Exactness of the first Born approximation in electromagnetic scattering

For the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of the medium under which the first Born approximation yields the exact expression for the scattered wave whenever the incident wavenumber $k$ does not exceed a pre-assigned value $\alpha$. We also show that under this condition the medium is omnidirectionally invisible for $k\le \alpha \mathrm{/}2$, i.e., it displays broadband invisibility regardless of the polarization of the incident wave.