Bimodal Hong-Ou-Mandel Interferometry

We investigate two-photon Hong-Ou-Mandel interference in several interferometric systems, in which each of the two interfering input photons exist in arbitrary linear superpositions of the first-order Hermite-Gaussian modes $HG_{10}$ and $HG_{01}$. We find that if both input photons are in balanced superpositions of the $HG_{10}$ and $HG_{01}$ modes, the resulting two-photon interference can be engineered to transform these diagonal Hermite-Gaussian inputs into output modes of the Laguerre Gaussian type, which are entangled with respect to both output path and transverse spatial mode. We show that such two-photon interference effects can occur even if the input photons are prepared with \emph{distinguishable} transverse spatial states.