We offer a simple route to perfect omnidirectional invisibility in a spectral band of desired width. Our approach is based on the observation that in two dimensions a complex potential v(x,y) is invisible for incident plane waves with a wavenumber not exceeding a pre-assigned value α, provided that its Fourier transform with respect to y, which we denote by v˜(x,Ky), vanishes for Ky≤2α. We can fulfill this condition for potentials modeling the permittivity profile of an optical slab. Such a slab is perfectly invisible for any transverse electric wave whose wavenumber is in the range [0,α]. Our results also apply to transverse magnetic waves propagating in a medium with a relative permittivity ϵ^(x,y) that is a smooth bounded function with a positive real part.