Kramers-Kronig relations and sum rules in nonlinear optical spectroscopy

Area of Science:

• Nonlinear Optics
• Spectroscopy
• Condensed Matter Physics

Background:

• Kramers-Kronig relations and sum rules are underutilized in nonlinear optical spectra analysis.
• Understanding nonlinear susceptibility is crucial for optical materials.
• Anharmonic oscillator models provide a framework for nonlinear optical phenomena.

Purpose of the Study:

• To investigate the application of Kramers-Kronig relations and sum rules in nonlinear optical spectra analysis.
• To demonstrate the utility of an anharmonic oscillator model for describing nonlinear susceptibility.
• To derive and apply various forms of Kramers-Kronig dispersion relations and sum rules.

Main Methods:

• Utilized a simple anharmonic oscillator model to describe nonlinear susceptibility.
• Derived conventional, multiply-subtractive, and generalized Kramers-Kronig dispersion relations.
• Applied these relations and sum rules to nonlinear optical spectra.

Main Results:

• Successfully derived various Kramers-Kronig dispersion relations and sum rules.
• Demonstrated practical application of these relations in nonlinear optical spectra analysis.
• Analyzed the third-harmonic wave generation spectrum from a polymer as a case study.

Conclusions:

• Kramers-Kronig relations and sum rules offer significant potential for nonlinear optical spectra analysis.
• The anharmonic oscillator model effectively describes nonlinear susceptibility and facilitates the application of these relations.
• The methods presented provide a robust framework for understanding and analyzing nonlinear optical phenomena.