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: