  We present a consistent analysis of linear spectroscopy for arrays of nearest
neighbor dipole-coupled two-level molecules that reveals distinct signatures of
weak and strong coupling regimes separated for infinite size arrays by a
quantum critical point. In the weak coupling regime, the ground state of the
molecular array is disordered, but in the strong coupling regime it has
(anti)ferroelectric ordering. We show that multiple molecular excitations
(odd/even in weak/strong coupling regime) can be accessed directly from the
ground state. We analyze the scaling of absorption and emission with system
size and find that the oscillator strengths show enhanced superradiant behavior
in both ordered and disordered phases. As the coupling increases, the single
excitation oscillator strength rapidly exceeds the well known Heitler-London
value. In the strong coupling regime we show the existence of a unique spectral
transition with excitation energy that can be tuned by varying the system size
and that asymptotically approaches zero for large systems. The oscillator
strength for this transition scales quadratically with system size, showing an
anomalous one-photon superradiance. For systems of infinite size, we find a
novel, singular spectroscopic signature of the quantum phase transition between
disordered and ordered ground states. We outline how arrays of ultra cold
dipolar molecules trapped in an optical lattice can be used to access the
strong coupling regime and observe the anomalous superradiant effects
associated with this regime.
