Mode amplitude force comparison

Isotope superlattices of nonpolar semiconductors gave an insight on how the coherent optical phonon wavepackets are created [49]. High-order coherent confined optical phonons were observed in 70Ge/74Ge isotope superlattices. Comparison with the calculated spectrum based on a planar force-constant model and a bond polarizability approach indicated that the coherent phonon amplitudes are determined solely by the degree of the atomic displacement, and that only the Raman active odd-number-order modes are observable. 

In the limit of small wave numbers of the forcing in comparison to the wave number of the fastest growing mode of the unforced system, q/km stationary solution yq can be determined and the neutral stability condition a(a,s,q) = 0 can be solved analytically in a perturbative way (see [114] for details). With the resulting analytical solution for A the following expression for the critical forcing amplitude is obtained ... 

Clearly, the best correlation pattern complying exactly with the expected Lorentzian form is obtained in the case of the AvAF amplitudes in connection with a comparison of frequencies with adiabatic internal frequencies (Og. Adiabatic internal modes, the amplitude definition of Eq. (64) and the force constant matrix f as a suitable metric for comparison provide the right ingredients for a physically well-founded CNM analysis. 

---