Lensing of gravitational waves: universal signatures in the beating
  pattern
  When gravitational waves propagate near massive objects, their paths curve
resulting in gravitational lensing, which is expected to be a promising new
instrument in astrophysics. If the time delay between different paths is
comparable with the wave period, lensing may induce beating patterns in the
waveform, and it is very close to caustics that these effects are likely to be
observable. Near the caustic, however, the short-wave asymptotics associated
with the geometrical optics approximation breaks down. In order to describe
properly the crossover from wave optics to geometrical optics regimes, along
with the Fresnel number, which is the ratio between the Schwarzschild diameter
of the lens and the wavelength, one has to include another parameter - namely,
the angular position of the source with respect to the caustic. By considering
the point mass lens model, we show that in the two-dimensional parameter space,
the nodal and antinodal lines for the transmission factor closely follow
hyperbolas in a wide range of values near the caustic. This allows us to
suggest a simple formula for the onset of geometrical-optics oscillations which
relates the Fresnel number with the angular position of the source in units of
the Einstein angle. We find that the mass of the lens can be inferred from the
analysis of the interference fringes of a specific lensed waveform.
