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We outline a method for constructing effectively two-dimensional isotropicoptical media that are perfectly and omnidirectionally invisible for both TEand TM waves provided that their wavenumber does not exceed a preassigned value$\alpha$. This relies on the observation that a complex scattering potential$v(x,y)$ displays perfect invisibility for wavenumbers $k\leq\alpha$ providedthat its Fourier transform with respect to $y$, which we denote by $\tildev(x,\mathfrak{K}_y)$, vanishes for $\mathfrak{K}_y\leq 2\alpha$. We use thisresult to construct the permittivity profile for a realistic optical slab thatis perfectly invisible in the wavenumber window $[0,\alpha]$.

Perfect Broadband Invisibility in Isotropic Media with Gain and Loss