Quantum effects of spatial/temporal modulation of the optical field

The quantum effects of temporal modulation and spatial confinement of optical field are theoretically analyzed using the continuous mode formalism. The effect of modulation is different from static attenuation regardless of whether the modulation bandwidth is broader or narrower than the photon bandwidth. This effect appears not only in single-photon interferometry but also in multi-photon interferometry, and shows the fundamental difference between deep modulation and static attenuation of the wave function. The effect of spatial confinement of photons in a cavity appears as an anomalous mode commutator inside the cavity, which is related to the spontaneous emission modulation. The canonical field commutator is guaranteed only when the Kramers-Kronig relations for the optical elements are properly incorporated.