DATA: 17-05-2017

The first part of the talk is devoted to the problem of excitation of the classical electromagnetic field in a cavity containing a thin slab with a time-dependent conductivity. This study was induced by the experiments on the Dynamical Casimir Effect in three-dimensional electromagnetic cavities, containing a thin semiconductor slab, periodically illuminated by strong short laser pulses, performed at Legnaro (MIR experiment). The main goal is to find the conditions, under which the initial nonzero classical field could be amplified after a single pulse (or a series of pulses). I have succeded to find approximate analytical solutions to the infinite set of coupled ordinary differential equations, describing the evolution of the classical electromagnetic field modes inside such a cavity, in the cases of small and big maximal values of the conductivity and variation of the dielectric permeability.I show that the single-mode approximation, used in the previous studies, can be justified in the case of small perturbations. But the initially excited field mode cannot be amplified in this case, if the laser pulses generate free carriers inside the slab. The amplification could be possible, in principle, for extremely high maximal values of conductivity and the concentration of free carries created inside the slab (the model of almost ideal conductor), under the crucial condition, that the variation of the dielectric permeability is negative. This result, following from a simple approximate analytical solution, is confirmed by exact numerical calculations. However, the evaluations show, that the necessary energy of laser pulses must be, probably, unrealistically high. The second part of the talk is devoted to analytical solutions to the problem of mode splitting caused by the presence ofa thin plain magnetized slab, placed in a rectangular electromagnetic cavity. Such solutions are found in two special cases: an infinite slab between two ideal infinite plain mirrors (1D model) and a 2D model of a cavity confined in the direction of permanent magnetization. Under the resonance conditions, the time-dependent magnetization vectors inside the slab are strongly enhanced, with opposite directions in the split modes. For realistic parameters, the frequency splitting does notdepend on the dielectric constant of the slab and the Landau--Lifshits--Gilbert damping coefficient, whereas the loadedcavity quality factor is not sensitive to the slab position.


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