Left-handed electromagnetic waves in materials with induced polarization and magnetization

We analyze the properties of electromagnetic waves inside materials with induced polarization and magnetization. We show that if the polarization and magnetization of the material are sufficiently large and appropriately phased, then the system supports the formation of left-handed waves. In some respects, such a system behaves similarly to materials with a negative index of refraction, yet there is one important advantage: Left-handed waves in materials with induced polarization and magnetization do not require as stringent material properties (such as the strength of resonances and the density of radiators). We numerically investigate the formation and propagation of such left-handed waves using finite-difference approximation to Maxwell’s equations. We also discuss possible experimental observation of these ideas in a rare-earth-doped crystal.