We theoretically study the properties of a dielectric plate with a modified Hong-Ou-Mandel interferometer. The fourth-order correlation functions are calculated in two regimes, which are divided depending on the relative size between the thickness of the dielectric plate and the one-photon coherence length. When the thickness of the dielectric plate is less than the one-photon coherence length, a novel modulation behavior of the coincidence rate is observed, which has not been discussed before. If the thickness of the dielectric plate is larger than the one-photon coherence length, coalescence and anti-coalescence are observed. The obtained results highlight the effects of a linear optical element on fourth-order interference.
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