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),
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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.
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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.