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Let's say we have light contained in a cavity (of initial length $L$) and then instantaneously remove the second mirror, thus removing the barrier between the first and a third mirror which is some further distance away (say $L$ again). If the light was on resonance before the change, do I think about it as two counter propagating wave pulses (trains) which then move out into the unexplored part of the larger cavity over a time equal to $2*L$ (in units where $c=1$)? If initially its off resonance can I still use the same conceptual picture?

Does this imply that the light pulse will remain localised to a length $2L$ and that if I reinsert the second mirror at exactly the right time (waiting for the pulse to 'bounce back') I can 'catch' the light back in the initial smaller cavity?

Can I think about a complimentary photon picture where the same 'catch' can be made as the photons all depart the initial cavity region over a time $2L$ and then return in concert? The reasoning behind the $2L$ being that a left moving photon could be at the second mirror (just after a reflecting collision) and takes a time $2L$ to return to the now vacant second mirror locale.

Is there anything in the statistics of the 'catch' that makes a distinction between photons versus waves?

For clarity, I'm thinking of the medium being a vacuum where there is no dispersion.

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You can do so in practice if the cavity length is at least few meters and you buy a fast Pockels cell driver. Within few nanoseconds you can efficiently redirect the light into a longer portion of the cavity. Or catch an incoming pulse if you properly tune the timing.

Notice that by introducing a temporal change in the light path, you always alter the spectrum of the light captured in the cavity. If it happens in the presence of the pulse in the modulator, it will be cut and its spectrum will change a lot, otherwise you only introduce tiny spectral modulation with finely-spaced peaks c/(2L) apart from each other. Anyway, if you measure the spectrum of the light captured in the resonator, it will always comply with the allowed modes.

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