Reducing unwanted reflections through impedance matching, called anti-reflection, has long been an important challenge in optics and electrical engineering. Beyond trial and error optimization, however, a systematic way to realize anti-reflection is still absent. Here, we report the discovery of an analytic solution to this long standing problem. For electromagnetic waves, we find the graded permittivity and permeability that completely remove any given impedance mismatch. We demonstrate that perfect broadband anti-reflection is possible when a dispersive, graded refractive index medium is used for the impedance-matching layer. We also present a design rule for the ultra-thin anti-reflection coating which we confirm experimentally by showing the anti-reflection behavior of an exemplary λ/25-thick coating made of metamaterials. This work opens a new path to anti-reflection applications in optoelectronic device, transmission line and stealth technologies.
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