  Periodic nanoparticle arrays can support surface lattice resonances (SLRs),
which arise from the hybridization between localized surface plasmons (LSPs)
and diffractive Rayleigh anomalies (RAs). In contrast to LSPs, SLRs enjoy a
much higher quality (Q) factor. As the Q factor depends on many system
parameters, a good understanding of them is essential for optimization. Here,
we study the dependence of the Q factor of SLR from 2D Au nanorod arrays on
nanorod orientation. It is found the Q factor is 112 when the nanorod is lying
perpendicular to the incident plane but gradually increases by more than 13
times to 1460 upon rotating it azimuthally. The increase of the Q factor is due
to the interplay between the coupling strength and the frequency detuning
between the LSP and RA as well as the decay rate of the LSP. By optimizing
these parameters, we can achieve a Q factor reaching over 12000, which is 6
times higher than the best reported so far.
