Half Maxwell's Fish Eye Lens - Dielectric Antenna (FDTD Animation )

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

Maxwell Fisheye Lens Propagation (FDTD Animation)

Similar to the previously presented Luneburg Lens, this time we demonstrate the electric field propagation through the Maxwell 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 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. We have utilized circles to represent the increasing dielectric permittivity of the lens.

In this simulation, propagation through a 10Lambda diameter Maxwell fish-eye 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 focusing at the opposite edge point.

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

Lüneburg Dielectric Lens - Propagation Animation (FDTD simulation)

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