  Low-dimensional excitonic materials have inspired much interest owing to
their novel physical and technological prospects. In particular, those with
strong in-plane anisotropy are among the most intriguing but short of general
analyses. We establish the universal functional form of the anisotropic
dispersion in the small $k$ limit for 2D dipolar excitonic systems. While the
energy is linearly dispersed in the direction parallel to the dipole in-plane,
the perpendicular direction is dispersionless up to linear order, which can be
explained by the quantum interference effect of the interaction among the
constituents of 1D subsystems. The anisotropic dispersion results in a
$E^{\sim0.5}$ scaling of the system density of states and predicts unique
spectroscopic signatures including: (1) disorder-induced absorption linewidth,
$W(\sigma)\sim\sigma^{2.8}$, with $\sigma$ the disorder strength, (2)
temperature dependent absorption linewidth, $W(T)\sim T^{s+1.5}$, with $s$ the
exponent of the environment spectral density, and (3) the out-of-plane angular
$\theta$ dependence of the peak splittings in absorption spectra, $\Delta
E(\theta)\propto\sin^2\theta$. These predictions are confirmed quantitatively
with numerical simulations of molecular thin films and tubules.
