Quantitative interpretation of time-resolved coherent anti-Stokes Raman spectroscopy with all Gaussian pulses

TL;DR

This paper develops an analytical framework for interpreting time-resolved coherent anti-Stokes Raman spectroscopy using Gaussian pulses, enabling extraction of pure resonant spectra from complex data.

Contribution

It provides closed-form solutions and a maximum enhancement formula, offering new insights into the interpretation of time-resolved coherent Raman spectra.

Findings

Analytic formulas for coherent Raman scattering are derived.

Maximum enhancement depends on probe pulse bandwidth.

Experimental pyridine data are quantitatively explained.

Abstract

Coherent Raman scattering spectroscopy is studied purposely, with the Gaussian ultrashort pulses as a hands-on elucidatory extraction tool of the clean coherent Raman resonant spectra from the overall measured data contaminated with the non-resonant four wave mixing background. The integral formulae for both the coherent anti-Stokes and Stokes Raman scattering are given in the semiclassical picture, and the closed-form solutions in terms of a complex error function are obtained. An analytic form of maximum enhancement of pure coherent Raman spectra at threshold time delay depending on bandwidth of probe pulse is also obtained. The observed experimental data for pyridine in liquid-phase are quantitatively elucidated and the inferred time-resolved coherent Raman resonant results are reconstructed with a new insight.