Strong electron-Boson coupling effect in the infrared spectra of Tl₂ Ba₂ Ca Cu₂ O_{8+δ}

We report on a study of the in-plane infrared response of a \TBCCO film with $T_c$=108 K. The fingerprint evidence for a strong electron-Boson coupling has been observed. The raw reflectance below T$_c$ exhibits a knee structure at around 650 \cm and the ratio of the reflectances below and above T$_c$ displays a pronounced minimum at around 1000 \cm. In particular, the features appear at higher energy scale than other bilayer cuprates with T$_c$ around 90-95 K. The gap amplitude and the Boson mode energy were extracted from the analysis of the bosonic spectral function. In comparison with several other optimally doped high-Tc cuprates, we find that the gap size scales with T$_c$, but Boson mode energy has a tendency to decrease.