lenses

Lens antennas are secondary radiators that can change to shape of the wave-front similar to the reflector antennas. Based on the material, they are delay (dielectric) lens or fast (metal plate) lens. Dielectric lenses are constructed of nonmetallic dielectric or metallic artificial dielectric.  Metal–plane lens antennas are from metal – plate plates that accelerate the phase velocity of propagation.

For theory see:

Orphanids, S: Electromagnetic Waves and Antennas, 2004-10, chapter 19, pp. 907-908: http://eceweb1.rutgers.edu/~orfanidi/ewa/ch19.pdf
Kraus, J.D., Marhefka, R.J.: Antennas for all applications, Mc Graw Hill 2003, chapter: Lens Antennas (17)

Simulations - Lenses:

Elliptic_lens Horn antenna with elliptic lens, E-field intensity.
 Hyperbolic_lens

Horn antenna with hyperbolic lens, E-field intensity.

 Duel_hyperbolic_lens Horn antenna with dual hyperbolic lens, E-field intensity.
 Duel_hyperbolic_lens_power_density Horn antenna with dual hyperbolic lens, distribution of power density.
 55193MHz-Efield-2x_cocka A model of Fabry-Perot resonator employing two lenses .

Links:

Maxwell Fish-eye lens

Luneburg lens

Gallery: