  When light waves propagate through disordered photonic lattices, they can
eventually become localized due to multiple scattering effects. Here we show
experimentally that while the evolution and localization of the photon density
distribution is similar in the two cases of diagonal and off-diagonal disorder,
the density-density correlation carries a distinct signature of the type of
disorder. We show that these differences reflect a symmetry in the spectrum and
eigenmodes that exists in off-diagonally disordered lattices but is absent in
lattices with diagonal disorder.
