Amplitude and phase fluctuations of gravitational waves magnified by
  strong gravitational lensing
  We discuss how small-scale density perturbations on the Fresnel scale affect
amplitudes and phases of gravitational waves that are magnified by
gravitational lensing in geometric optics. We derive equations that connect the
small-scale density perturbations with the amplitude and phase fluctuations to
show that such perturbative wave optics effects are significantly boosted in
the presence of macro model magnifications such that amplitude and phase
fluctuations can easily be observed for highly magnified gravitational waves.
We discuss expected signals due to microlensing by stars, dark matter
substructure, fuzzy dark matter, and primordial black holes.
