Nils Berglund | Filming a moving source with a gradient index lens @NilsBerglund | Uploaded April 2024 | Updated October 2024, 2 hours ago.
Like the video youtu.be/KB_Roqs38F8 , this one shows a simulation of light from a nearby source crossing a gradient index lens. The difference is that here, the source is moving on a path perpendicular to the axis of the lens. Note that the speed of the source is very large, about 33% of the speed of light, but the simulation does not take any relativistic effects into account. The refractive index along the central axis of the lens is quite large, with a value of 1.82, in order to obtain the small focal distance required by the simulation. I'm not quite sure what causes the "echo" of the transmitted waves, which was not present in other simulations with a static source. Is might be due to light reflecting on the horizontal boundaries of the lens. If someone has a better explanation, please feel free to leave a comment.
Lenses focus incoming rays of light by delaying them more near the center of the lens than at its periphery. This is often done with a material of constant index of refraction, by making the lens thicker near the center, as shown for instance in the simulation youtu.be/rrJJBh9ubUE . However, one can also build lenses of constant thickness, by making the index of refraction of their material depend on the location in the lens. In this simulation, the index decreases like sqrt(n0² - a*r²), where r is the distance to the axis of symmetry. This results in the incoming waves being focused on the (estimated) focal plane, marked by a vertical line. The plot to the right shows a time-averaged value of the field along that plane.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:39
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 signal along the focal plane, which is indicated by a vertical line.
Render time: 51 minutes 32 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Runner" by Silent Partner
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 hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: 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 #lens #gradient_index
Like the video youtu.be/KB_Roqs38F8 , this one shows a simulation of light from a nearby source crossing a gradient index lens. The difference is that here, the source is moving on a path perpendicular to the axis of the lens. Note that the speed of the source is very large, about 33% of the speed of light, but the simulation does not take any relativistic effects into account. The refractive index along the central axis of the lens is quite large, with a value of 1.82, in order to obtain the small focal distance required by the simulation. I'm not quite sure what causes the "echo" of the transmitted waves, which was not present in other simulations with a static source. Is might be due to light reflecting on the horizontal boundaries of the lens. If someone has a better explanation, please feel free to leave a comment.
Lenses focus incoming rays of light by delaying them more near the center of the lens than at its periphery. This is often done with a material of constant index of refraction, by making the lens thicker near the center, as shown for instance in the simulation youtu.be/rrJJBh9ubUE . However, one can also build lenses of constant thickness, by making the index of refraction of their material depend on the location in the lens. In this simulation, the index decreases like sqrt(n0² - a*r²), where r is the distance to the axis of symmetry. This results in the incoming waves being focused on the (estimated) focal plane, marked by a vertical line. The plot to the right shows a time-averaged value of the field along that plane.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:39
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 signal along the focal plane, which is indicated by a vertical line.
Render time: 51 minutes 32 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Runner" by Silent Partner
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 hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: 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 #lens #gradient_index
