One- and two-dimensional correlation spectroscopy analyses for resonant and non-resonant coherent nonlinear optical processes

Three-color coherent anti-Stokes Raman scattering represents non-degenerate four wave mixing process that includes both a non-resonant and resonant processes, the contributions of which depend on how the molecular vibrational modes are being excited by the input laser pulses. Non-degenerate four wave mixing processes are complex and understanding these processes requires rigorous data analytical tools, which still lack in this research field. In this work, we introduce one- and two-dimensional intensity-intensity correlation functions in terms of a new variable (e.g., probe pulse delay) and new perturbation parameter (e.g., probe pulse linewidth). In particular, diagonal projections are defined here as a tool to reduce both synchronous and asynchronous two-dimensional correlation spectroscopy analyses down to one-dimensional analysis, revealing valuable analytical information. Detailed analyses using the all Gaussian coherent Raman scattering closed-form solutions and the representative experimental data for resonant and non-resonant processes are presented and compared. This intensity-intensity correlation analytical tool holds a promising potential in resolving and visualizing resonant versus non-resonant four wave mixing processes for quantitative label-free species-specific nonlinear spectroscopy and microscopy.