  We theoretically study an optomechanical system, which consists of a
two-sided cavity and a mechanical membrane that is placed outside of it. The
membrane is positioned close to one of its mirrors, and the cavity is coupled
to the external light field through the other mirror. Our study is focused on
the regime where the dispersive optomechanical coupling in the system vanishes.
Such a regime is found to be possible if the membrane is less reflecting than
the adjacent mirror, yielding a potentially very strong dissipative
optomechanical coupling. Specifically, if the absolute values of amplitude
transmission coefficients of the membrane and the mirror, $t$ and $t_m$
respectively, obey the condition $ t_m^2< t\ll t_m\ll 1$, the dissipative
coupling constant of the setup exceeds the dispersive coupling constant for an
optomechanical cavity of the same length. The dissipative coupling constant and
the corresponding optomechanical cooperativity of the proposed system are also
compared with those of the Michelson-Sagnac interferometer and the so-called
"membrane-at-the-edge" system, which are known for a strong optomechanical
dissipative interaction. It is shown that under the above condition, the system
proposed here is advantageous in both aspects. It also enables an efficient
realization of the two-port configuration, which was recently proposed as a
promising optomechanical system, providing, among other benefits, a possibility
of quantum limited optomechanical measurements in a system, which does not
suffer from any optomechanical instability.
