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It is often assumed that spontaneous emission by an emitter placed inside a Fabry-Perot resonator into one of the longitudinal resonator modes occurs with the spectral shape of that mode, because it is triggered by a vacuum photon that has the same spectral shape as the resonator mode. More generally, broadband luminescence by many such emitters would then have to occur with the spectral shape of the Airy distribution of the Fabry-Perot resonator [1]. The assumption is incorrect in several respects. (i) The uncertainty principle for energy and time predicts that a vacuum photon at 1 μm wavelength survives approx. τ = 1 fs, i.e., it travels a hundred nanometers, shorter than the length of most optical resonators, except for nano-resonators. Consequently, it does not experience interference after one round trip, hence vacuum energy should occur as white light. (ii) Spontaneous emission typically occurs over a time that is much longer than one resonator-round-trip time [2]. If the emission time were infinite, then white-light vacuum energy would induce spontaneous emission that establishes the Airy distribution, because the emission interferes with itself over an infinite number of round trips. (iii) If vacuum energy resembled the spectral properties of the mode, the spectral distribution would be narrower. (iv) When also considering the finite emission lifetime, we find surprising relations between different resonator parameters. |
