Numerical simulations
Wave propagation in periodic media
Here are some numerical simulations of electromagnetic wave propagations in
periodic waveguides and photonic crystals.
In all the pictures showing the dielectric medium, the background medium (blue)
has a delectric permittivity equal to 1 and the inclusions (red) have a
delectric permittivity equal to 5.
Click on the links below to see the movies.
- Junction between homogeneous and periodic waveguide: an incident wave from a homogeneous
waveguide (left) is reflected by the periodic waveguide (right) because its frequency
lies in its gap.
- incident wave
- reflected wave
- total field
- The first picture shows the medium and the second picture shows the total field of a non guided solution.
- The same situation as the previous one except for the frequency which is now taken
within the spectrum of the periodic waveguide.
In this case a part of the incident wave is guided in the periodic waveguide while the other part is reflected back to the
homogeneous waveguide.
- incident wave
- transmitted and reflected waves
- total field
- The picture below shows the total field of a partially guided solution.
- Here is the non physical solution to the previous problem where the transmitted
wave is traveling from right to left.
- Diffraction of a plane wave incident from a homogeneous half-plane
(upper half) on a half-plane photonic crystal (lower half) with a frequency
lying in its gap.
- incident, scattered, and total fields
- The left picture shows the medium and the right picture shows the total field of a reflected solution.
- Localized mode in a photonic cavity: a photonic cavity is a bounded domain
surrounded by a photonic crystal. Such a cavity can have very localized modes with
frequencies lying in the gap of the photonic crystal.
- Trapped mode
- The left picture shows the medium and the right picture shows the energy distribution of an eigenmode of the photonic cavity.
- Photonic waveguide: a plane wave incident from the free space penetrates a photonic waveguide.
- Incident plane wave, the dashed lines indicate the location of the guide and the half-plane.
- Wave scattered by all the structure
- Wave scattered by the guide
- Total field
- The pictures below show the medium, the wave scattered by all the structure, the wave scattered by the guide, and the total field.
- T-junction: a T-junction connects a photonic waveguide to a homogeneous
half-plane. A guided wave is incident from the upper branch. It is partially reflected
by th T-junction which transmits waves to the other branches. The horizontal branch
transmits the wave to the half-plane. By modifying the inclusion in the T-junction, one
can transmit more energy to the lower or to the horizontal branch. Below are two examples
with 2 different inclusions.
- Incident wave, the dashed lines indicate the location of the guides and the half-plane.
- Example 1: diffracted field, total field
- Example 2: diffracted field, total field
- The pictures below show for each example the medium and the total electromagnetic field.
- Waveguide intersection: here the horizontal waveguided is extended
to the right. An incident wave comes from upper guide and is transmitted to
the other guides.
- Incident wave, the dashed lines indicate the location of the guides and the half-plane.
- Diffracted field
- Total field
- The pictures below show the medium and the total electromagnetic field.
