Research case study: Designing reflectionless media

In general, electromagnetic waves are partially reflected at the boundary between two materials of different permittivities (the permittivity of a material measures how light interacts with the electric charges in the material).

Our research is concerned with theoretically designing inhomogeneous media with suppressed reflection. Such materials may be useful as anti-reflection coatings for lenses, such as can be found on glasses, and may also be useful in the development of cloaking, where an object can be hidden by bending the path of light around it. We consider media whose permittivity ε varies smoothly in space, and it is the nature of this variation determines the relative amount of reflection, transmission and absorption. It is possible to construct such graded-index media using metamaterials.

We have derived a family of one-dimensional permittivity profiles ε(x), which don't reflect waves incident from one side for any angle of incidence. We have also obtained a subset of such media which, in addition to being reflectionless, also give perfect transmission (thus no absorption), and subset that, in addition to being reflectionless, also gives perfect absorption (thus no transmission).

Following this work we are considering how to extend these ideas about designing reflectionless media to two dimensions. Specifically, we have considered periodic gratings which don't diffract and non-reflecting beamshifters.

Figure 1. A light wave is incident on a material with permittivity ε(x), which varies with the spatial coordinate x. In general, the wave will be partially reflected from, partially transmitted through, and partially absorbed by the material.

Figure 2. A light source is placed to the left (i) and right (ii) of an object satisfying the spatial Kramers-Kronig relations and the electric field is plotted. The lack of ripples in (i) indicates that none of the light incident gets reflected for all angles of incidence whereas the ripples in (ii) indicate that there is reflection from the object. This is an example of a one-way reflectionless material.