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Getting to grips with the detrimental influence of disordered environments onwave propagation is an interdisciplinary endeavour spanning diverse researchareas ranging from telecommunications \cite{basar_wireless_2019} andbio-medical imaging \cite{kubby_wavefront_2019} to seismology\cite{Campillo2003} and material engineering \cite{Chen2010,Molesky2018}.Wavefront shaping techniques are highly promising to overcome the effect ofwave scattering as even opaque media feature open channels for which theincident light is fully transmitted\cite{Dorokhov1984,Gerardin2014,Sarma2016,Jeong18}. With this feature beingrestricted, however, to just a small subset of judiciously engineered states itremains out of reach to render an opaque sample translucent for any incidentlight field. Here we show that a structureless medium composed of randomlyassembled scattering elements can be made fully transmitting to all incomingwavefronts by putting a customized complementary medium in front of it. Thisspecial situation is achieved when the reflection matrices of the two mediasurfaces facing each other satisfy a matrix generalization of the condition forcritical coupling. We implement this protocol both numerically andexperimentally for the design of electromagnetic waveguides with several dozenscattering elements placed inside of them. The translucent scattering media weintroduce here also have the promising property of being able to store incidentradiation in their interior for remarkably long times.

Customized anti-reflection structure for perfect transmission through complex media