Refraction into an Isotropic Medium with Negative Permittivity and Permeability

Abstract

Generalized representations of the refraction law are obtained for electromagnetic waves at the interface of transparent isotropic media with positive and/or negative permittivity and permeability.The phenomenon of reversed (negative) refraction has been well known among physicists for a long time. Sir Horace Lamb [1], responding to the model proposed by Lord Rayleigh (John Strutt) of a device in the form of a clamped wire subjected to tension and torsion [2], conjectured that in a cylindrical wire under certain conditions vibrations can also arise having group velocity that is negative with respect to the phase velocity. He considered the passage of a one-dimensional wave from a segment of the wire with the usual vibrational regime to a segment with the anomalous regime and was the first to observe that the transmitted wave should have a phase velocity oppositely directed relative to the phase velocity of the wave incident on the inhomogeneity. That same year, A. Schuster noticed and graphically elucidated [3, p. 317, Fig. 179] the curious result of the negative angle of the refracted light wave in a medium with opposed phase and group velocities, which was necessary to ensure unidirectional translation of the intersection lines of the wave fronts of the incident and refracted wave with the boundary of the two media. In optics and electrodynamics the simplest isotropic medium, at the boundary with which negative refraction can take place, is a magnetodielectric with negative values of its electric permittivity ( 0   ) and magnetic permeability ( 0   ), which was first pointed out by D. V. Sivukhin [4] and V. G. Veselago [5-7]. Negative refraction is most graphically manifested, for example, for oblique incidence of a plane wave from vacuum ( 0    and 0    ) into anti-vacuum (this term was proposed in [8], 0    and 0    ), where 0 and 0  are the electric and magnetic constants. In this case, reflection of a wave from the interface does not take place, but the initial direction of propagation as the wave propagates into the second medium is changed to the direction of the wave vector of the absent reflected wave. Here the refracted wave, being a backward wave, transfers energy in accordance with the radiation condition from the interface into the periphery of the second medium. References [9][10][11] are dedicated to historical and other aspects of the electrodynamics of media with backward waves and their discussion in the literature. A modification of Snell's refraction law was proposed in [5][6][7] relevant to the interface with a hypothetical lefthanded medium with both  and  negative, presaging the introduction of the new concept of a negative refractive index. After the first experimental confirmation of the phenomenon of negative refraction for microwaves [12] and the appearance of the concept of electromagnetic metamaterials, the English-language version [7] of Veselago's paper [6] acquired some fame and became widely cited and much in demand. Despite some doubts and objections [13][1...

On the Sign of the Refractive Index for Metamaterials

“…n is a positive value. This formula is in complete agreement with the vector version of the negative refraction law [11]. For the incident and refracted wave rays, formula (1) should be changed:…”

“…with the subsequent use of the algebraic form of the complex number. In [27], Eq. ( 10) was solved using unimodular material parameters of the form   (complex sign functions) given in the algebraic form.…”

“…In formula (11), only one root is given; the second root differs by changing the signs of the real and imaginary components in the right-hand side of the formula. Comparing with the Maxwell formula…”

Normal Waves in a Metachiral Post Medium

“…Forward and backward waves refract differently into the same medium. The interface of two birefringent metachiral media is the cause of a number of unusual refraction phenomena; however, one does not need to introduce the term negative refractive index to describe negative refraction as in the case of non-chiral metamaterials (Veselago media) [14]. If the presence of a backward wave is taken as a criterion of metachirality, then metachirality arises in a Post medium (for real impedance Z ), as only the permittivity or the permeability, but not both, takes a negative value.…”