A radar reflector can be made from a Luneburg lens by metallizing parts of its surface. Radiation from a distant radar transmitter is focussed onto the underside of the metallization on the opposite side of the lens; here it is reflected, and focussed back onto the radar station. A difficulty with this scheme is that metallized regions block the entry or exit of radiation on that part of the lens, but the non-metallized regions result in a blind-spot on the opposite side.
A material with a different but constant homogeneous reflective index throughout will 'bend' waves in a straight line. Very simplified explanation wave bends/scatters at discontinuities in electromagnetic properties (which is often in most cases also where there are physical discontinuities, such as the boundary between water and air, or glass),
The Luneburg lens makes use of layered varying reflective index in it's material to bend and refocus waves from a given direction on a same point. It is in effect introducing gradually varying discontinuities to shepard waves towards a desired redistribution. The blue hue in the pic below shows the gradual varying of reflective index in the material to bend parallel rays (and we can assume waves emitted from a source a long enough distance away to be arriving in parallel, i.e. if the distance between emitter and receiver is very large compared to the effective emitting aperture ) incoming from a given direction to a point on the opposite inner surface of the sphere.
![lunberg.png lunberg.png](https://www.sinodefenceforum.com/data/attachments/15/15612-f2a57f1fa033b183f3fea133f6d34540.jpg)
In the above pic, if we line the point at 'a' with a reflective material (like plating the underside of a mirror), we can reflective everything that concentrates at 'a' back towards the direction of 'A', since the wave lines now traces from a to A going out the same way it came in. This modifies the lens into a radar reflector. If we plate the arc region between a and b then all signal coming from the orientation range from A to B will be reflect back as if we have directed a corner reflector in the needed direction in each case. Of course the plated region from A to B will obstruct waves arriving from that direction and not allowing the lens to work properly for these cases. However we can always position it so that those regions faces direction where signals are not likely to arrive, such as the belly of the plane. And the fact that these parts are coated with reflective material means they will still reflect/scatter quite well, just not in a controlled and focused way.
That's my quick and amateurish explanation.
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The invisibility cloak guys, instead of wanting to reflect waves back the way they came, want them to bend around the object and pass through on the other side in the same orientation. So a invisibility device will have a layered hollowed ring rather than a sphere in which the object that is to be hidden is placed inside and light designed to bend around the objects in the layers of refractive material to emerge out the other side in the same orientation that they went in. This would be why making a flexible, durable and practical coat is quite a challenge.
Below is very simplified illustration. A is the object to be hidden, B is the exaggerated hiding device with designed layered refractive index. C is an object behind A that would otherwise be obscured by it but is what D sees instead.
![inv.png inv.png](https://www.sinodefenceforum.com/data/attachments/15/15614-1c62caa3c433206b93e63a99638ec92d.jpg)