  In this paper, we report on the first evidence of guided resonances (GRs) in
aperiodically-ordered photonic crystals, tied to the concept of "quasicrystals"
in solid-state physics. Via a full-wave numerical study of the transmittance
response and the modal structure of a photonic quasicrystal (PQC) slab based on
a representative aperiodic geometry (Ammann-Beenker octagonal tiling), we
demonstrate the possibility of exciting GR modes, and highlight similarities
and differences with the periodic case. In particular, we show that, as for the
periodic case, GRs arise from the coupling of the incident plane-wave with
degenerate modes of the PQC slab that exhibit a matching symmetry in the
spatial distribution, and can still be parameterized via a Fano-like model.
Besides the phenomenological implications, our results may provide new degrees
of freedom in the engineering of GRs, and pave the way for new developments and
applications.
