  Typically the use of the Rayleigh-Sommerfeld diffraction formula as a photon
propagator is widely accepted due to the abundant experimental evidence that
suggests that it works. However, a direct link between the propagation of the
electromagnetic field in classical optics and the propagation of photons where
the square of the probability amplitude describes the transverse probability of
the photon detection is still an issue to be clarified. We develop a
mathematical formulation for the photon propagation using the formalism of
electromagnetic field quantization and the path-integral method, whose main
feature is its similarity with a fractional Fourier transform (FrFT). Here we
show that, because of the close relation existing between the FrFT and the
Fresnel diffraction integral, this propagator can be written as a Fresnel
diffraction, which brings forward a discussion of the fundamental character of
it at the photon level compared to the Huygens-Fresnel principle. Finally, we
carry out an experiment of photon counting by a rectangular slit supporting the
result that the diffraction phenomenon in the Fresnel approximation behaves as
the actual classical limit.
