Controlling and understanding reflection and transmission
The propagation of electromagnetic waves in inhomogeneous materials remains a subject of intense interest and activity. This is partly because the challenge is not merely computational; there is also a need for improved analytical techniques. The issue of reflection by inhomogeneous materials illustrates the point well. It would be naively expected that inhomogeneity always causes some reflection and that this becomes very significant if the refractive index changes appreciably over a wavelength. But there are many inhomogeneous index profiles that have strictly zero reflection even when the geometrical-optics approximation is arbitrarily bad. I will describe techniques that explain some aspects of this interesting physics in a very visual manner. These techniques can be used to derive recipes for materials with interesting reflection and transmission properties. I also consider to what extent reflection can in principle be eliminated at all frequencies, given fundamental physical constraints. This last question has direct application to the Casimir effect.