Storage of Light

Question

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.

Answer 1

Suppose your reflector was insanely close to perfect. Light would lose a tiny amount of energy on every bounce. But the mirror is so good that it would take a million bounces before half was lost.

Suppose the ball is $10$ cm across. Light flows in, travels across the ball, bounces, travels across again, and so on. It reaches a million bounces after traveling $100,000$ meters, or $100$ km.

The speed of light is $300,000$ km/sec. So $100$ km takes $1/3$ of a millisecond. At this time, half the energy is still stored.

After another $1/3$ millisecond, there is $1/4$ of the light light. Another, and there is $1/8$ of it. Total time so far: $1$ millisecond.

You can't store light for any appreciable time with even an insanely good mirror.

Answer 2

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 – 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 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.

Answer 3

Yes, in theory, the perfectly reflected sphere would eventually be filled with enough light that the backflow along the fiber would exactly equal the inflow. Or, if closed, have an electromagnetic field wobbling forever.

In practice, reflectance is usually below 99%, so after about a few bounces the light will be absorbed by the walls and just heat them up. This is really fast due to the high speed of light. In microwave resonators with superconducting walls the reflectance is really good and a wave can remain for nearly a second, but for visible light absorption is much much quicker.

Answer 4

If we stretch your scenario to the extreme imagining some kind of light valve at the entrance of the sphere and perfect reflection, then one can imagine the formation of a Kugelblitz, that is a hypothetical black hole formed only by light.

Answer 5

After the light intensity inside this hypothetical sphere exceeds a certain limit, light back scattering might start, thereby some light coming out of the hole meant for adding light.

After the light intensity exceeds a certain (high) limit, nonlinear phenomena might start, thereby creating some additional holes in the sphere, wherefrom light of various wavelengths might come out.

In any case, it will not be possible to keep inputting light indefinitely.

Answer 6

Basically your analysis is correct. Light will be stored in the sphere until an equilibrium is reached.

That happens when the amount of introduced light is equal to the light that is "lost". These losses can due to

1. reflection losses (if we have < 100% wall reflectivity)
2. light escape through the input hole.

Note: 2. is not the same as stopping light flow. It just means light is reflected back into the fiber. In fact the sphere will just appear as a mirror to the fiber. Just as if you would put a (diffuse) mirror in place of the sphere opening.

Another interesting fact is that light is indeed accumulated in the sphere, in the sense that the circulating light power can be very high, much higher than the input.

Example: If the only 1% of light currently inside the sphere is escaping the sphere, the power level inside the sphere is 100 times the input power (because at equilibrium the losses equal the input power). This 1% could be the ratio of the input hole to the whole sphere surface area for a perfect reflectivity.

Such a sphere is actually a technical device, it is called integrating sphere.

Losses are small, but still too high for storing light over significant times. Such spheres can have ring-down times in the order of 10s of µs. Larger spheres of course longer, smaller ones shorter.

Answer 7

What you are describing already exists, and is called a "quantum memory" because it stores the light for some amount of time. (although these are typically done just by using two mirrors facing eachother)

While the theorists here are saying that such a device is useless because you can only "store" the light for a few milliseconds are incorrect in thinking this is useless. Light pulses can be made to be much much faster than milliseconds, so you have quite a large degree of control when working with these mirrors.

You are also correct that the light that is trapped inside the "cavity" will affect things:

1. The light will PUSH against the mirrors with each bounce. However, many many hits of photons is not typically enough to really cause a big pushing force.
2. while light will mostly reflect, it will sometimes get absorbed by the mirror and heat the mirror. Use too much light and you'll burn your chemical coatings which are made to help it reflect better.
3. The light that wants to come out, will constructively interfere with the light that is trying to enter. This happens even for a single photon, and you have to carefully choose the length of the mirrors such that the wavelength of light can fit inside the cavity. Otherwise the stuff entering will always cancel with the stuff exiting and you cant get anything inside.