Rate equation analysis and energy transfer of Er3+-doped Ga2S3–GeS2–La2S3 glasses

Decay curves of 1.5 μm (4I13/2) and 1.0 μm (4I11/2) emissions from Er3+ ions in Ga2S3–GeS2–La2S3 glasses were measured by the excitation of a 1.5 μm and a 980 nm laser diode pump. The decay curves were simulated using rate equations for a model consisting of six levels of the Er3+ from the ground state. The rate equations contained five unknown parameters, i.e., excited state absorption cross sections of 4I13/2 → 4I9/2 (σesa24) for 1.5 μm excitation and 4I11/2 → 4F7/2 (σesa36) for 980 nm excitation, cooperative upconversion coefficients of (4I13/2, 4I13/2) → (4I9/2, 4I15/2) (C2) and (4I11/2, 4I11/2) → (4F7/2, 4I15/2) (C3), and an energy back-transfer coefficient of (4I9/2, 4I15/2) → (4I13/2, 4I13/2) (C2r). These parameters were estimated by fitting the simulated curves to the measured ones. The obtained values were σesa24=0.3×10−20 cm2, σesa36=0.5×10−20 cm2, C2=30–40×10−18 cm3/s, C3=20–25×10−18 cm3/s, and C2r=5×10−18 cm3/s.