This video is the continuation of the series on Luneburg and Maxwell's Fish Eye Lenses (dielectric antennas & lenses). Specifically, we demonstrate the electric field propagation through the Half Maxwell's Fish-Eye lens proposed by James Clark Maxwell in 1860 (J. C. Maxwell, Scientific Papers, I, New York, Dover Publications, 1860).
The relative dielectric permittivity of the full Maxwell fish-eye lens drops from 4 to 1 from its center to the edges via the following formula: epsr(r)=4/(1+(r/a)^2)^2 for r less than "a" (and greater than zero) where "a" is the radius of the lens and r is the radial distance from its center. Since the dielectric permittivity is 1 at the edges and slightly increases towards the center, no surface reflection occurs. Half Lens is basically half of the full Maxwell's lens. We have utilized half circles to represent the increasing dielectric permittivity of the lens. Also at the bottom figure, we plot the exact dielectric permittivity distribution of the lens over the space.
In this simulation, propagation through a 10Lambda diameter Half Maxwell fish-eye lens is demonstrated via 2-dimensional Finite-difference time-domain (FDTD) simulations. A point source is located at the a point on the edge of the lens and correspondingly, we observe propagation of a monochromatic sinusoidal source (left) and a short pulse (right) through the lens and onwards. Collimation is clearly observed once the waves emerge from the flat edge of the lens.
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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