Abstract

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 $\alpha$, provided that its Fourier transform with respect to $y$, which we denote by $\tilde{v}(x,{\mathfrak{K}}_y)$, vanishes for ${\mathfrak{K}}_y\le 2\alpha$. 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 $[0,\alpha ]$. Our results also apply to transverse magnetic waves propagating in a medium with a relative permittivity $\widehat{ϵ}(x,y)$ that is a smooth bounded function with a positive real part.

© 2017 Optical Society of America

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