# How does light get into a stable optical cavity in the first place?

It is supposedly possible to trap a beam of light bouncing back and fourth between two mirrors in a stable configuration. As I understand it, this means the configuration will prevent further spread of the beam angle so it stays between the two mirrors, since it certainly couldn't decrease the beam spread as that would violate the 2nd law of thermodynamics.

Wikipedia has an enlightening section on this, and I found this illustrative, showing the region of stable configurations:

As has come up in other questions, this method has been used by researchers to get beams of light to bounce between mirrors over 100,000 times.

Wouldn't any given photon make it back to the point where it was emitted in the first place? Then, since it's not possible to have a one-way mirror (would also violate thermodynamics), then it would ultimately cause the destruction of the photon because it exits the cavity. That would imply that in order to get 100,000 bounces, the mirror's area would have to be 100,000x the area of the emission point. Is that how it's done? Or is there a better way that researchers have to keep the light in such a cavity from being destroyed at its emission point?

Maybe if you were using a laser, you could let the photon physically go back into the laser and stimulate more emission or bounce off the back wall?

Regarding the question "how to get light into the resonator in the first place":

It is done through the mirrors of the resonator. All mirrors are transparent to a certain degree, e.g. have high reflectivity but also a certain amount of transmittivity (e.g 0.1%).

The amount of bounces is usually only an effective one.

To understand how the number of bounces is measured consider the following: Assume a narrowband light source (e.g. a laser) that shines light onto the back of one of the mirrors. Assume also that the wavelength of this light matches a cavity resonance (that is the cavity length of a multiple of the half wavelength). Assume further that one waits long enough that a steady state is achieved. Since the second cavity mirror is transmittive to certain degree as well, we see also light "leaking" out of the second mirror.

If one now immediately switches off the light source, then one sees a slow decay from this second output (high Q cavities achieve 100 micro-seconds maximum). We dont see an instantaneous turn-off at the output, because the light energy that is stored in the resonator is released "slowly" through the mirrors.

This decay time (or ring-down time) is a measure for the effective number of bounces.

• So I'm getting that one way or the other, the reflectivity to keep the light in has some tradeoff with the transparency to let new light in. I'm not quite clear on the importance of the resonance. What are the implications? Why would that affect anything? – Alan Rominger Feb 6 '13 at 21:34
• Hmm, no there is no tradeoff. If the light wavelength matches one resonance of the cavity, it enters the cavity without reflection! Only if the light wavelength does not match a cavity resonance, the mirror (or cavity as whole) will reflect the light. Actually a cavity is a very narrowband filter, that will reflect back light that is off resoance and transmits light that is on resonance. See e.g. the Wikipedia article on the Fabry Perot resonator (there you find transmission curves). – Andreas H. Feb 6 '13 at 22:53
• I read a bit about the Fabry Perot cavity stuff, but I didn't mention anything about it because I thought it was pretty irrelevant to this. Provided we're talking about something close to visible light, any cavity that actually accomplishes a resonance will probably be microscopic. Because of that I haven't been considering such interference effects. The optical cavity stability topic is accomplished with entirely classical optics. So I guess maybe I'm misinterpreting the experiments with high resonance times, as they relied on resonance concepts beyond just classical stability? – Alan Rominger Feb 6 '13 at 23:04
• Actually the cavities you show above are all of the Fabry Perot Type, only with different mirror configuration (that is more of a "technical" issue, not a fundamental one). The transmission behavior is in principle the same for all. The ratio of cavity length to wavelength only determines the distance of the "frequency comb" in the transmission (that is the frequency spacing of these). A cavity for optical frequecies does not need to be microscopic, typically it is very macroscopic. And yes all the cavity stuff can be derived by classical (Maxwell) theory. – Andreas H. Feb 6 '13 at 23:11
• Hmm, the above image in the original post, only refers to mechanical stability, i.e. how much mechanical tolerance is allowed (so that the resonator is still a resonator). If you e.g. change the mirrors in the plane-parallel configuration to slightly concave mirrors, you have no resonator anymore (the light will bounce off the cavity), Thie is reflected by the fact that if you make g1 and g2 larger than 1 (i.e. the mirrors concave) the region of resonance is left (the red line leaves the region to the topright). – Andreas H. Feb 6 '13 at 23:50