What happens if the Source is Inside the PML region in FDTD simulations?

In most of the FDTD simulations, perfectly matched layers play an indispensable role by their ability to absorb the incoming waves to mimic free space propagation. Triggering effect for this animation is the simple curiosity of what would happen if a point source was embedded in the PML rather than the inner domain.

To illustrate this, we utilized the uniaxial PML (UPML) formulation in a 2D FDTD scenario in homogeneous medium. We present three parallel simulations in which the point sources are located (left) deep inside the PML, (middle) slightly inside the PML and (right) outside but close to the PML. As can be observed, the PML performs great in eliminating portions of the wave impinging normal (or close to the normal) to the PML surface. But for high oblique incidences, the decaying of the wave is not completely satisfied.

For the leftmost case where the source is deeply embedded in the PML, the wave cannot propagate in the -x and +x directions and quickly decay in both directions. However, along the -/+ y directions, the PML acts as a waveguide. Thanks to the upper and lower PML regions, the wave inside the PML continues to decay along the -/+ y directions.

Optical Ring Resonator (FDTD Animation)

Here, we demonstrate the propagation phenomena in a double optical ring resonator structure. A windowed cosine excitation is pumped in the bottom dielectric straight waveguide and as this input mode propagates past the circular waveguides, the optical coupling occurs yielding wave propagation in the circular waveguide. The structure is chosen for illustration purposes only and it is possible to see several coupling between the circular and straight waveguides. In practice, various combinations are used to obtain optical filtering. For more information, you can check the wikipedia page


Also see below:
Oblique Plane Wave Reflection From Half Space
Radiation from a Circularly Tapered Dielectric Waveguide
Right Hand Circular Polarization (RHCP) Animation
Linear Polarization Animation
Left Hand Elliptical Polarization (LHEP) Animation
Standing Wave Pattern (SWR) Animation
Electromagnetic Propagation of UWB Short Pulse in Random Medium 
Half Wavelength Dipole Antenna Radiation 
Dipole Antenna Radiation 
Dish Antenna Animation (Parabolic reflector) 
FDTD Simulation of a Half Convex Lens
Diffraction from a Single Slit (FDTD Animation)
Ground Penetrating Radar (GPR) B-Scan Collection (FDTD Animation )
Ground Penetrating Radar (GPR) FDTD Animation

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

Effect of Perfectly Matched Layers (PML) in FDTD Simulations

Although it is pretty straightforward for researchers in the field of modeling via FDTD or FEM, PML can puzzle those who do not have any modeling background. Therefore, here we try to simply show what happens with and without a PML in a free space propagation modeling.

Basically, we demonstrate the effects of the perfectly matched layers in finite-difference time-domain (FDTD) simulations. Here, a point source transmits a spherical wave and the simulation domain is truncated in two different ways. In the first case (left one) no PML region is utilized whereas in the second one (right) PML region is included. It is clearly observed that PML absorbs the incoming waves mimicking a infinite domain simulation whereas the simulation without PML, spurious reflections occur due to termination of the computational boundary.