Radial and angular coordinate transformations for subwavelength confinement of light

In this contribution, we will use transformation optics to design several electromagnetic cavities starting from the invisibility cloak. First, we will derive a general dispersion relation of a cylindrical transformation-optical medium in which both the radial and angular coordinates are transformed. This relation can then be used to evaluate the bounded electromagnetic modes of several cavities. It turns out, e.g., that the perfect invisbility cloak has no bounded modes. Other transformations, however, result in cavities that exhibit a wide range of high quality (with respect to radiation losses) subwavelength electromagnetic modes. One of these designs is based on a hyperbolic map, which transforms one boundary to infinity (or at least up to a very large value) and thus simulates the entire electromagnetic space within the finite physical cavity. Another approach is that of the so-called perfect cavity, whose functionality is based on a folded map of the radial coordinate.