  Resonance energy transfer (RET) is an inherently anisotropic process. Even
the simplest, well-known F\"orster theory, based on the transition
dipole-dipole coupling, implicitly incorporates the anisotropic character of
RET. In this theoretical work, we study possible signatures of the fundamental
anisotropic character of RET in hybrid nanomaterials composed of a
semiconductor nanoparticle (NP) decorated with molecular dyes. In particular,
by means of a realistic kinetic model, we show that the analysis of the dye
photoluminescence difference for orthogonal input polarizations reveals the
anisotropic character of the dye-NP RET which arises from the intrinsic
anisotropy of the NP lattice. In a prototypical core/shell wurtzite CdSe/ZnS NP
functionalized with cyanine dyes (Cy3B), this difference is predicted to be as
large as 75\% and it is strongly dependent in amplitude and sign on the dye-NP
distance. We account for all the possible RET processes within the system,
together with competing decay pathways in the separate segments. In addition,
we show that the anisotropic signature of RET is persistent up to a large
number of dyes per NP.
