  Gravitational-wave (GW) observations by a network of ground-based laser
interferometric detectors allow us to probe the nature of GW polarizations.
This would be an interesting test of general relativity (GR), since GR predicts
only two polarization modes while there are theories of gravity that predict up
to six polarization modes. The ability of GW observations to probe the nature
of polarizations is limited by the available number of linearly independent
detectors in the network. (To extract all polarization modes, there should be
at least as many detectors as the polarization modes.) Strong gravitational
lensing of GWs offers a possibility to significantly increase the effective
number of detectors in the network. Due to strong lensing (e.g., by galaxies),
multiple copies of the same signal can be observed with time delays of several
minutes to weeks. Owing to the rotation of the earth, observation of the
multiple copies of the same GW signal would allow the network to measure
different combinations of the same polarizations. This effectively multiplies
the number of detectors in the network. Focusing on strongly lensed signals
from binary black hole mergers that produce two observable "images", using
Bayesian model selection and assuming simple polarization models, we show that
our ability to distinguish between polarization models is significantly
improved.
