Anti-reflection structure for perfect transmission through complex media

The scattering of waves when they propagate through disordered media is an important limitation for a range of applications, including telecommunications¹, biomedical imaging², seismology³ and material engineering^4,5. Wavefront shaping techniques can reduce the effect of wave scattering, even in opaque media, by engineering specific modes-termed open transmission eigenchannels-through which waves are funnelled across a disordered medium without any back reflection^6-9. However, with such channels being very scarce, one cannot use them to render an opaque sample perfectly transmitting for any incident light field. Here we show that a randomly disordered medium becomes translucent to all incoming light waves when placing a tailored complementary medium in front of it. To this end, the reflection matrices of the two media surfaces facing each other need to satisfy a matrix generalization of the condition for critical coupling. We implement this protocol both numerically and experimentally for the design of electromagnetic waveguides with several dozen scattering elements placed inside them. The translucent scattering media we introduce here also have the promising property of being able to store incident radiation in their interior for remarkably long times.