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

Here, we demonstrate the group and phase velocity phenomena as observed when two signals with different temporal and spectral frequencies (wavelength) are added to each other. The addition creates time varying constructive and destructive interferences along the space. The resulting wave packet travels with the so-called group velocity which is faster than the phase velocity in this case. The wave packet envelope is shown in magenta color in dashed lines. Note that in this particular case, both group and phase velocities are positive. An important interpretation of group velocity is that it represents the velocity at which the energy or information is conveyed along a wave (see Wikipedia for further details). 

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

Corner Reflector (FDTD Animation)

Two corner reflectors with two different tilt angles have been simulated for demonstrating their reflection properties. The simulations are rendered using the total-field/scattered-field finite-difference time-domain algorithm. An identical incoming plane wave in the negative vertical direction hits the corner reflectors. Although having different tilt angles, they reflect the incoming way in the same positive vertical direction. Corner reflectors are known to be retro-reflectors and consists of 2 or more mutually perpendicular and intersecting flat surfaces. They automatically reflect the waves back towards to the source. In practice, they are used for calibration purposes (e.g. meteorological radars) and range detection. Also in maritime and air navigation, they are used to mark the desired objects on the radar screen (e.g. buoys, ships, runways etc). Corner reflectors are also used to as safety reflectors for cars, bikes, traffic signs and similar devices. Here, the reflectors are in the passive mode, but can also be used in semi-active mode to enhance the directivity of dipole antennas. Basically, by placing the dipole antenna in front of a corner reflector, the combined corner-reflector dipole antenna has a better directivity.

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

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.

Standing Wave Patterns in Medium with Multiple Interfaces

The generation of standing wave patterns in a medium with three different dielectric permittivities. The reflection and transmission along the two interfaces are shown. Since there are infinitely many reflections, only the overall left and right traveling and the total waves are shown in the animation. When the total traveling field is plotted in space at different time instants (as in the bottom figure), the standing wave patterns can easily be observed.

For similar animations involving a single interface, see below:



Standing Wave Pattern (SWR) and Propagation in Lossy Medium

Standing Wave Pattern (SWR) and Propagation in a Lossless Medium

Phased Array Beam Steering Animation

Beam steering via phased antenna arrays is demonstrated. The arrays are  composed of 7 point sources uniformly spaced in a linear fashion (uniform linear array (ULA). The antenna separation is denoted by the parameter d. When the separation is smaller, the directivity of the array is narrower. Each antenna element in the array is fed with a relative phase shift of "delta" with respect to the adjacent on (the rightmost antenna is the reference antenna where no phase shift is applied, i.e. delta=0).

Standing Wave Pattern (SWR) and Propagation in Lossy Medium

This animation serves as complementary to a previously uploaded one (http://www.youtube.com/watch?v=s5MBno0PZjE) where the medium were lossless. This time, the medium onto which the wave is impinging is lossy and we demonstrate the time-domain propagation of a uniform plane wave traveling in the +z direction and normally incident on the medium interface (at z=0). Again, only the electric field intensity is shown.

The top figure shows the incident (blue), reflected (red), incident+reflected (teal) and transmitted field in both media. In the bottom figure, the standing wave patterns created in both media are shown. Also, the decaying nature of the electromagnetic wave due to lossy nature of the medium is evident in the lossy medium.

Doppler Effect Animation

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.

Evanescent and Propagating Waves

Time domain simulation of a plane wave for different wavenumbers (k). At first the wavenumber is positive real number and keeps reducing down to 0. This constitutes the propagating region where the spatial wavelength (lambda) increases as the wavenumber (k) decreases. Then, wavenumber becomes negative imaginary and increases in magnitude. This region demonstrates the non-propagating or decaying properties of evanescent waves. In the evanescent region, the greater the magnitude of the wavenumber, the faster the wave decays.

Periodic Band Gap (PGB) Waveguide and Propagation - FDTD Simulation

Inspired by the following video:
http://www.youtube.com/watch?v=O-6l0bvAda0

Guiding EM waves via periodic structure. The frequency of operation is 11.085 GHz. The relative dielectric permittivity of the square blocks are 11.56 and the ambient medium is air. Each block is 3.5 mm x 3.5 mm.

The main reference is the below dissertation:
Marcelo Bruno Dias, "Estudo da Propagação de Ondas Eletromagnéticas em Estruturas Periódicas". Graduation Dissertation - Electrical Engineering Course, Universidade Federal do Pará (UFPA), Belém, Pará Brazil, 2003.

More details can be found in their lab web site:
www.lane.ufpa.br/publicacoes.html

Standing Wave Pattern

Uniform plane wave traveling in the +z direction and normally incident on a medium interface at z=0. Only the electric field intensity is shown.
The top figure shows the incident (blue), reflected (red), incident+reflected (brown) and transmitted field in both media. In the bottom figure, the standing wave patterns created in both media are shown.

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

Linear Polarization Animation

Uniform plane wave traveling in the +z direction. The x and y component of the electric fields are in phase thus the polarization of the electric field is constant over all space (linearly polarized).


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

Left Hand Elliptical Polarization (LHEP) Animation

Uniform plane wave traveling in the +z direction. The x and y component of the electric fields have a phase shift with results in a elliptically rotating polarization in the left hand direction.


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

FDTD Simulation of a Half Convex Lens

Finite-difference time-domain (FDTD) simulation of a half convex lens when a point source is located at its focal plane in both on-axis (left) and off-axis (right) cases. The points indicated by the small circle are the actual source locations and the third point with the cross sign is the location of symmetry for the off-axis source.

The source locations are located at the focal plane to demonstrate the collimation property of the lenses. Again, to demonstrate the frequency independency of the lens behavior, two short pulses at different central frequencies are fired consecutively and both cases show collimation after exiting the lens.

The lens employed here has a parabolic surface and obviously, it is not perfectly optimized hence the directed signals are not perfectly smooth. For desired far field performance the shape of the lens can be further designed using optimization algorithms integrated with electromagnetic solvers.

Two related papers are:
1) A. V. Boriskin, A. Rolland, R. Sauleau and A. I. Nosich, Assessment of FDTD Accuracy in the Compact Hemielliptic Dielectric Lens Antenna Analysis, IEEE Trans. Antennas and Prop. vol.56, no.3 pp. 758-764, March 2008
2) G. Godi, R. Sauleau and D. Thouroude, Performance of Reduced Size Substrate Lens Antennas for Millimeter-Wave Communications, IEEE Trans. Antennas and Prop. vol.53, no.4 pp. 1278-1286, April 2005

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

Right Hand Circular Polarization (RHCP) Animation

Uniform plane wave traveling in +z direction

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

Dipole Antenna Radiation

Dipole Antenna Radiation

Finite-difference time-domain (FDTD) simulation of a 2 wavelengths long dipole antenna at 400 MHz in free space. The radiation pattern is very different than that of the traditional half-wavelength dipole antenna. Nulls in the broadside and endpoints are clearly visible

Dish Antenna Animation (Parabolic reflector)