  In this paper we present with full details a systematic quantification, on an
even-by-event basis, of the hard probe response to the geometry and
fluctuations of the hot QCD matter created in heavy ion collisions at both the
Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). The
azimuthal anisotropy of jet quenching is extracted and decomposed as harmonic
responses (for n=1,2,3,4,5,6) to the corresponding harmonics in the fluctuating
initial condition. We show that such jet response harmonics are sensitive to
the jet quenching models as well as to the bulk matter initial compositions. By
studying these for all centralities at both RHIC and LHC energies we put a
strong constraint on the path-length and medium-density dependence of jet
energy loss. We also examine the hard-soft di-hadron correlation arising from
the hard and soft sectors' responses to the common initial fluctuations. We
demonstrate that the experimentally observed "hard-ridge" can be explained this
way and that its dependence on the trigger-azimuthal-angle could also be
qualitatively understood.
