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There had already several questions about light-trapping curves, such as drawing a curve captures light or photon-trapping curve, and well known cases had been answered such as ellipse or hyperbola.

With a proper rotation of ellipse or hyperbola, it is easy to find surface can trap light. Except these case which are 2D cases by nature, can we find some true 3D cases which can not reduce the problem to 2D by rotation, mirror operations?

Especially, here I also ask whether a light-trapping path exists in a ellipsoid?

Mountain
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  • Each reflection involves two line segments, which by nature must be two-dimensional. So any case of light-trapping which requires three dimensions must involve at least two reflections simultaneously. – abiessu Nov 11 '23 at 06:56
  • Thanks for your comments, @abiessu, do you mean that the segments will approach to a plane if light-trapping path exists? But for normal paths, the vertices scattered in a 3D space. Is my understanding correct? – Mountain Nov 11 '23 at 07:06
  • I'm only considering each pair of light rays around individual reflections, which is a set of strictly two dimensional cases. There is nothing inherent in that which makes any consideration beyond two dimensions necessary, therefore a minimum of two reflections is required to reach the necessary complexity for three dimensional light trapping schemes. Yes, real light scatters, but such a consideration might be better suited for the physics stack exchange. – abiessu Nov 11 '23 at 07:35

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