A Backward Zenneck Wave Propagating along a Plane Interface between Media
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ICAL OPTICS
A Backward Zenneck Wave Propagating along a Plane Interface between Media M. V. Davidovich* National Research Saratov State University, Saratov, 410012 Russia *е-mail: [email protected] Received December 3, 2019; revised April 22, 2020; accepted May 4, 2020
Abstract—We consider a surface Zenneck wave that propagates along a plane interface between a vacuum and a medium that is described by an isotropic dielectric permittivity and a surface Zenneck wave that propagates along a plane interface between a vacuum and a medium that is described by isotropic dielectric permittivity and magnetic permeability. In the latter case, we also consider an H wave and the possibility that the real parts of the permittivity and permeability are negative. Forward and backward waves at the boundary of a material with inhomogeneous profiles of the dielectric permittivity and magnetic permeability are considered. The conditions of the existence of forward and backward surface and volume waves, as well as of fast and slow surface waves are investigated. Keywords: Zenneck wave, plasmon–polaritons, backward waves, dispersion equation DOI: 10.1134/S0030400X20090064
INTRODUCTION Backward waves are an interesting phenomenon in wave processes. They have been known since the appearance of classical Lamb’s work [1] and are widely used in technology (e.g., in backward-wave oscillators). In structures, e.g., in slowing systems and photonic crystals, they are caused by infinite reflections and interference, which leads to a zone dispersion structure. In slowing systems and photonic crystals, losses are usually weak, and, an anomalous negative dispersion corresponds to a backward wave. Since 2000, volume backward waves have been intensely searched and investigated in structures and metamaterials (artificial media), which are tried to be described by negative dielectric permittivity ε and magnetic permeability μ. Apart from volume backward waves, surface backward waves, e.g., in thin metal films can also occur [2–4]. In the present work, we will consider surface waves that propagate along simplest structures— vacuum–dielectric and vacuum–magnetodielectric interfaces with dielectric permittivity ε and magnetic permeability μ. The possibility of the existence of surface and volume backward waves will be analyzed. We will also consider the case of simultaneously negative real parts of the permittivities and permeabilities Re(ε) < 0 and Re(μ) < 0, omitting the very controversial issue of the possibility of creating such isotropic artificial media that are described only by two scalar parameters, ε and μ. Also, waves will be considered that propagate along the vacuum–medium boundary with permeabilities or layers that are inhomogeneous
along the normal. Such tasks are more complex, but they allow one to construct a boundary carrying the backward wave. A WAVE PROPAGATING ALONG THE VACUUM–DIELECTRIC BOUNDARY The dispersion relation for a plasmon–polariton propagating along a metal wire was obtained for the first time by Sommerfeld by the
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