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We put forward the use of transformation optics to map surface waves that exist as one-dimensional modes supported by anisotropic structures into bound states in two-dimensional geometries. Specifically, we show the conformal mapping of Dyakonov waves existing in infinite planar surfaces separating birefringent media into bound modes supported by a cylindrical structure made of suitable metamaterials. In contrast with the original Dyakonov waves, the resulting fiber-like modes are highly dispersive, may exist as fundamental as well as higher-order states, feature helical wave fronts, and exhibit a lower and upper frequency cutoff. The program we put forward can be applied to all wave phenomena currently known to occur only in planar geometries in different types of anisotropic media.

Conformal transformation of Dyakonov surface waves into bound states of cylindrical metamaterials