  We theoretically investigate the design of thin subwavelength gratings
possessing high-reflectivity and high-$Q$ resonances when illuminated at normal
incidence by a Gaussian beam. We compare the performances of single-period and
dual-period rectangular gratings using Finite Element Method-based optimization
and predict one to two orders of magnitude improvement in their transmission
loss-linewidth product, which is the relevant figure of merit for e.g. resonant
mirror-based microcavity applications.
