Hong–Ou–Mandel effect in terms of the temporal biphoton wave function with two arrival-time variables

The well-known Hong–Ou–Mandel effect is revisited. Two physical reasons are discussed for the effect to be less pronounced or even to disappear: differing polarizations of photons coming to the beamsplitter and delay time of photons in one of two channels. For the latter we use the concepts of biphoton frequency and temporal wave functions depending, correspondingly, on two frequency continuous variables of photons and on two time variables t ₁ and t ₂ interpreted as the arrival times of photons to the beamsplitter. Explicit expressions are found for the probability densities and total probabilities for photon pairs to be split between two channels after the beamsplitter and to be unsplit, when two photons appear together in one of two channels. (letter)