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

Ground Penetrating Radar (GPR) FDTD Animation

Finite-difference time-domain (FDTD) animation of a sample ground penetrating radar (GPR) in action. Basically, a transmitting antenna shoots a short electromagnetic pulse (with a central frequency of 600 MHz) into the subsurface where the relative dielectric permittivity is 4. The short pulse is reflected from the air-soil interface and then either the rectangular or circular targets embedded in the subsurface. Then, the scattered signals are recorded by the receiving antenna of the GPR unit. This constitutes a single A-scan for the GPR measurement. Collection of A-scans along a spatial range constitutes the so called B-scans. Depending on the reflectivity of the target and soil properties, the success of GPR detection varies.

Ground Penetrating Radar -  Propagation within the subsurface

Diffraction from a Single Slit (FDTD Animation)

The single slit diffraction is illustrated via the use of finite-difference time-domain (FDTD) simulation in which slits with various widths are illuminated by electromagnetic plane waves at a single frequency. When the impinging plane waves reach the slits, they are diffracted into a series of circular waves and the emerging wavefront from the slits become cylindrical waves.

Diffraction is basically the phenomenon involving the bending of waves around obstacles and the spreading out of the waves past small openings. Huygen's Principle states that every point on a wavefront acts as a source of tiny wavelets moving forward with the same speed as the wave and the wavefront is the surface tangent to these wavelets.