Reversal of wave momentum in isotropic left-handed media

The electromagnetic wave momentum is derived for a Lorentz medium and applied to study the momentum transfer to stationary, isotropic left-handed materials. The model includes material dispersion and losses, which are necessary for a causal medium with negative index of refraction. The results provide a rigorous proof of the force on free currents in a lossy medium and a validation of the theoretical separation of force based on the real and imaginary parts of the permittivity and permeability. The resulting electromagnetic wave momentum conservation theorem proves that the momentum flux of a monochromatic wave in an isotropic left-handed material is opposite to the power flow direction. However, the momentum density in a lossy medium with a negative index of refraction may be parallel or antiparallel to the power flow. The results are applied to predict the reversal of radiation pressure on free currents in a material with a negative index of refraction. Furthermore, conservation of momentum at a material boundary states that the tangential component of the wave momentum is conserved. Thus there is no electromagnetic shear force at the boundary between isotropic media, regardless of the sign of the refractive index.