  We analyze the radiation pressure induced interaction of mirror motion and
light fields in Michelson-type interferometers used for the detection of
gravitational waves and for fundamental research in table-top quantum
optomechanical experiments, focusing on the asymmetric regime with a (slightly)
unbalanced beamsplitter and a (small) offset from the dark port. This regime,
as it was shown recently, provides new interesting features, in particular a
stable optical spring and optical cooling on cavity resonance.
  We show that generally the nature of optomechanical coupling in
Michelson-type interferometers does not fit into the standard
dispersive/dissipative dichotomy. In particular, a symmetric Michelson
interferometer with signal-recycling but without power-recycling cavity is
characterized by a purely dissipative optomechanical coupling; only in the
presence of asymmetry, additional dispersive coupling arises. In gravitational
waves detectors possessing signal- and power-recycling cavities, yet another,
"coherent" type of optomechanical coupling takes place.
  We develop here a generalized framework for the analysis of asymmetric
Michelson-type interferometers which also covers the possibility of the
injection of carrier light into both ports of the interferometer. Using this
framework, we analyze in depth the "anomalous" features of the Michelson-Sagnac
interferometer which where discussed and observed experimentally in previous
works [1-3].
