  We examine and explain the spatial emission patterns of ultracold excited
fermions in anisotropic trapping potentials in the presence of a spin polarised
Fermi sea of ground state atoms. Due to the Pauli principle, the Fermi sea
modifies the available phase space for the recoiling atom and thereby modifies
its decay rate and the probability of the emitted photon's direction. We show
that the spatial anisotropies are due to an intricate interplay between Fermi
energies and degeneracy values of specific energy levels and identify a regime
in which the emission will become completely directional. Our results are
relevant for recent advances in trapping and manipulating cold fermionic
samples experimentally and give an example of a conceptually new idea for a
directional photon source.
