Gravitational lensing of gravitational waves: wave nature and prospects
  for detection
  We discuss the gravitational lensing of gravitational wave signals from
coalescing binaries. We delineate the regime where wave effects are significant
from the regime where geometric limit can be used. Further, we focus on the
effect of micro-lensing and the combined effect of strong lensing and
micro-lensing. We find that micro-lensing combined with strong lensing can
introduce time varying phase shift in the signal and hence can lead to
detectable differences in the signal observed for different images produced by
strong lensing. This, coupled with the coarse localization of signal source in
the sky for gravitational wave detections, can make it difficult to identify
the common origin of signal corresponding to different images and use
observables like time delay. In case we can reliably identify corresponding
images, micro-lensing of individual images can be used as a tool to constrain
properties of micro-lenses. Sources of gravitational waves can undergo
microlensing due to lenses in the disk/halo of the Galaxy, or due to lenses in
an intervening galaxy even in absence of strong lensing. In general the
probability for this is small with one exception: Extragalactic sources of
gravitational waves that lie in the galactic plane are highly likely to be
micro-lensed. Wave effects are extremely important for such cases. In case of
detections of such sources with low SNR, the uncertainty of occurrence of
microlensing or otherwise introduces an additional uncertainty in the
parameters of the source.
