  Interference of scattered waves is fundamental for modern light-scattering
techniques, such as optical wavefront shaping. Recently, a new type of
wavefront shaping was introduced where the extinction is manipulated instead of
the scattered intensity. The underlying idea is that upon changing the phases
or the amplitudes of incident beams, the total extinction will change due to
interference described by the cross terms between different incident beams.
Here, we experimentally demonstrate the mutual extinction and transparency
effects in scattering media, in particular, a human hair and a silicon bar. To
this end, we send two light beams with a variable mutual angle on the sample.
Depending on the relative phase of the incident beams we observe either nearly
zero extinction, mutual transparency, or almost twice the single-beam
extinction, mutual extinction, in agreement with theory. We use an analytical
approximation for the scattering amplitude, starting from a completely opaque
object and we discuss the limitations of our approximation. We discuss the
applications of the mutual extinction and transparency effects in various
fields such as non-line-of-sight communications, microscopy, and biomedical
imaging.
