  We study and realize asymmetric fiber-based cavities with optimized mode
match to achieve high reflectivity on resonance. This is especially important
for mutually coupling two physical systems via light fields, e.g. in quantum
hybrid systems. Our detailed theoretical and experimental analysis reveals that
on resonance the interference effect between the directly reflected
non-modematched light and the light leaking back out of the cavity can lead to
large unexpected losses due to the mode filtering of the incoupling fiber.
Strong restrictions for the cavity design result out of this effect and we show
that planar-concave cavities are clearly best suited. We validate our
analytical model using numerical calculations and demonstrate an experimental
realization of an asymmetric fiber Fabry-P\'erot cavity with optimized
parameters.
