Quantization of propagating modes in optical fibres

The electromagnetic fields of a single optic fibre mode are quantized based on the observation that these fields can be derived from a scalar harmonic oscillator function depending on only time and the axial wavenumber. Asymptotic results for both the one-photon probability density and two-photon correlation density functions within the forward light cone are presented, showing an algebraic decay for large times or distances. This algebraic decay, increasing the uncertainty in the arrival time of the photons, also remains in the presence of dispersion shift, in qualitative agreement with experimental results. Also presented are explicit formulae to be used in parameter studies to optimize quantum optic fibre communications.