Stable optical spring in aLIGO detector with unbalanced arms and in Michelson-Sagnac interferometer

Optical rigidity in aLIGO gravitational-wave detector, operated on dark port regime, is unstable. We show that the same interferometer with excluded symmetric mechanical mode but with unbalanced arms allows to get stable optical spring for antisymmetric mechanical mode. Arm detuning necessary to get stability is shown to be a small one - it corresponds to small power in signal port. We show that stable optical spring may be also obtained in Michelson-Sagnac interferometer with both power and signal recycling mirrors and unbalanced arms.