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We apply the complex two-dimensional stationary-phase method for problems of electromagnetic waves radiation from the moving modulated sources in dispersive and lossy medium. The explicit formulas for fields generated by a moving source, the Doppler effect, and the retarded time are obtained. We apply the developed approach to numerical study of the Cherenkov radiation in a dispersive medium (Drude model). Our simulations have shown that in double negative dispersive metamaterials, the Cherenkov cone splits in two branches. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We numerically studied the spectrum of Cherenkov optical radiation by a nonrelativistic anisotropic electron bunch crossing 3D dispersive metamaterial. A practically important case when such a medium is described by Drude model is investigated in details. In our theory only parameters of a metamaterial are fixed. The frequency spectrum of internal excitations is left to be defined as a result of the numerical simulation. It is found that a periodic field structure coupled to plasmonic excitations is arisen when the dispersive refractive index of a metamaterial becomes negative. In this case the reversed Cherenkov radiation is observed. [ABSTRACT FROM AUTHOR]