[eng] Gravitational wave astronomy has become a reality after the first gravitational
wave detections done by advanced LIGO detectors. The availability of
accurate waveform templates is crucial for the optimal detection of signals, and
for the reliable identification of the source, in order to filter the astrophysical signals
from the noise of the detector. In this work we treat a phenomenon that can
significantly affect the gravitational wave signal: gravitational lensing. The presence
of matter inhomogeneities in the propagating path of gravitational waves
from the source to the detector can modify the signals, both in amplitude and
phase. If these effects are not included in the search templates, there can be a
loss of detected signals. However, as in the well-known case of gravitational lensing
of light, lensing magnification can increase the number of detectable events
if lensing effects are included in the search templates. For gravitational lensing
of light, the geometrical optics framework is sufficient for analyzing almost all
astrophysical situations of interest, but in the last decade the work of Takahashi,
Nakamura and others showed that for lensing of gravitational waves the correct
framework is wave optics.
In this work we discuss the fundamental theory for understanding lensing effects
on gravitational wave signals in the wave optics formalism, and we study two
interesting situations of lensing of coalescing black hole binary signals, currently
the only detected systems by gravitational wave detectors. First, we study how
the signal-to-noise ratio of a lensed signal can decrease by the employ of unlensed
templates for the search, and how the estimated binary parameters can be biased
with respect the right ones due to the incomplete templates. Second, we study
the increase in the number of detectable events per year for advanced LIGO due
to lensing magnification if lensing effects are included in the templates.