Spatial resonances of the Cherenkov emission in dispersive metamaterials
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Spatial resonances of the Cherenkov emission in dispersive metamaterials GennadiyBurlak and Erika Martinez-Sanchez Center for Research on Engineering and Applied Sciences, Autonomous State University of Morelos, Cuernavaca, Mor.Mexico ABSTRACT We systematically study the Cherenkov optical emission by a nonrelativistic modulated source crossing 3D dispersive metamaterial. It is found that the interference of the field produced by the modulated source with the periodic plasmonic-polariton excitations leads to the specific interaction in the frequency range where the dispersive refractive index of a metamaterial is negative. Such resonance considerably modifies the spatial structure of the Cherenkov fieldand the reversed Cherenkov emission. In our study parameters of metamaterial and modulated source are fixed while the frequency spectrum of the plasmonic excitations is formed due to the fields interplay in the frequency domain. INTRODUCTION Nanophotonics is the study of the behaviour of light on the nanometer scale with involving the interaction of light with nano-structures. Novel optical properties of materials results from their extremely small size that have a variety of applications in nanophotonics and plasmonics. The investigations of optical negative-index [1] metamaterials (NIM) using the nanostructured metal-dielectric composites already have led to both fundamental and applied achievements that have been realized in various structures [2]-[33]. The main applications of negative index metamaterials (or left-handed materials (LHM)) are connected with a remarkable property: the direction of the energy flow and the direction of the phase velocity are opposite in NIM that results unusual properties of electromagnetic waves propagating in these mediums. Cherenkov radiation by a charged source that moves in a left-handed material and has not the intrinsic frequency has been studied in number of works [17]-[23]. Both experimental and theoretical frameworks are investigated; see review [18] and references therein. However in some important cases a moving particle has the intrinsicfrequency [27] Z 0 , for instance the ion oscillating at the transition frequency Z 0 . In this paper the Cherenkov optical radiation in 3D metamaterials by a nonrelativistic modulated source having the intrinsic frequency Z 0 with an emphasis on the dispersive properties of the medium is numerically studied. We performed the FDTD simulations with the use of the material parameters at various modulating frequencies Z 0 , however without references to the operational frequency range. THEORY In metamaterials, it is necessary to treat electromagnetic wave interactions with a metal ingredient using a dispersive formulation that allows correct description of the internal electron dynamics. In this paper we exploit the Drude model that became widely used for modelling in complex materials where for a range of frequency the negative refraction index n is expected. The Maxwell equations read
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