Fluctuations of Photon Beams and their Correlations

The distribution of counts from a photoelectric detector illuminated by light of bandwidth Δν0 is analysed by associating the photons with Gaussian random waves. This is shown to lead to a full statistical description of the counts. It is shown that the number nT in a time interval T << 1/Δν0 obeys pure Bose-Einstein statistics, and that the fluctuations in longer intervals T >> 1/Δν0 are simply the density fluctuations of a boson assembly in a phase space of ~ Δν0T cells. The correlation coefficient ρ of the fluctuations of counts from two detectors illuminated by partially coherent beams is found to be proportional to the local time average of the square of the coherence function ⟨γ122⟩. The correlation is shown to depend on the degeneracy of the beams in such a way that ρ → 2⟨γ122⟩ for highly degenerate beams. The results are all consistent with those obtained by Hanbury Brown and Twiss in 1957.