We examine the coherence properties and photon statistics of stationary light obtained by the superposition of nonstationary emissions occurring at random times, in accordance with a homogeneous Poisson point process. The individual emissions are assumed to be in a coherent, chaotic, or
n state. The statistical nature of the emission times results in fluctuations of the relative contributions of different emissions at a given time. This is manifested by an additional positive term, exhibiting particlelike properties, in the normalized second-order correlation function. Thus, the photon-counting variance is increased. For coherent emissions, interference between the randomly delayed emissions produces additional wavelike noise. In the limit when the emissions overlap strongly, the field exhibits the correlation properties of chaotic light, regardless of the statistics of the individual emissions. In the opposite limit, when emissions seldom overlap, the light intensity is describable by a shot-noise stochastic process, and the detected photocounts show an enhanced particlelike noise, which has its largest value when the counting time is long. In that limit, the photocounts obey the Neyman type-
A and generalized Polya-Aeppli distributions, when the individual emissions are coherent and chaotic, respectively. When the individual emissions correspond to the
n state, the Poisson emission times result in bunching which reduces or eliminates the inherent antibunching associated with the
n state.
We examine the coherence properties of stationary light obtained by the superposition of nonstationary independent emissions occurring at random space–time points. The positions of the points are independent and uniformly distributed over the volume of the source. The emission times fluctuate in accordance with a stationary renewal point process. This process admits of super-Poisson, sub-Poisson, or Poisson behavior. The individual emissions are assumed to be in a coherent, chaotic, or n state. The statistical nature of the random-emission space–time points plays an important role in determining the coherence properties and photon statistics of the total field. This is manifested in the normalized second-order correlation function, which turns out to have the usual form for chaotic light with two additional terms. The first of these is determined by the statistical nature of the individual emissions (it is positive for coherent or chaotic, but zero for single-photon, emissions). The second term is governed by the statistics of the primary excitations (it is positive for super-Poisson, zero for Poisson, and negative for sub-Poisson excitations). Both additional terms become small for light with a high degeneracy parameter (many total photons per emission lifetime). The behavior of the light is then asymptotically chaotic. In the opposite limit, when the degeneracy parameter is small (or the emissions are instantaneous), the correlation properties of the primary excitations are directly transferred to the correlation properties of the photons. The first-order spatial-coherence properties of the field turn out to be identical with those of chaotic light (i.e., the van Cittert–Zernike theorem is obeyed), although the second-order properties differ. The photon-counting distribution reflects the character of the correlation function. Thus sub-Poisson primary excitations, together with n-state emissions, can lead to sub-Poisson photon counts under certain conditions. Such nonclassical light may be made arbitrarily intense if interference effects are eliminated by detecting many spatial modes. As an example of our theory, we cite a Franck–Hertz experiment excited by a space-charge-limited electron beam. If the electron excitations are represented as a sub-Poisson renewal point process, and the photon emissions as one-photon states, the light generated should be antibunched and sub-Poisson.