Mechanism of transient population inversion in graphene with multi-splitted (interdigitated) top-gate and grounded back gate is suggested and examined for the mid-infrared (mid-IR) spectral region. Efficient stimulated emission after fast lateral spreading of carriers due to drift-diffusion processes is found for the case of a slow electron-hole recombination in the passive region. We show that with the large gate-to-graphene distance the drift process always precedes the diffusion process, due to the ineffective screening of the inplane electric field by the gates. Conditions for lasing with a gain above 100 cm$^{-1}$ are found for cases of single- and multi-layer graphene placed in the waveguide formed by the top and back gates. Both the waveguide losses and temperature effects are analyzed.
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