Скачать или смотреть [Flash warning] 3D view of a primitive laser based on a parabolic trap

The second half of this video shows some rapid wave movement that may be unpleasant to watch of you are sensitive to that kind of thing.
This is 3D rendering of a simulation similar to    • A primitive laser made from a parabolic tr...   , where the z-coordinate indicates the wave height or the averaged wave energy.
The set-up consists in a "parabolic light trap" with a semi-transparent window, working roughly like a laser. The shape of the window is that of a semi-circular lens (one face is flat, the other face is a circular arc), in order to try to focus the outgoing beam. The index of refraction of the window material has been chosen as 2.5 here, which is quite high. This is in order to increase the reflectivity, which can be computed from the Fresnel equations. The radius of curvature has been chosen based on the lensmaker's equation, to transform a wave originating in the common focal point of the parabolas into a roughly planar beam (the second focal point is at infinity).
The 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.
Average wave energy: 0:00
Wave height: 1:27
In part 1, the color hue depends on the wave wave energy, averaged from the beginning of the simulation. In part 2, it depends on the wave height. The boundary conditions are absorbing.


Render time: 1 hour 30 minutes
Compression: crf 25
Color scheme: Part 1- Plasma by Nathaniel J. Smith and Stefan van der Walt
Part 2 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
https://github.com/BIDS/colormap

Music: "Energetic" by Silent Partner

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