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Storage of Light

Hypothetically speaking, if one had a hollow sphere that had a perfectly polished mirrored interior surface with little to no light absorption, and then sought to fill the interior space by introducing light via a very small opening (perhaps using fiber optic?). What happens to the light that is introduced? If light is continuously projected the space, is there a point of saturation; where the 'light pressure' become greater than the incoming beam, and thus causes the incoming light to be stopped or even to back flow? Can the sphere be sealed off with 'captured' light therein; light that can be released as light? Is this studied in the field of photonics?

Yes, I am aware that my knowledge of particle physics is minimal, and I am not feigning otherwise. Merely an inquisitive and imaginative mind that happens to be seeking knowledge concerning such curiosities.

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First of all, it is impossible to create a perfect mirror (although cavities of *very* high Q-factor exist – think tens of thousands of reflections within the cavity).

Classical electromagnetism is linear, so solutions just add up. Light can't "press" other light out of the ball (unless you reach intensities where you have to consider the quantum field theory effect of [photon-photon scattering](https://en.wikipedia.org/wiki/Two-photon_physics) – but that would require incredibly intense field strengths).

But even long before you run into trouble: The light you shine in will always reach your aperture again after some time. You can see this from a simple ray optics argument: Assume you shine in a ray of light into the cavity. There will be a plane through the center of the sphere and the ray of light. All reflected rays will lie within that plane, because the surface of the sphere is perpendicular to a plane through the origin.

So it reduces to the 2d problem of a ray reflecting of a circle. Either the angle of incidence is commensurable with $2\pi$, then it will reach exactly the aperture after some time, or it is not – then it will come arbitrarily close to the aperture after some time (this is a basic property of the real numbers). As your aperture will have some finite size the ray will leave the aperture again.

In summary, there is simply no way to couple a ray into the sphere in a way, that keeps the light within the sphere beyond some finite time.

With wave-optics it gets even worse, since you have diffraction, so the smaller you get your aperture, the worse the ray optics approximation will get (but not in a way that helps your idea): The wave-front will spread and you can't keep a lot of your light close to such a "many-reflections" path.

So the average light intensity in the sphere will approach some limit point, where the same amount of radiation goes out as goes in. Not because the light pushes back, but simple due to the propagation of the light allowing no paths that keep the light within the sphere indefinitely.

The question also discusses the scenario of closing the aperture while some light is within the sphere. Assuming perfect conditions not achievable in nature when you open it again the light will exit again. The problem being that this doesn't work in reality as the mirrors won't be perfect and a switchable mirror even less so.

Similar setups to your sphere are used in real optical setups. They are called optical cavities. In some quantum optics experiments they are even used to store emitted photons for some time in a confined space (but not in the sense of putting them in and retrieving them later, rather in the sense of keeping them around and confined to increase the probability of some interaction).

A simple example of the application of optical cavities is a [Fabry-Pérot interferometer](https://en.wikipedia.org/wiki/Fabry%E2%80%93P%C3%A9rot_interferometer) is a cavity where the mirrors allow partial transmission. By using multiple internal reflection you get a much narrower interference peaks compared to a setup where you split up the beam in two and let those interfere. So in a way, light stored in a cavity is use there to allow interference of multiple reflections of the same signal.

Lasers also use optical cavities (however the medium in the cavity emits light itself) and each emitted photon statistically makes several round trips in the cavity before it leaves through the partially reflective end.

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5
$\begingroup$Just one pedantic nitpick:Classical electromagnetism is linear. :)$\endgroup$
hft
– hft
2025-01-27 00:29:24 +00:00
CommentedJan 27 at 0:29
1
$\begingroup$@Tofandel the orbits along the photon sphere are unstable. The light would not go around the black hole forever. That being said, the photon sphere only exists in the Schwarzschild spacetime, which is unphysical.$\endgroup$
paulina
– paulina
2025-01-27 18:25:20 +00:00
CommentedJan 27 at 18:25
1
$\begingroup$@hft Fixed that with an edit to make it clearer.$\endgroup$
Sebastian Riese
– Sebastian Riese
2025-01-27 19:14:52 +00:00
CommentedJan 27 at 19:14
2
$\begingroup$@ChristophilosBlu yes, impossible. Even superconductors aren't perfect reflectors. It is exceedingly rare that the physics of our universe allows perfection.physics.stackexchange.com/a/556329/11645$\endgroup$
llama
– llama
2025-01-28 20:29:22 +00:00
CommentedJan 28 at 20:29
2
$\begingroup$@ChristophilosBlu"Do you believe in the possibility of discovery" Note that claims like these in physics are not "we haven't found a perfect mirror so one probably doesn't exist" but rather "the theory that explains amazingly well how light interacts says that perfect mirrors don't exist". Sure, the theorycan be wrong but the discovery would need to be something that completely breaks our current understanding but still agrees with our current understanding in most cases.$\endgroup$
JiK
– JiK
2025-01-29 13:10:30 +00:00
CommentedJan 29 at 13:10

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