A systematic approach to investigate lasing and net amplification in plasmonic structures with a finite-difference time-domain method coupled to the rate equations of four-level and six-level atomic systems is developed. The experiment-fitted kinetic parameters are fed into the model to study the mechanism of the coupling of metamaterials and metasurfaces with the gain medium. With the help of such an accurate model, net amplification can be distinguished from time-resolved lasing dynamics for the plasmonic systems coupled with gain.
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