  We analyze the dynamic optomechanical back-action in signal-recycled
Michelson and Michelson-Sagnac interferometers that are operated off dark port.
We show that in this case --- and in contrast to the well-studied canonical
form of dynamic back-action on dark port --- optical damping in a
Michelson-Sagnac interferometer acquires a non-zero value on cavity resonance,
and additional stability/instability regions on either side of the resonance,
revealing new regimes of cooling/heating of micromechanical oscillators. In a
free-mass Michelson interferometer for a certain region of parameters we
predict a stable single-carrier optical spring (positive spring and positive
damping), which can be utilized for the reduction of quantum noise in
future-generation gravitational-wave detectors.
