On electromagnetic waves with a negative group velocity
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MA PHYSICS
On Electromagnetic Waves with a Negative Group Velocity V. P. Makarov, A. A. Rukhadze, and A. A. Samokhin Prokhorov Institute of General Physics, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991 Russia Received January 22, 2009
Abstract—Recent publications devoted to the electrodynamics of media in which waves with a negative group velocity can exist are discussed. The properties of such waves have been studied from the beginning of the past century, and the most important results in this field were obtained by Soviet physicists in the 1940s– 1950s. However, in most recent publications, this circumstance has not been taken into account. DOI: 10.1134/S1063780X10130076
1. INTRODUCTION In this paper, we discuss recent publications initi ated by [1–3] and devoted to the electrodynamics of media in which waves with a negative group velocity can exist. It has long been known from electrodynam ics of continuous media and wave theory that the phase and group velocities of a wave propagating in a medium are not equal and may, in particular, be directed oppositely [4–19]. In works and lectures by L.I. Mandelstam [7–9], it was noted that, when a wave is incident obliquely from vacuum onto a medium in which the phase and group velocities have opposite directions, the refracted wave is deflected toward the other side from the normal as compared to the com mon case of media in which these velocities are directed alike. It is stressed in [9] that the questions under review are utterly general and concern propaga tion of waves of various types. As early as 1904, Lamb [4] devised mechanical models of onedimensional “media” in which the group velocity could be negative, i.e., could be directed against the phase velocity. Later on, Mandel stam wrote in [9] about actual media in which, within a certain range of frequencies, the phase and group velocities were indeed directed toward one another, as is the case for “optical” modes of acoustic spectrum of a crystal lattice considered by M. Born. Situations in which the phase and group velocities are directed toward one another and the peculiarities of wave refraction at the boundaries of such media were also discussed in the book by Schuster [6] with a reference to [4]. Paper [4] was also cited in the context of the negative group velocity in the book [5], which was published in many editions in England and the United States. The book by Schuster [6] has run through several English and Russianlanguage edi tions, too. D.V. Sivukhin [10] pointed out that the case in which both the dielectric permittivity ε and magnetic
susceptibility μ are negative corresponds to antiparal lel directions of the phase and group velocities; how ever, he considered that the question of the possibility of existence of such media remained open. In his Course of General Physics [15], this question was not discussed directly and the statement that the wave phase and energy in isotropic media propagate in the same directions [15, Section 64] in fact concerns media with a magneti
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