Optical properties of the optimally doped Ca$_{8.5}$La$_{1.5}$(Pt$_3$As$_8$)(Fe$_{2}$As$_{2}$)$_5$ single crystal

We have measured the reflectivity of the optimally doped Ca$_{8.5}$La$_{1.5}$(Pt$_3$As$_8$)(Fe$_{10}$As$_{10}$) single crystal ($T_c$ = 32.8K) over the broad frequency range from 40 to 12000 $cm^{-1}$ and for temperatures from 8 to 300 K. The optical conductivity spectra of the low frequency region ($< 1,000$ $cm^{-1}$) in the normal state (80 K $< T \leq$ 300 K) is well fitted with two Drude forms, which indicates the presence of multiple bands at the Fermi level. Decreasing temperature below 80 K, this low frequency Drude spectra develops pseudogap (PG) hump structure at around $\approx 100$ $cm^{-1}$ and continuously evolves into the fully opened superconducting (SC) gap structure below $T_c$. Theoretical calculations of the optical conductivity with the preformed Cooper pair model provide an excellent description of the temperature evolution of the PG structure above $T_c$ into the SC gap structure below $T_c$. The extracted two SC gap sizes are $\Delta_S$ = 4.9 $meV$ and $\Delta_L$ = 14.2 $meV$, suggesting Ca$_{8.5}$La$_{1.5}$(Pt$_3$As$_8$)(Fe$_{10}$As$_{10}$) as a multiple gap superconductor with a mixed character of the weak coupling and strong coupling superconductivity.