Скачать или смотреть Waves of two different frequencies crossing a biconvex lens

Someone asked about the effect of the light's frequency on the working of a lens. The theory of geometrical optics, or ray optics, considers an idealized situation in which the wavelength is negligibly small, and much of basic optics relies on this approximation. Increasing the wavelength results in effects such as diffraction, which may degrade the quality of the lens.
In this simulation, two sources at different frequencies emit light crossing a biconvex lens. The frequency of the lower source is three times the frequency of the upper one. While the difference of frequencies has an effect on the waves' interference, the energy profile in the focal plane does not show any important difference.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:15
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the right shows the square of the signal along the focal plane, averaged over a time window. The focal plane and the plane containing the sources are roughly symmetrical with respect to the vertical symmetry axis of the lens.

Render time: 34 minutes 41 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
https://github.com/bastibe/twilight
Part 2 - Plasma by Nathaniel J. Smith and Stefan van der Walt
https://github.com/BIDS/colormap

Music: "Bright Idea" by Geographer‪@geographermusic‬

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 #lens #focus