  Metasurfaces with linear phase gradients can redirect light beams. We propose
controlling both phase and amplitude of a metasurface to extend Snell's law to
the realm of complex angles, enabling a non-decaying transmission through
opaque media with complex refractive indices. This leads to the discovery of
non-diffracting and non-decaying solutions to the wave equation in opaque
media, in the form of generalised cosine and Bessel-beams with a complex
argument. While these solutions present nonphysical exponentially growing side
tails, we address this via a windowing process, removing the side tails of the
field profile while preserving significant transmission enhancement through an
opaque slab on a small localized region. Such refined beam profiles may be
synthesized by passive metasurfaces with phase and amplitude control at the
opaque material's interface. Our findings, derived from rigorous solutions of
the wave equation, promise new insights and enhanced control of light
propagation in opaque media.
