## 2 Material Properties
### Optical Constants  
The fast non-volatile phase transition of GST is accompanied by a large change of optical constants, which results in large contrast in optical reflectivity [40]. This large optical contrast is employed in optical data storage, such as rewritable DVD's. The optical constants of GST are important in describing how the light wave interacts with the GST-based optical devices. Exact evaluation of the optical constants is critical for practical applications in integrated and free-space optical devices, such as spatial light modulators, filters, integrated modulators, and optical switches. Since the amorphous state of GST is constructed from predominantly covalent bonds, it tends to have a lower refractive index [54]. On the other hand, the large refractive index at crystalline state is a result of highly polarizable delocalized \(p\)-orbital resonant bonding [55]. [PERSON] et al. demonstrate the remarkable change of the short-range order upon crystallization of amorphous GST [2] and GeTe [56] by performing the Extended x-ray-absorption fine structure spectroscopy (EXAFS) study. Since this short-range order change does not show in the conventional covalent semiconductors, suggesting the short-range order variation is related with the optical contrast in GST alloys. [PERSON] et al. provided an explanation for the change of the optical absorption upon amorphization in Ge\({}_{1}\)Sb\({}_{2}\)Te\({}_{4}\) and GeTe [57]. They conclude that the changes in the number of bonds and in the local order upon amorphization result in significant changes in the oscillator strength, which results in a profound optical contrast between amorphous and crystalline states. [PERSON] et al. also proposed the large optical contrast relays on the significant change in bonding which was studied by measurements of the electronic polarizability [55].  
A standard technique for describing the dispersion relation in an absorbing material is through an oscillator model. the Lorentz, Harmonic, and Gaussian models as the standard and commonly used ones. For transparent materials, on the other hand, the index can be described by the Cauchy model or the Sellmeier relationship. The Cauchy model is given by:  
\[n(\lambda)=A_{0}+\frac{10^{6}A_{1}}{\lambda^{2}}+\frac{10^{12}A_{2}}{\lambda^{ 4}}+\frac{10^{18}A_{3}}{\lambda^{6}}\]  
\[\kappa(\lambda)=B_{0}+\frac{10^{6}B_{1}}{\lambda^{2}}+\frac{10^{12}B_{1}}{ \lambda^{4}}\]  
where A, and B parameters are used to fit the refractive index of the material.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & \multicolumn{6}{c}{**Peak Position (cm\({}^{-1}\))**} \\ \hline Amorphous & 55 & 65 & 80 & 136 & 146 & 158 & 209 \\ Crystalline (hcp) & 55 & 72 & 94 & 113 & 142 & 173 & 195 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The assignments of phonon modes in GST material by using seven Gaussian oscillators.  
Figure 10: The experimental Raman spectra and the corresponding fitted spectra of GST at (**a**) amorphous state and (**b**) hcp crystalline state. Adapted with permission from Reference [51]. ©2018 International Society for Optics and Photonics.  
As an example, Figure 11, the fitted refractive index and extinction coefficient along the phase transition were reported [15] recently. The optical constants extraction of the optical constants was realized by fitting the measured reflection and transmission spectra from GST thin films to the above Cauchy model. The reflection and transmission of the samples in infrared were measured by Fourier-transform infrared spectroscopy (FTIR). By calculating the optical absorption coefficient, other researchers have reported similar dispersion relations for GST [58; 59; 60; 61].  
As shown in Table 3, the degree of the optical contrast change \((n_{c},k_{c}-n_{a},k_{a})\) at 405 nm wavelength were summarized. The larger content of Ge in the material, the higher degree of contrast in optical constants, which indicates that the GeTe-rich composition is suitable for the Blu-ray Discs from the viewpoint of optical constant [8].