Rate equation analysis and energy transfer of Er 3+-doped Ga 2S 3–GeS 2–La 2S 3 glasses

Abstract

Decay curves of 1.5 μm ( 4I 13/2) and 1.0 μm ( 4I 11/2) emissions from Er 3+ ions in Ga 2S 3–GeS 2–La 2S 3 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 Er 3+ from the ground state. The rate equations contained five unknown parameters, i.e., excited state absorption cross sections of 4I 13/2 → 4I 9/2 ( σ esa24) for 1.5 μm excitation and 4I 11/2 → 4F 7/2 ( σ esa36) for 980 nm excitation, cooperative upconversion coefficients of ( 4I 13/2, 4I 13/2) → ( 4I 9/2, 4I 15/2) ( C 2) and ( 4I 11/2, 4I 11/2) → ( 4F 7/2, 4I 15/2) ( C 3), and an energy back-transfer coefficient of ( 4I 9/2, 4I 15/2) → ( 4I 13/2, 4I 13/2) ( C 2 r ). These parameters were estimated by fitting the simulated curves to the measured ones. The obtained values were σ esa24=0.3×10 −20 cm 2, σ esa36=0.5×10 −20 cm 2, C 2=30–40×10 −18 cm 3/s, C 3=20–25×10 −18 cm 3/s, and C 2 r =5×10 −18 cm 3/s.