  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.
