Nonlinear optics
• Microscopy
• Materials science

Background:

• Second-harmonic generation (SHG) and sum-frequency generation (SFG) microscopy are powerful tools for probing material properties.
• Extracting quantitative nonlinear optical susceptibility tensors and sample orientation from these techniques can be challenging.
• A unified theoretical approach is needed to reliably interpret experimental data.

Purpose of the Study:

• To develop a unified theoretical framework for recovering second-order nonlinear susceptibility tensors and sample orientations.
• To extend the Jones formalism to nonlinear optics for bridging experimental observables and local-frame tensor elements.
• To validate the framework using polarization-dependent SHG microscopy on Z-cut quartz.

Main Methods:

• Developed a unified theoretical framework based on an extension of the Jones formalism for nonlinear optics.
• Explored four common experimental architectures: polarization rotation, polarization-in/polarization-out, and polarization modulation (with and without postsample optics).
• Performed polarization-dependent second harmonic generation measurements on Z-cut quartz.

Main Results:

• Successfully recovered second-order nonlinear susceptibility tensors and sample orientations.
• The extended Jones formalism effectively bridged experimental observables and local-frame tensor elements.
• Calculated local-frame tensor elements for Z-cut quartz, which agreed with symmetry-dictated values.

Conclusions:

• The developed theoretical framework provides a robust method for quantitative analysis in SHG and SFG microscopy.
• The approach allows for accurate determination of both material nonlinear optical properties and sample orientation.
• This work advances the application of nonlinear optical microscopy for materials characterization.