Non-Linear Spectroscopy TPA and EA

Since it is known that localized states have a weak contribution to the EA spectra due to their low polarizability [33], the EA result indicates that localized states are indeed involved in bands II and III. This, however, cannot resolve the controversy of the origin of band II, since band II in the leading models is partially due to localized states. 

There are three main EA spectral features in the energy range of band I a derivative-like feature with zero-crossing at 2.29 eV, followed by vibrational features, and an induced absorption band between 2.9 and 3.2 eV. The features below 2.5 eV are the results of a redshifted 1B exciton energy, and its phonon side-bands (Stark shift). These features are more easily observed in EA than in 

The induced absorption band at 3 eV does not have any corresponding spectral feature in a(m), indicating that it is most probably due to an even parity state. Such a state would not show up in a co) since the optical transition Mg mAg is dipole forbidden. We relate the induced absorption bands to transfer of oscillator strength from the allowed Mg (absorption band I) to the forbidden 

We successfully simulated the EA spectrum by calculating the imaginary part of the third order optical non-linear susceptibility [35]. The sum over states (SOS) model developed by Orr and Ward [34] was used to calculate the third-order optical susceptibility % (-(o a)i,a)2,(of) and simulate the transient PM and EA spectra reported here [35]. This particular model is useful because its formulation is not affected by singularities as are some other common formulations 

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