On the counterpropagation of waves

Abstract

This work analyses the counterpropagation of transversal plane waves in a linear, homogeneous, nondispersive, and isotropic medium. Although this is a traditional subject in disciplines associated with wave phenomena, a propagation analysis is not found in the literature. With this purpose, the resultant wave and consecutively its phase velocity in such system are obtained analytically. Instead of what happens with the individual waves, the analytical results demonstrate that the phase velocity of the resultant wave actually is not a constant and depends explicitly of the time or the spatial coordinates, and principally depends of the amplitudes of the individual waves. This last remarkable feature, when considering as example electromagnetic systems, can be used to adequately control and accelerate particles in a charged medium. Full agreement between the analytical and numerical results is found.