Can photons get captured in a Fabry-Perot cavity, and if so, what happens when it's detuned? I'm imagining a three-step experiment with a Fabry-Perot cavity, and I'm not sure what would happen at each step.
First, suppose there is input light exactly resonant with the cavity. If I turn off the input, does it take some time for the electric field inside the cavity to dissipate? I would naively guess something like the field after time $t$ is proportional to $e^{-tLT}$ where $T$ is the transmissitivity of the mirrors and $L$ is the cavity length.
If so, suppose I turn off the input with a low transmissitivity cavity. Before the field dissipates, can I then increase the transmissitivity to effectively 0, to "capture" the electric field and keep it for a long time? Certainly a thick, opaque material has transmissitivity of ~0, but I suppose what I really want is reflectivity of 1. Would the electric field end up being absorbed in that case? Is there some way to use, e.g., total internal reflection to keep the internal electric field for a very long time?
Finally, suppose that I have captured some resonant electric field that is stable inside this cavity. If I move the mirrors in the cavity so that it's no longer resonant with this electric field, then presumably the electric field dissipates. Where does it go? Does it end up transmitted (in the case of a partially reflected mirror) or absorbed (in the case of a not-quite-perfectly reflected mirror? In cases where reflectivity is extremely high, how long would this process take?
 A: This is effectively a question about the behavior of resonances in the time domain. Some notes:

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*For the first question, the answer is yes, it takes time for the electric field to disappear. For a single mode cavity, there will be a particular field distribution (corresponding to a quasi-mode) which survives much longer than other contributions to the initial field.

*The decay of this field distribution is indeed of the form $e^{-\gamma t}$, but $\gamma$ is not necessarily $LT$ (although it may be related to this quantity, it can depend on other quantities such as the mode number). Instead, $\gamma$ can be determined via the width of the modes Lorentzian resonance signature in the transmission spectrum.

*For a good cavity with high-quality mirrors, this distribution can simply be approximated by a standing wave with node boundary conditions at the mirrors.

*I may not quite understand the second part of the question. To me, it is somewhat covered by the first part. "Keeping the electric field for a very long time" is precisely the task of engineering a long-lived cavity resonance. The latter does correlate with mirror quality. Tuning the transmission to zero is, however, a different task entirely. There is this formalism for the reflection case, which probably also applies to transmission in the case of one-dimensional cavities (3D resonators do not really have a notion of "transmission", instead they have many out-put channels; reflection on the other hand as the "return channel" is always defined).

*The last part of the question strongly depends on how you move the mirror and there are all kinds of fascinating phenomena that can be created with such setups. E.g. coupling the mirror movement to other quantum mechanical degrees of freedom is the study of cavity optomechanics.

