  One of the most striking predictions of quantum electrodynamics is that
vacuum fluctuations of the electromagnetic field can lead to spontaneous
emission of atoms as well as photon-mediated interactions among them. Since
these processes strongly depend on the nature of the photonic bath, a current
burgeoning field is the study of their modification in the presence of photons
with non-trivial energy dispersions, e.g., the ones confined in photonic
crystals. A remarkable example is the case of isotropic Dirac-photons, which
has been recently shown to lead to non-exponential spontaneous emission as well
as dissipation-less long-range emitter interactions. In this work, we show how
to further tune these processes by considering anisotropic Dirac cone
dispersions, which include tilted, semi-Dirac, and the recently discovered type
II and III Dirac points. In particular, we show how by changing the anisotropy
of the lattice one can change both the spatial shape of the interactions as
well as its coherent/incoherent nature. Finally, we discuss a possible
implementation where these energy dispersions can be engineered and interfaced
with quantum emitters based on subwavelength atomic arrays.
