Bent Waveguide

Here, we demonstrate the propagation through bent waveguides with different bending radii. The thickness of all waveguides are same and let's denote as "d" here. Then we have 3 cases where the radius of bending is d, 2d or 3d. With the smaller radius, the leakage from the bending is stronger compared to the other ones.

FDTD simulations - Why Smooth Turn-on of Source is Needed?

In Finite-Difference Time-Domain (FDTD) simulations, source injection needs to be smoothly done in order to suppress the undesired high frequency components excited during turn on. To visualize this problem, we provide two cases with and without turn-on source injection. On the right simulation, total field/scattered field injection is done using the cosine excitation without any smooth turn-on which effectively mimics the step function operation. This results in the injection of high frequency components creating the ripples and fluctuations in the signal propagating in the domain. On the contrary, the left simulation has a smooth turn of by using a half Hanning window ramp-up which effectively acts as low pass filter for the injected source. As a result, the signal propagating in the domain is free of high frequency components, hence no ripples and fluctuations.

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

Diffraction from a wedge - TMz case [FDTD simulation]

Here, we demonstrate the diffraction from a wedge when a plane wave with electric field component normal to the surface is impinging on it. The wedge corner acts as a secondary source to generate cylindrically propagating waves which are clearly seen when the scattered field plots on the right is analyzed. The left side of the animation shows the total field where both the scattered and incident fields are plotted together.





Beugung, Difracción, Diffrazione, Kırınım, 回折, Дифракция, Diffractie, Difração, 衍射, Dyfrakcja, Diffraktion, Interferenz, Interferencia

Diffraction from Double Slits (Young's Double Slits)

The double slit diffraction is illustrated via the use of finite-difference time-domain (FDTD) simulation. Two sets of double slits with different widths and a single slit - for comparison - are illuminated by normally incident plane waves. When the impinging plane waves reach the slits, they are diffracted into a series of circular waves. In the case of double slits, constructive and destructive interferences create dark (null) and bright spots. 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. 

Keywords:

Beugung, Difracción, Diffrazione, Kırınım, 回折, Дифракция, Diffractie, Difração, 衍射, Dyfrakcja, Diffraktion, Interferenz, Interferencia, Young's slit,

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

Ground Penetrating Radar (GPR) B-Scan Collection (FDTD Animation )

Here, B-scan data collection of a simple ground penetrating radar (GPR) is animated through the use of Finite-difference time-domain (FDTD) method. The upper part of the animation shows the 2D spatial propagation of the short pulse transmitted from the antenna at different spatial locations. The 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 from the target embedded in the subsurface. Then, the scattered signals are recorded by the same antenna in the receiving mode. The lower part of the animation corresponds to the received signals (A-scan) at the same antenna for each of the positions. This constitutes the so-called B-scan data collection.

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

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.

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.

Electromagnetic Propagation of UWB Short Pulse in Random Medium

Finite-difference time-domain (FDTD) simulation of electromagnetic propagation of a short ultrawideband pulse (central frequency 700 MHz) in random medium. The randomness is achieved via the randomly fluctuating of the dielectric permittivity of the environment.

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

Power Divider Waveguides using Periodic Band Gap Structure - FDTD Simulation

This is the third of the series for the waveguiding structures using the periodic band gap materials (The first one is at: http://www.youtube.com/watch?v=gZkFVco4kL4).

In this video, a power divider made out of periodic boundary conditions is demonstrated. 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.

Originally, this was inspired by the following video:
http://www.youtube.com/watch?v=O-6l0bvAda0

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


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

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

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

Radiation from a Circularly Tapered Dielectric Waveguide

Finite-difference time-domain (FDTD) simulation of a dielectric waveguide terminated with a circular tapering. The dielectric permittivity of the waveguide is 2.2 and air is the ambient medium. Such antennas are developed for ground penetrating technology (GPR) technology to reduce the footprint of the antenna.

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