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21 December 1994 Mathematical modeling of the light pulse generation by a thin layer of inverted medium
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Using the semiclassical approach the simulation of the light pulse generation by a thin layer of quantum two-level dipoles has been performed. The state of each dipole is governed by Bloch equations for individual density matrix elements under condition of phase relaxation absence. Identical dipoles are located at the nodes of 2-D grating with corresponding sizes Lx, Ly and are considered as pointlike sources of classical field. At the initial moment all the dipoles are in an inverted state Initiation of the pulse was carried out by either incoherent spontaneous decay (superfluorescence mode simulated by setting of small random polarisation with *-correlation) or coherent initial state. Based on the numerical solution the kinetics of dipoles characteristics and evolution of the radiation directivity pattern have been calculated. The influence of the initial state and short-range Coulomb dipole-dipole interaction on the pulse characteristics have been analysed. Tending of axis X to be a direction of primary amplification of pulse with increasing of inequality Lx > Ly has been traced. The comparison of the results obtained with the results of paraxial approximation that uses the concept of slowly varying along axis X amplitudes of the electric field and medium polarisation has been done.
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Yuri A. Avetisyan "Mathematical modeling of the light pulse generation by a thin layer of inverted medium", Proc. SPIE 2312, Optics in Atmospheric Propagation and Random Phenomena, (21 December 1994);

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