  We demonstrate laser-written concave hemispherical structures produced on the
endfacets of optical fibers that serve as mirror substrates for tunable
open-access microcavities. We achieve finesse values of up to 250, and a mostly
constant performance across the entire stability range. This enables cavity
operation also close to the stability limit, where a peak quality factor of
$1.5\times 10^4$ is reached. Together with a small mode waist of $2.3\;
\mathrm{\mu m}$, the cavity achieves a Purcell factor of $C \sim 2.5$, which is
useful for experiments that require good lateral optical access or otherwise
large separation of the mirrors. Laser-written mirror profiles can be produced
with a tremendous flexibility in shape and on various surfaces, opening new
possibilities for microcavities.
