  A recent work [PRL, 126, 208002 (2021)] has explored how thermal
noise-induced randomness in a self-assembled photonic crystal affects photonic
band gaps (PBGs). For the system of a two-dimensional photonic crystal composed
of a self-assembled array of rods with square cross sections, it was found that
its PBGs can exist over an extensive range of packing densities.
Counterintuitively, at intermediate packing densities, the transverse magnetic
(TM) band gap of the self-assembled system can be larger than that of its
corresponding perfect system (rods arranged in a perfect square lattice and
having identical orientations). Due to shape anisotropicity, the randomness in
the self-assembled system contains two kinds of randomness, i.e., positional
and orientational randomness of the particles. In this work, we further
investigate how PBGs are influenced solely by positional or orientational
randomness. We find that compared to the perfect situation, the introduction of
only orientational randomness decreases the transverse electric (TE) band gap
while having no obvious effects on the transverse magnetic (TM) band gap. In
contrast, the introduction of only positional randomness decreases the TE band
gap significantly, while it can widen or narrow the TM band gap, depending on
the parameter range. We also discuss the thermal (i.e., self-assembled) system
where two kinds of randomness are present. Our study contributes to a better
understanding of the role orientational randomness and positional randomness
play on PBGs, and may benefit the PBG engineering of photonic crystals through
self-assembly approaches.
