  Two-photon interference is a fundamental quantum optics effect with numerous
applications in quantum information science. Here, we study two-photon
interference in multiple transverse-spatial modes along a single beam-path.
Besides implementing the analogue of the Hong-Ou-Mandel interference using a
two-dimensional spatial-mode splitter, we extend the scheme to observe
coalescence and anti-coalescence in different three and four-dimensional
spatial-mode multiports. The operation within spatial modes, along a single
beam-path, lifts the requirement for interferometric stability and opens up new
pathways of implementing linear optical networks for complex quantum
information tasks.
