Raytracing Metamaterials with POV-Ray

Materials with a negative index of refraction are an area of intensive research although most practical experiments in this field are made in the longer wavelength range than visible light. Using the raytracing technique we can simulate how such materials would interact with light in the visible range even if such materials do not exist yet in reality. Several interesting effects can be observed when doing ray optics with such materials.

Negative index of refraction most of all means that light is refracted the other way round - following Snell's law the light leaves the surface on the same side of the surface normal as it enters. This is quite counter-intuitive so objects of such a material appear quite unusual in raytracing simulations.

positive index of refraction negative index of refraction

POV-Ray's way of handling refraction (using Heckbert's method) correctly deals with negative values for the refractive index so simulating metamaterials is as simple as changing the sign of the ior value. The consideration of the index of refraction when calculating variable reflection is compatible to negative values as well. Both refraction and reflection handling work equally for normal backwards raytracing and photon mapping so all ray-optical effects that can be simulated for normal materials using POV-Ray can be studied for metamaterials as well.

One interesting effect of a negative index of refraction is that refractions tend to move in the opposite direction of what you expect when moving or rotating the refracting object as can be seen here:

positive index of refraction (mpeg4 version) negative index of refraction (mpeg4 version)

Below you can adjust the index of refraction of the transparent cube by moving the mouse along the bar in the middle.

• positive index of refraction negative index of refraction

One possible application of optical metamaterials could be the creation of lenses. For normal glass lenses convex forms tend to have a light focussing effect while concave lenses defocus light. Lenses made of negative ior material would have the opposite effect:

positive index of refraction negative index of refraction

The absolute value of the ior is 1.5 in both cases so as can be seen above the focussing/defocussing effect of the negative ior 'lenses' is stronger with the same geometry. One other interesting effect of negative ior materials is that a flat plate has a focussing effect inside the material but the light rays leave the material in the same direction as they enter just like in normal optical materials:

positive index of refraction negative index of refraction

Using the raytracing technique materials with a negative index of refraction can of course also be applied in real life objects like the following glass filled with a liquid that has been created for an Article in Optics Express, Vol. 14, No. 5 (Photorealistic images of objects in effective negative-index materials).