We calculated analytic expressions for the absorption coefficient (ACF) of a weak electromagnetic wave (EMW) by confined electrons in cylindrical quantum wires (CQW) in the presence of laser radiation by using the quantum kinetic equation for electrons in the case of electron-optical phonon scattering. The ACF of a weak EMW depends on the intensity E01 and frequency Ω1 of the external laser radiation (E1 = E01sin(Ω1t+φ1)); the intensity E02 and frequency Ω2 of the weak EMW (E2 = E02sin(Ω2t)), the temperature T of the system and the radius R of CQW. Then, the analytic results are numerically calculated and discussed for GaAs/AlAs CQW. The numerical results show that the ACF of a weak EMW in a CQW can have negative values. So, in the presence of laser radiation, under proper conditions, the weak EMW is increased. This is different from the similar problem in bulk semiconductors and from the case of the absence of laser radiation.
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