  Using computer simulations, we explore how thermal noise-induced randomness
in a self-assembled photonic crystal affects its photonic band gaps (PBGs). We
consider a two-dimensional photonic crystal comprised of a self-assembled array
of parallel dielectric hard rods of infinite length with circular or square
cross section. We find the PBGs can exist over a large range of intermediate
packing densities. Counterintuitively, the largest band gap does not always
appear at the packing density where the crystal is most ordered, despite the
randomness inherent in any self-assembled structure. For rods with square cross
section at intermediate packing densities, we find that the transverse magnetic
(TM) band gap of the self-assembled (i.e. thermal) system can be larger than
that of identical rods arranged in a perfect square lattice. By considering
hollow rods, we find the band gap of transverse electric (TE) modes can be
substantially increased while that of TM modes show no obvious improvement over
solid rods. Our study suggests that particle shape and internal structure can
be used to engineer the PBG of a self-assembled system despite the positional
and orientational randomness arising from thermal noise.
