# New Candidate Multicomponent Chalcogenide Glasses for Supercontinuum Generation
## 5 Nonlinear Optical Property Variation
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Composition \& FormOptical Constant**} & **20 mol\% PbSe** & **40 mol\% PbSe** \\ \cline{2-4}  & & **Bulk** & **Bulk** & **Film** \\ \hline \multirow{8}{*}{
\begin{tabular}{c} Sellmeir coefficient [90] \\ \(n=\sqrt{A+\frac{R3^{2}}{\lambda^{2}-C^{2}}+\frac{D13^{2}}{\lambda^{2}-E^{2}}\)} \\ \end{tabular} } & A = \(-\)20.6611 & A = 4.1428 & A = \(-\)17.9359 \\  & B = 28.5635 & B = 4.7716 & B = 27.7528 \\  & C = 0.2312 & C = 0.5591 & C = 0.1949 \\  & D = 10.4782 & D = 41.6340 & D = 1.4171 \\  & E = 90.4186 & E = 168.4897 & E = 36.6873 \\  & 2.8387 at \(\lambda=3\)\(\mu\)m & 3.0118 at \(\lambda=3\)\(\mu\)m & 3.1495 at \(\lambda=3\)\(\mu\)m \\  & Linear refractive index & 2.2845 at \(\lambda=4\)\(\mu\)m & 2.9977 at \(\lambda=4\)\(\mu\)m & 3.1409 at \(\lambda=4\)\(\mu\)m \\  & index & 2.8164 at \(\lambda=5\)\(\mu\)m & 2.9897 at \(\lambda=5\)\(\mu\)m & 3.1358 at \(\lambda=5\)\(\mu\)m \\  & Abbe Number [91] & \(\frac{n_{1-\mu,\mu-1}-1}{n_{1-\mu,\mu-2}-n_{2}}=81.82\) & \(\frac{n_{1-\mu,\mu-1}-1}{n_{1-\mu,\mu-1}-n_{1-\mu,\mu-2}}=90.39\) & \(\frac{n_{1-\mu,\mu-1}-1}{n_{1-\mu,\mu-2}-n_{1-\mu,\mu-1}}=156.27\) \\  & Nonlinear refractive index & \(7.14\times 10^{-5}\)cm\({}^{2}\)/GW & \(11.17\times 10^{-5}\) cm\({}^{2}\)/GW & In progress \\  & Four-photon absorption & at \(\lambda=4\)\(\mu\)m & at \(\lambda=4\)\(\mu\)m & \\  & coefficient & \(4.50\times 10^{-3}\) cm\({}^{5}\)/GW\({}^{3}\) & \(11.05\times 10^{-3}\) & \\  & Nonlinear figure of merit [92] & \(4.8\times 10^{-3}\) at \(\lambda=4\) & \(1.58\times 10^{-3}\) at \(\lambda=4\) & \\  & Linear refractive merit [92] & \(\mu\)m & \(\mu\)m & In progress \\  & Linear refractive index & 2.8007 at \(\lambda=8\)\(\mu\)m & 2.9738 at \(\lambda=8\)\(\mu\)m & 3.1248 at \(\lambda=8\)\(\mu\)m \\  & index & 2.7906 at \(\lambda=10\)\(\mu\)m & 2.9634 at \(\lambda=10\)\(\mu\)m & 3.1168 at \(\lambda=10\)\(\mu\)m \\ (8 \(\mu\)m–12 \(\mu\)m) & 2.7793 at \(\lambda=12\)\(\mu\)m & 2.9517 at \(\lambda=12\)\(\mu\)m & 3.1071 at \(\lambda=12\)\(\mu\)m \\  & Abbe Number [91] & \(\frac{n_{1-\mu,\mu-1}-1}{n_{1-\mu,\mu-2}-n_{1-\mu,\mu-1}}=83.67\) & \(\frac{n_{1-\mu,\mu-1}-1}{n_{1-\mu,\mu-2}-n_{1-\mu,\mu-1}}=88.84\) & \(\frac{n_{1-\mu,\mu-1}-1}{n_{1-\mu,\mu-2}-n_{1-\mu,\mu-1}}=119.59\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Key optical constants including Sellmeier coefficients, linear refractive index, Abbe number, and nonlinear figure of merit for bulk and film glasses with 20 and 40 mol% PbSe. where \(T_{O\alpha(nPA)}\), \(n\), \(\alpha_{n}\) correspond to normalized transmittance in an open-aperture mode, integer, and multiphoton absorption coefficient, respectively [78; 100; 101; 102; 103]. Figure 4c shows nonlinear refractive indices collected from four different locations of 20 and 40 mol% PbSe bulk glasses at 4.5 \(\upmu\)m. The horizontal dotted lines, corresponding to average values, indicate that the nonlinear refractive index of the glasses increases from \(\sim\)7.14 \(\times\) 10\({}^{-6}\) to \(\sim\)1.17 \(\times\) 10\({}^{-6}\) cm\({}^{2}\)/GW as the concentration of PbSe increases from 20 to 40 mol%. This corresponds to a change in the Pb-rich phase, changing from the secondary phase (in the 20% samples) to the matrix phase (40%) and a corresponding increase of absolute Pb content from (5.0 to 11.4 at%). While the magnitudes of the measured four-photon absorption coefficient are low for the glasses, the values likewise increase from \(\sim\)4.50 \(\times\) 10\({}^{-3}\) to \(\sim\)11.05 \(\times\) 10\({}^{-3}\) cm\({}^{5}\)/GW\({}^{3}\) with increasing PbSe concentration, as shown in Figure 4d. [PERSON]'s rule dictates that an increase in optical linearity induces an increase in nonlinearity (\(n_{2}\)) and reduced optical band gap energy (\(E_{\rm g}\)) [20].