# Full Characterization of a Molecular Cooper Minimum Using High-Harmonic Spectroscopy
## 3 Results and Discussion  
### Intensity Scaling and Calibration  
Before applying the SFA attochirp removal to the CM of methyl chloride, we first confirmed its validity in the case it was initially meant to describe: the ionization of an atomic target. Xenon was chosen due to its low ionization energy relative to the other noble gases, which provided a better comparison to these molecular targets. Shown in Figure 1 are the \(\tau_{HHG}\) values resulting from HHG in xenon at five intensities ranging from 6.37 \(\times\) 10\({}^{13}\) to 10.50 \(\times\) 10\({}^{13}\) W/cm\({}^{2}\), and the fitted recombination times (of which the derivative is the attochirp [20]) plotted as solid lines. For all scans, the GD from the aluminum filter and atomic detection gas were removed before fitting for the attochirp, such that only the laser intensity and an arbitrary offset were involved in the fitting. Because the focal geometry was unchanged when using different input powers, the laser intensity was expected to scale linearly with the measured power. This was tested by fitting the SFA intensity to the curve with the lowest energy, and, for the remainder of the datasets, by scaling using the measured input power, such that their ratios were fixed by the experiment. Details of the quality of the fit can be found in Appendix A, where it is shown that all datasets were, within experimental error, of zero deviation from the calculated SFA.  
Next, we extended the SFA to the molecular case. The applicability of the SFA emission time to HHG in polyatomic molecules is nontrivial; along with distortion of the GD from the CM, interference between multiple ionization centers [30] or multiple orbitals can affect the GD [31; 32]. Furthermore, an implicit assumption in the SFA calculation is that the electron, following tunneling ionization, is unaffected by  
Figure 1: Laser intensity scaling in xenon. Measured extreme ultraviolet (XUV) group delays (circles) are shown from harmonic generation in xenon gas, fitted with intensities as shown in the legend. The lowest-intensity curve was fitted for intensity using Equation (9), and this fitted intensity was scaled according to the measured input power ratio for each additional scan (curves). Each intensity was separated by 0.2 fs for visual clarity.  
the ionic potential. The application of this assumption to species with a larger spatial extent is unclear, and it may break down in the case of molecules where the hole density is comparable in size to the electron trajectory. For molecules much smaller than the electron's excursion length (up to several nm for MIR driving fields), we expect this assumption to remain valid; the experiment confirmed its validity for methane.  
Figure 2 shows \(\tau_{HHG}\) at varying laser intensities in methane. As discussed above, the attochirp fitting is best done for targets with negligible contribution to the GD beyond the SFA. Because we did not expect the CM in methyl chloride to be negligible compared to the SFA contribution, we calibrated in a gas with a similar molecular structure to simultaneously maximize the HHG spectral intensity and GD comparisons. Methane was chosen to represent the singular structural dissimilarity of the chlorine substitution to methyl chloride, thus demonstrating that any feature in methyl chloride beyond the SFA was related entirely to the addition of the chlorine atom. Once again, the lowest-intensity dataset was fitted for the laser intensity and the arbitrary shift which minimized the argument of Equation (9), and all other datasets were scaled for intensity by the ratios of their measured input powers, and were fitted only for the arbitrary shift, \(t_{offset}\). As with the xenon result, the quality of the fits is discussed in Appendix A, again demonstrating good agreement with the SFA, and validating its use in describing methane as a reference gas.