Interlopers speak out: Studying the dark universe using small-scale
  lensing anisotropies
  Strongly lensed systems are powerful probes of the distribution of dark
matter on small scales. In this paper, we show that line-of-sight halos between
the source and the observers give rise to a distinct anisotropic signature in
the two-point function of the effective lensing deflection field. We show in
particular that the nonlinear coupling between line-of-sight halos and the main
lens plane imprints a characteristic quadrupole moment on this two-point
function whose amplitude reflects the abundance of such halos within the
strongly lensed field. We discuss how, by taking ratios of different multipole
moments, such observables could be made robust under the mass-sheet transform.
We also demonstrate that future extremely large telescopes have the ability to
detect the quadrupole moment due to this unique anisotropic signature. Our
approach opens the door to statistically distinguish the effect of
line-of-sight halos from that of the main-lens substructure on lensed images,
hence allowing one to probe dark matter physics in a new way.
