Varying the thickness of a beam splitter
Channel: Nils Berglund
Date: 2024-02-08

Like the recent video https://youtu.be/GtiN-Cn6uTs , this one shows the simulation of a beam splitter, and how it is able to filter out certain frequencies of a coherent light source, such as a laser beam. The difference is that here, the light is monochromatic, while three different thicknesses of the beam splitter are shown. 
The beam splitter consists of a slab of material with index of refraction equal to 2. At each interface of the beam splitter, part of the light is transmitted, and another part is reflected. By changing the width of the beam splitter, one changes the distance traveled by the part that is transmitted at the first interface, and reflected back at the second one. Depending on the phase shift along that path, when compared to light that is reflected at the first interface, one gets various amounts of constructive or destructive interference. In this case, destructive interference is most important in the second part of the simulation. Then the phase shift is approximately pi, so that very little light is reflected upwards.
This video has three parts, showing situations with three different thicknesses of the beam splitter, resulting in different phase shifts:
Phase shift 3*pi/2: 0:00
Phase shift pi: 1:08
Phase shift pi/2: 2:15
The color hue depends on the wave height (or electric field intensity). 
There are absorbing boundary conditions on the top, bottom and right boundaries, and a time-periodic signal is imposed on the left boundary. The displays at the bottom and right show the wave height along the horizontal and vertical lines that splits the displayed region into two equal parts.

Render time: Part 1 - 17 minutes 27 seconds
Part 2 - 18 minutes 4 seconds
Part 3 - 17 minutes 25 seconds 
Compression: crf 23
Color scheme: Twilight by Bastian Bechtold
https://github.com/bastibe/twilight

Music: "Feelin Diff" by Text Me Records@textmerecords and 
Jorge Hernandez@theknox

See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html for more explanations (in French) on  a few previous simulations of wave equations. 

The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf 
C code: https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

#wave #interferenceoflight #beam_splitter