I'm working on a thought experiment and I have a question about trapping a pulse inside a looped preparation . If a pulsed particle beam is prepared with a definite energy(E), bandwidth(ΔE) and positional uncertainty/coherence length(Δx) is the pulse able to be trapped inside of a loop type preparation(a cavity) if the total length of the loop/cavity is shorter than the positional uncertainty of the particles. Typical cavities in optics all have open input and output ports. I'm talking specifically about a loop which is enabled by a switch which opens and closes the loop. A simple example in optics would use a polarizing beam splitter as the entry point of the loop, only allowing in one polarization. Secondary rigid mirrors could be used to redirect the beam towards the back side of the beam splitter where the beam would be deflected because of its polarization. This would constitute a loop/cavity where the transmitted photons are trapped inside. In order to open the loop to release the photons you simply insert a wave plate which rotates the polarization and allows it to exit through the beam splitter. In total this would constitute a switched loop preparation which can trap photons and release them upon command of the experimenter. My question is, if the loop length is shorter than the uncertainty in position,Δx(the linewidth of the photon distribution) is it still possible for photons to become trapped inside or does the loop act as a forbidden region?