Numerical study on upconversion random lasing in strong scattering disordered medium

The upconversion random lasing properties in two-dimensional (2D) disordered medium was studied. Based on the time-dependent theory, a model for upconversion random laser was established. The Maxwell equations and rate equations were combined and solved by using the finite different time domain (FDTD) method. Results show that the emission at 381 nm is determined by the pumping intensity. For low pumping rates, the 381 nm signal is mainly contributed from the transition 4D3/2 → 4I11/2 while the transition 4D7/2 → 4I13/2 is negligible. When the pumping rate increases to a certain value, the intensity of these two upconversion signals are comparable. The duration of the pulse from the transition 4D7/2 → 4I13/2 is short while the emission from 4D3/2 → 4I11/2 has a long fall time. As the pumping rate increases, the width and the peak interval of two pulses will decrease simultaneously. The simulation results may provide a control method of upconversion random lasers.