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.

Total Field / Scattered Field (TF/SF) Implementation in FDTD

Here, the plane wave excitation using the total field / scattered field (TF/SF) formulation in finite-difference time-domain (FDTD) algorithm is demonstrated. The interface between the "total" and "scattered" field regions is shown using the square box. The plane wave polarized in the -z direction (with respect to screen surface) is injected into the medium along the -y direction and then the scattering phenomena from two different scatterers (one metallic triangular wedge and another circular dielectric scatterer) are animated. The reflected wavefronts from the scatterers can explicitly be observed in the scattered field regions, whereas total field is observed within the box.




Keywords: Scattering from prism, 三角柱, Prisme triangulaire, 삼각기둥,முப்பட்டகம், Триъгълна призма

Group Velocity / Phase Velocity Animation - Case 2: Zero Group Velocity

In this second video of the series, we demonstrate the case where the group velocity is zero while the phase velocity is positive number. The individual wave components comprising the total wave are first shown at the top along with a corresponding "dot" representing the phase velocity of each component.

In the bottom figure, we have the resulting wave that travels along the +x direction with a positive phase velocity but the group velocity remains to be zero. The wave packet envelope is shown in magenta color in dashed lines.

For the other videos in the series, check the below links:
1) Group Velocity larger than Phase Velocity: https://www.youtube.com/watch?v=tlM9vq-bepA


Групповая скорость, Gruppengeschwindigkeit, Voortplantingssnelheid, Velocidad de grupo, Grupa rapido, Vitesse de groupe, Velocità di gruppo, 군속도, מהירות חבורה, ჯგუფური სიჩქარე, 群速度, Gruppefart, Prędkość grupowa, Групова швидкість, 群速度, Vận tốc nhóm, Grupphastighet, Grupinis greitis, Phasengeschwindigkeit, Velocidad de fase, 相速度, Vitesse d'une onde, Velocità di fase, Фазовая скорость, 位相速度

Fast Fourier Transform (FFT) Animation using Matlab

We show the progress of Fast Fourier Transform (FFT) of a time-domain signal as it changes in time. Matlab's fft() function is used for illustration, hence it should be noted that the function is assumed to be periodic. The number of FFT point is assumed to be same as the time domain signal to prevent zero padding when the full domain is filled. In the beginning a sinusoidal signal at 50 Hertz (1*sin(2pi*50*t)) starts to develop and slowly fills the full domain. Then, another sinusoidal signal at a higher amplitude and 100 Hertz (1.5*sin(2pi*100*t)) is added to this signal. Later, a third sinusoidal signal at 200 Hz replaces the 100 Hz one. Following this, a DC component (0 Hz) is inserted and finally, the DC component is removed. At each stage, the the development of frequency components can clearly be observed. In the frequency spectrum, first a 50Hz component starts to build up along with lower and higher frequencies. The reason for wider spectrum is the fact that sinusoidal signal fills the domain within an increasing time window (hence introduction of sinc components). Once the full domain is filled with the sinusoidal, then only 50 Hz component remains due to the fact that the signal assumes to be periodic in Matlab fft function.