# Quantitative Ultrafast Spectroscopy and Microscopy of Traditional and Soft Condensed Matter
## 1 Introduction  
Applications of nonlinear optics have been widely regarded as powerful tools that are capable of providing quantitative spectral information in condensed matter characterization. These applications span from plasma to solid-state materials and nanostructures, as well as to interfaces and biological media [1; 2; 3; 4; 5]. Raman effect based spontaneous and coherent scattering techniques are of special attention due to their selectivity and sensitivity down to a chemical bond level, and that in turn provides access to important physical mechanisms and fundamental interactions. However, in spontaneous Raman spectroscopy, reliable data on weak resonances is difficult to obtain. In the last decade, coherent Raman spectroscopy methods have been successfully demonstrated in optical microscopy [6; 7; 8; 9; 10]. Spectral responses with a resolution of a few cm\({}^{-1}\) have been demonstrated in various applications that focused on the characterization of biological matter. It is worth noting that these approaches provide only dispersion for the imaginary part of the resonant optical nonlinearity. The overwhelming majority of studies are in the frequency domain, with a recent focus on novel solid-state materials [11; 12; 13; 14] and molecular/biological media [15; 16; 17; 18]. The coherent Raman based microscopy techniques were recently applied to image biological tissue and cells with sub-micron spatial resolutions capable of resolving the spatial structures of key constituents when their characteristic Raman active vibrations are targeted [19; 20]. The spontaneous Raman microscopy has been applied with a greater focus towards the analysis of specific vibrations within cells, tissues and their spectral features. Multi-line spectra were analyzed with respect to relative changes in the intensities and spectral shifts for main phonon lines, depending on growth techniques for solid-state materials as well as scattering geometries with respect to crystal axes [21; 22]. For biological media, efforts were focused towards the goal of correlatingthose with bio-molecular alterations occurring on cellular and sub-cellular levels [23; 24]. Resolving lattice or molecular vibration damping rates \(\Gamma\) (or linewidths, \(\Delta\
u\) = 1/\(\Gamma\)) and line shapes, which are ultimately key parameters in characterizing atomic/molecular bonds, has not been of specific effort primarily due to insufficient detection sensitivity and spectral resolution. The vibration damping rate is strongly influenced by unit cell structure and respective phonon properties in crystals and inter- and intra-molecular interactions in soft media. Therefore, the ability to measure Raman line shapes and sub-structures with high precision is absolutely important from the standpoint of having access to fine inter- and intra-molecular interactions and their physical mechanisms. Spontaneous Raman spectroscopy has a typical resolution of \(\sim\)3-7 cm\({}^{-1}\) and often requires the application of data post-processing algorithms to retrieve spectra. Thus, for current state-of-the-art spectral domain techniques, the ability to access critical inter- and intra- molecular interactions of key molecular groups within biological specimens is limited. Coherent Raman microscopy, which employs picosecond pulses to attain high peak powers, cannot provide a better spectral resolution due to the pulse bandwidths (\(\sim\)5-20 cm\({}^{-1}\)). Additional measurement artifacts and sources of imprecision come from a need to mechanically tune laser wavelengths in point-by-point spectral measurements with an obvious adverse impact on precision. Thus, the desired precision in detecting Raman line shapes and bandwidths may not be achieved. Precise information on dispersion of the nonlinear optical susceptibility in Raman active media is essential in order to gain insight into the physics of intra- and inter-atomic and molecular interactions.