Crank-Nicholson method for rate equations in powder random lasers

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

García-Ramiro, B.^1 ; Illarramendi, M.A.^2 ; Zubia, J.^3

Department of Applied Mathematics, E.U. Ingeniería Técnica Industrial de Bilbao, Universidad Del País Vasco UPV/EHU, Paseo Rafael Moreno Pitxitxi 3, Bilbao

48013, Spain^1

Department of Applied Physics i, Escuela Superior de Ingeniería, Universidad Del País Vasco UPV/EHU, Alda. Urquijo s/n, Bilbao

48013, Spain^2

Department of Communications, Escuela Superior de Ingeniería, Universidad Del Pais Vasco UPV/EHU, Alda. Urquijo s/n, Bilbao

48013, Spain^3

关键词: Coupled equation;    Crank-Nicholson method;    Diffusion equations;    Dopant molecules;    Incident pulse;    Light diffusion;    Pumping schemes;    Two-photon excitations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012077/pdf
DOI  :  10.1088/1742-6596/574/1/012077

来源: IOP

【 摘 要 】

In this work, we show the resolution of the rate equations in powder random lasers by using the Crank-Nicholson finite difference method. Light propagation in our powders is described by the model of light diffusion. The generalized time-dependent random laser equations describing our system are formed by three differential coupled equations: two diffusion equations for the pump and emitted light and a rate equation for the density of the dopant molecules in the excited state. The system has been solved for two pumping schemes (one-photon and two-photon excitation) and for a wide range of temporal incident pulses (from femtoseconds to nanoseconds).