%In addition, in situ characterization of dipole strength can also be very important in the case of quantum dots, because states have been known to degrade by bleaching, thus mainly destroying the dipole moment strength of the sample.  
%Our measurements use solution-phase CMDS to quantitate the non-linear magnitude of quantum dot resonance.  
%We first discuss how our measurements in the context of the photobleach mechanism.  
%We then discuss how our measurements compare to the other measurements of the photobleach.  
%These measurements provide a framework to describe the photobleach mechanism in the same language as TA (the imaginary analogue of our measurement).  
%This measurement can be quantitatively connected to the non-linear mechanism, which in this case is a fractional photobleach.  
%The method could also be applied to TSF to extract displacements responsible for Franck-Condon vibronic structure. 

We have shown that ultrafast CMDS can isolate the non-linearities of resonant signal and background solvent in manner similar to classic three-wave mixing analyses of the past.  
%Ultrafast CMDS spectroscopy can be contaminated by partially resonant and non-resonant contributions of the solvent.  
At pulse overlap, featureless solvent contributions can be especially large.  
The resonant Raman contributions decrease in prominence when pulses are shorter than the Raman lifetimes.  
Solvent contributions can also be suppressed by using large sample concentrations, in which case spectra have to be corrected by well-defined absorptive correction factors.  
The solute and solvent interference can be separated using simple, few parameter models, as we have demonstrated here with quantum dots.  
We have employed simple, few-parameter fits to easily disentangle the role of solvent and solute.  
These methods should be applicable to other CMDS spectroscopies, but the description of the solvent may change, especially when non-co-polarized excitations are used.\cite{Deeg1989}  
In fact, the polarization behavior provides a useful way to alter the balance of solvent and solute contributions in a predictable way, and is likely a viable method for separating solvent and solute contributions.

Solvent may be used as an internal standard to measure the solute non-linearity, but there are still large uncertainties in the non-linear susceptibility that propagate to the solute optical constants.  
More work should be done to reduce this uncertainty and characterize the dispersion of non-linear susceptibility of solvents.  

Absolute nonlinearities are an important property to study in material systems because their relation to linear susceptibilities informs on the underlying physics.  For MR-CMDS, it is important to identify how to extract these non-linearities.  
We have demonstrated ultrafast MR-CMDS as a viable method to extract the absolute non-linear susceptibility by using CCl$_4$ as an internal standard.  
The extraction requires accounting for the impulsive population creation, as well as absorptive propagation effects within the sample.  
These absorptive effects are also crucial factors for general analysis of MR-CMDS spectra.


