Electromagnetic analysis of complex media via helical coordinates

摘要

A general framework for the analysis of chiral electromagnetic media is discussed via the analysis of Maxwell's equations in a coordinate system that rotates uniformly along the z-axis. We are motivated in this study by the knowledge that exact solutions exist in at least two canonical cases: (a) natural optical activity and (b) structurally chiral dielectrics. In the latter case the so-called Oseen transformation has previously been used to render a completely analytic solution. However, we show that this transformation is not a true rotation of real physical space, but that when such a rotation is applied via the helical transformation, identical solutions are generated. These ideas provide a basis for constructing solutions in chiral media in general, and it is speculated how they can be applied in novel contexts.