We demonstrate the electric field propagation through one of the well-known inhomogeneous dielectric lens, namely the Luneburg Lens proposed by Rudolf Luneburg in 1944 (R. K. Luneburg, The Mathematical Theory of Optics, Providence, Rhode Island, Brown University Press, 1944). The dielectric permittivity of the Luneburg lens drops from 2 to 1 from its center to the edges via the following formula: epsr(r)=2-(r/Radius)^2. Since the dielectric permittivity is 1 at the edges and slightly increases towards the center, no surface reflection occurs. We have utilized circles to represent the increasing dielectric permittivity of the lens.
In this simulation, propagation through a 10Lambda diameter Luneburg lens is compared against the free space. 2-dimensional Finite-difference time-domain (FDTD) method is utilized for the simulations. A point source is located at the focal point on the surface and once the waves emerge from the other side of the lens, the collimation effect is observed (i.e. cylindrical waves converge to plane waves) where the waves propagate towards the other focal point at infinity.
References:
A. D. Greenwood and Jian-Ming Jin, "A Field Picture of Wave Propagation in Inhomogeneous Dielectric Lenses", IEEE Antennas and Propagation Magazine, Vol. 41, No. 5, October 1999
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