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Hong-Ou-Mandel (HOM) effect is known to be one of the main phenomena inquantum optics. The effect occurs when two identical single-photon waves entera 1:1 beam splitter, one in each input port. When the photons are identical,they will extinguish each other. One of the main elements of the HOMinterferometer is the beam splitter, which has its own coefficients ofreflection $R = 1/2$ and transmission $ T = 1/2 $. In this work, the generalmechanism of the interaction of two photons in a beam splitter is consideredusing an analytical solution, which shows that in the HOM theory of the effectit is necessary to know (including when planning the experiment) not only $ R =1/2 $ and $ T = 1/2 $, but also their root-mean-square fluctuations $ \Delta R^ 2, \Delta T ^ 2 $, which arise due to the dependence of $R = R(\omega_1,\omega_2) $ and $ T = T (\omega_1, \omega_2) $ on the frequencies where$\omega_1, \omega_2$ are the frequencies of the first and second photons,respectively. Under certain conditions, specifically when the dependence of thefluctuations $ \Delta R^2 $ and $ \Delta T^2 $ can be neglected and $ R=T=1/2 $is chosen, the developed theory coincides with previously known results.

Hong-Ou-Mandel interference on a real beam splitter