# Characterization of Chirality in Diffractive Metasurfaces by Photothermal Deflection Technique
## 3 Results
### Determination of the Induced Temperature of the Metasurface
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Wavelength, nm**} & \multirow{2}{*}{**Quantity**} & \multicolumn{6}{c}{**Diffraction Order m**} \\  & & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \multirow{4}{*}{514} & \(R\), mm & 1.78 & 3.78 & 8.93 & 3.78 & 1.78 & 1.22 \\  & \(d\), mm & +0.01 \({}^{2}\) & \(-3.13\) & \(-8.70\) & \(-1.89\) & +0.77 \({}^{1}\) & +1.19 \({}^{1}\) \\  & \(\beta\), deg & 77 & 133 & 180 & 227 & 283 & 0 \\  & \(\theta\), deg & 42 & 62 & 77 & 62 & 42 & 31 \\ \hline \multirow{4}{*}{496} & \(R\), mm & 1.66 & 3.36 & 6.08 & 3.36 & 1.66 & 1.14 \\  & \(d\), mm & \(-0.03\)\({}^{2}\) & \(-2.79\) & \(-5.93\) & \(-1.69\) & +0.70 \({}^{1}\) & +1.11 \({}^{1}\) \\  & \(\beta\), deg & 78 & 133 & 180 & 227 & 282 & 0 \\  & \(\theta\), deg & 40 & 59 & 72 & 59 & 40 & 30 \\ \hline \multirow{4}{*}{458} & \(R\), mm & 1.45 & 2.72 & 4.00 & 2.72 & 1.45 & 0.98 \\  & \(d\), mm & \(-0.07\)\({}^{2}\) & \(-2.28\) & \(-3.90\) & \(-1.41\) & +0.57 \({}^{1}\) & +0.95 \({}^{1}\) \\ \cline{1-1}  & \(\beta\), deg & 80 & 134 & 180 & 226 & 280 & 0 \\ \cline{1-1}  & \(\theta\), deg & 36 & 54 & 63 & 54 & 36 & 26 \\ \hline \hline \end{tabular} \({}^{1}\) The scan in Figure 3b,d are from d = \(-\)1 mm to 1.5 mm; only \(m=5\) and \(m=6\) fall in such a range. \({}^{2}\) The diffracted order \(m=1\) cannot be seen because it is hidden by the central heat source at \(d=0\).  
\end{table} 
Table 2: Oblique incidence: theoretical expectation of the geometrical parameters of the heat sources produced by the absorption of the diffracted beams. 514 nm, which, from numerical simulations, seems responsible for the enhancement of the chirality in this structure (see Table 1). The values of the maximum temperature rise and chirality are reported in Table 3 for each heat source, for both 514 and 458 nm. Circular dichroism as a percentage is calculated from the temperature peaks as CD% = 100% (\(T_{LCP}-T_{RCP}\))/(\(T_{LCP}+T_{RCP}\)). The values of CD agree with those reported in [13; 26]. Results for \(m=1\) are missing because the signals from the heat source are hidden by the higher signal coming from source \(m=0\), and Equation (8) cannot be applied. Results for \(m=2\) at 458 nm are only partially plotted due to data corruption, and interference effects with the heat source for \(m=3\) in Figure 3a. Finally, we apply the numerical method from Section 2.2 to visualize the power absorbed in the unit cell at 514 nm, at a normal incidence, for orders 5 and 6 (from Figure 6). In Figure 7, we confirm that, when the metasurface is excited with LCP, the order with \(m=5\) results in higher absorption in the unit cell than for the RCP excitation. The opposite behavior is found for the order with \(m=6\). We can clearly see that this order results in higher absorption in the unit cell, especially in the volume of the ENHA. In conclusion, numerical simulations of the single metasurface unit cell are in good agreement with the thermal reconstruction from the PDT data. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Wavelength, nm**} & \multirow{2}{*}{**Peak Temp**} & \multirow{2}{*}{**Pump**} & \multicolumn{5}{c}{**Diffraction Order m**} \\  & & **0** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \multirow{3}{*}{514} & \(T_{RCP}\)\({}^{\circ}\)C & \(11.5\) & - & 0.22 & 0.25 & 0.98 & 0.38 & 0.45 \\  & \(T_{LCP}\)\({}^{\circ}\)C & \(11.5\) & - & 0.16 & 0.35 & 0.78 & 1.47 & 0.10 \\  & CD, \% & 0 & - & \(-16\) & 17 & \(-11\) & +59 & \(-64\) \\ \hline \multirow{3}{*}{458} & \(T_{RCP}\)\({}^{\circ}\)C & \(11.0\) & - & 0.16 & 0.15 & 0.75 & 1.02 & 0.41 \\  & \(T_{LCP}\)\({}^{\circ}\)C & \(11.0\) & - & 0.14 & 0.13 & 0.71 & 0.98 & 0.41 \\ \cline{1-1}  & CD, \% & 0 & - & \(-6\) & \(-7\) & \(-3\) & \(-2\) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum local temperature rise for each diffracted order, as calculated by Equation (8) from PDT data in Figure 3, for excitation at 514 and 458 nm. The peak temperature is calculated for both RCP and LCP.