# Quantitative Ultrafast Spectroscopy and Microscopy of Traditional and Soft Condensed Matter
## 4 Conclusions  
In conclusion, we have demonstrated femtosecond time-domain coherent anti-Stokes Raman scattering spectroscopy and microscopy to characterize solid state and biological media. We demonstrated well-resolved Raman active vibrations with a complex line structure that are not routinely resolved by other Raman based spectroscopy techniques. We can obtain distinctly different parameters for complex vibrational lines. Real and imaginary parts of the third-order nonlinear susceptibility near Raman resonances in KTP crystal, oil and animal fat have been obtained with an equivalent spectral resolution of better than 0.1 cm\({}^{-1}\). KTP crystal was studied by accessing TiO\({}_{6}\) octahedron vibrations. Namely, we have resolved a Raman doublet with a 62 cm\({}^{-1}\) frequency difference and slightly different phonon decay times of 495 fs and 515 fs for the two closely spaced vibrations. For phonons representing Ti-O-P intergroup vibrations, we found three components with decay times within the 0.95-1.2 ps range that translate to phonon linewidths of 9.1 \(\pm\) 0.4 cm\({}^{-1}\), 7.5 \(\pm\) 0.6 cm\({}^{-1}\), and 11.2 \(\pm\) 0.5 cm\({}^{-1}\). Comparing Raman active C-C stretching vibrations in fat tissue and oil, we found close similarity between the two. Picosecond dephasing times within the 1.6-2.7 ps range has been detected. Based on the time-domain CARS data, we are able to deduce linewidths as narrow as 4.1 cm\({}^{-1}\) in fat tissue, which has not been resolved in prior works that used spontaneous scattering and frequency domain coherent Raman spectroscopy methods. The experiments have been implemented in a microscopy arrangement, giving strong promise and providing an additional dimension in the comprehensive characterization of condensed matter and biological media. This can lead to a strong impact and important applications in the field of electronic materials that help to identify mechanisms that limit electronic transport parameters. This can also become an effective method in detecting bio-molecular alterations in cells and tissue that are critical for molecular level disease diagnosis.  
Conceptualization, F.G.; Methodology, F.G.; Software, A.C.; Validation, M.M.; Formal Analysis, A.C., M.M.; Investigation, A.C., M.M.; Resources, F.G.; Data Curation, A.C.; Writing-Original Draft Preparation, F.G.; Writing-Review & Editing, A.C.; Visualization, F.G.; Supervision, F.G.; Project Administration, F.G.; Funding Acquisition, F.G. This research was funded by National Science Foundation grant number [DBI-1355307] and Air Force Office of Scientific Research grant number [18 RT0214]. Article processing charges were covered by Department of Physics, University of Rhode Island.  
The authors thank technical support and provision of samples from [PERSON] (Stevens Institute of Technology) and 2D Semiconductors, Inc. (Scottsdale, AZ, USA), software support from the Department of Physics and administrative support from [PERSON] (Department of Physics, University of Rhode Island) is acknowledged.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.