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The concept of an impedance is a valuable means to access how light couples among adjacent half-spaces. Being a quantity linked to the eigenmodes of a medium, it is well established for plane waves in free space; but a unique definition for modes propagating in more complicated nanostructured media is a challenging task. We show here that the introduction of an absolute impedance is usually not possible since its definition crucially depends on a referential mode. We lift this problem by introducing a relative impedance that only requires the fields of the fundamental modes in each medium. At the example of nanostructured metallic waveguides, we outline the concept and provide evidence for its applicability to predict the reflection among different waveguides in a simple way. It therefore constitutes a valuable design tool for sophisticated waveguiding structures for many applications.

impedance; nanophotonics; nanostructured waveguides; metamaterials