# Indirect evaluation of $SnO_{2}$ - $Er^{3+}$ energy transfer coefficient.`

Falconi M.C., Laneve D., Thi Ngoc Tran L., Zur L., Balda R., Fernandez J., Gluchowski P., Lukowiak A., Ferrari M., Prudenzano F.

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VI - Fisica applicata, acceleratori e beni culturali
GSSI Ex ISEF - Aula A - Martedì 24 h 09:00 - 12:00
A theoretical model of the $SiO_2$ - $SnO_{2}:Er^{3+}$ glass-ceramics system is developed in order to investigate the energy transfer occurring between the $SnO_2$ and the erbium ions. Two different pumping schemes are considered: the direct pumping and the indirect pumping. The former employs a 521 nm optical beam to directly excite the erbium ions in the (${}^{4}S_{3/2}$, ${}^{2}H_{11/2}$) energy level, therefore bypassing the excitation path through the $SnO_2$. The latter scheme, on the other hand, aims to excite the $SnO_2$, which exhibits an absorption band around 330 nm, to exploit the strong energy transfer between the $SnO_2$ and the (${}^{4}G_{11/2}$, {{}^{4}G_{9/2}},${}^{2}K_{15/2}$, ${}^{2}G_{7/2}$) energy level of erbium ions. A Finite Element Method simulation of a slab waveguide is performed in order to evaluate the overlap coefficient of the electromagnetic field with the active region. Then, a homemade code solving the rate equations and the small-signal gain at 1533 nm, is implemented for both the direct and indirect pumping schemes. The ratio between the two optical gains is compared with the emission intensity measurement and the estimated value for the $SnO_{2}$ - $Er^{3+}$ energy transfer $K_{tr} = 1.678 \times 10^-{23}$ m${}^{3}$/s is obtained.