  We demonstrate that when a waveguide beam splitter (BS) is excited by N
indistinguishable photons, the arising multiphoton states evolve in a way as if
they were coupled to each other with coupling strengths that are identical to
the ones exhibited by a discrete fractional Fourier system. Based on the
properties of the discrete fractional Fourier transform, we then derive a
multiphoton suppression law for 50/50 BSs, thereby generalizing the
Hong-Ou-Mandel effect. Furthermore, we examine the possibility of performing
simultaneous multiphoton quantum random walks by using a single waveguide BS in
combination with photon number resolving detectors. We anticipate that the
multiphoton lattice-like structures unveiled in this work will be useful to
identify new effects and applications of high-dimensional multiphoton states.
