An invisibility cloak should completely hide an object from an observer, ideally across the visible spectrum and for all angles of incidence and polarizations of light, in three dimensions. However, until now, all such devices have been limited to either small bandwidths or have disregarded the phase of the impinging wave or worked only along specific directions. Here, we show that these seemingly fundamental restrictions can be lifted by using cloaks made of fast-light media, termed tachyonic cloaks, where the wave group velocity is larger than the speed of light in vacuum. On the basis of exact analytic calculations and full-wave causal simulations, we demonstrate three-dimensional cloaking that cannot be detected even interferometrically across the entire visible regime. Our results open the road for ultrabroadband invisibility of large objects, with direct implications for stealth and information technology, non-disturbing sensors, near-field scanning optical microscopy imaging, and superluminal propagation.

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In this paper, we study the electromagnetic scattering of a plane wave by a prolate or oblate dielectric spheroid, which can be lossless or lossy. The presented efficient solution is obtained by applying a perturbation technique to the problem of the sphere using the spherical eigenvectors. This method allows a closed-form solution for the fields and the scattering cross sections, which is valid for small eccentricities of the spheroid. Alternatively, we construct the exact solution of the problem using the separation of variables in terms of the spheroidal eigenvectors and updated spheroidal algorithms that allow complex arguments. We compare the closed-form solution versus the exact solution and we conclude about its accuracy. Both polarizations are studied and numerical results are given for various values of the parameters.