The backward-wave phenomenon in an isotropic medium is investigated from a purely wave propagation point of view. The functional form for the index of refraction necessary to produce such behavior is derived using the condition that the phase and group-velocity vectors are antiparallel. It is shown that, in the case considered, the backward-wave propagation can be attained only in a medium where the index is negative. A more general case is then considered where the angle between the phase velocity and group velocity is allowed to vary between 90° and 270°. It is shown that such behavior requires propagation through an anisotropic medium where at least one of the axes has a negative index and the general form of the index along each of the three principal axes is derived. The condition that the group velocity must be positive in the transmission passband is then used to obtain the required minimum dispersion for a medium with negative index for both the isotropic and the anisotropic cases.
© 2006 Optical Society of AmericaPDF Article