Dear Nikolay Pavlov, if you can help me look at those two pictures, I had the inverse result for the one mixe with 980nm. The one mixte with 980nm is slower with decay excite just with 808nm.
I might be wrong but what I see: both 808 and 980nm illumination cause shortening of lifetime. 980 nm seems just to be more efficient than 808 nm regarding this effect. The effect only visible at low 355nm excitation power ( at high 355nm power direct recombination beside the traps may indeed dominate).
Regarding why 980nm is more efficient than 808nm - it might be it is better aligned with energy of the traps.
Jocelyne Neema Angelani Also note that recombination under high excitation might be 'quadratic' = proportional to square of carrier concentration (or better to say to product of approx equal electron and hole concentration). In that case it decays roughly as ~ 1/time not as exp(-t/tau).
1) Regarding difference in 1/e ... 1/eee - My guess you may see a superposition of some fractions of traps having different lifetimes perhaps you may look into techniques like that for analysis : https://rdcu.be/cBdEb
2) The trapping/detrapping energy might be corresponding to infrared quanta you mentioned 808 / 980nm. It might be rather wide, but still kind of resonant absorption. Also, if it is more toward 980nm note that you have a bit more quantas per mW at longer wavelength and also the near-resonant absorption cross-section may scale as Lambda^2.