Скачать или смотреть [Flash warning] Can one trap a beam of light between two parabolic reflectors?

Towards the end of the first half, the video shows some flashing due to the wave interference.
This simulation was suggested to me by viewer André Pscherer. It is based on a question on stackexchange, asking whether it is possible to trap a laser beam between reflectors: https://puzzling.stackexchange.com/qu... . One proposed solution involves two parabolic reflectors sharing the same focal point: https://puzzling.stackexchange.com/a/... . While this set-up works in the approximation of geometric optics (or ray optics), which describes the zero wavelength limit, it was unclear whether the same principle works for real waves, that show dispersion, diffraction and interference phenomena.
This simulation attempts to answer the question by sending a beam of waves towards the set-up of two confocal parabolas. It is not that easy to create a stable beam from an oscillating boundary condition, and the beam used here shows quite some dispersion (less visible in the energy picture). Nevertheless, the simulation shows how much of the energy is trapped for a while between the reflectors.
This video has two parts, showing the same simulation with two different color gradients.
Wave height: 0:00
Wave energy: 1:44
In part 1, the color hue depends on the wave height. In part 2, it depends on the wave energy, averaged over a time window. The boundary conditions are absorbing.

Render time: 43 minutes
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
https://github.com/BIDS/colormap

Music: "Ascension" by National Sweetheart‪@CumbiaDeli‬

See also
https://images.math.cnrs.fr/des-ondes... 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...
C code: https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!

#wave #reflection #parabola