  Ground-state cooling of mechanical resonators is a prerequisite for the
observation of various quantum effects in optomechanical systems and thus has
always been a crucial task in quantum optomechanics. In this paper, we study
how to realize ground-state cooling of the mechanical mode in a Fano-mirror
optomechanical setup, which allows for enhanced effective optomechanical
interaction but typically works in the (deeply) unresolved-sideband regime. We
reveal that for such a two-sided cavity geometry with very different decay
rates at the two cavity mirrors when using an appropriate single-sided coherent
feedback, it is possible to cool the mechanical mode down to its ground state
within a broad range of parameters. This is possible even if the total optical
loss is more than seven orders of magnitude larger than the mechanical
frequency and the feedback efficiency is relatively low. Importantly, we show
that a more standard two-sided feedback scheme is not appropriate to cooperate
with a Fano-mirror system.
