  The coherent dipole-dipole interactions of atoms in an atomic array are
studied. It is found that the excitation probability of an atom in an array
parallel to the direction of laser propagation ($\boldsymbol{\hat{k}}$) will
either grow or decay logarithmically along $\boldsymbol{\hat{k}}$, depending on
the detuning of the laser. The symmetry of the system for atomic separations of
$\delta r = j\lambda/2$, where $j$ is an integer, causes the excitation
distribution and scattered radiation to abruptly become symmetric about the
center of the array. For atomic separations of $\delta r < \lambda/2$, the
appearance of a collection of extremely subradiant states ($\Gamma\sim 0$),
disrupts the described trend. In order to interpret the results from a finite
array of atoms, a band structure calculation in the $N\rightarrow \infty$ limit
is conducted where the decay rates and the Collective Lamb Shifts of the
eigenmodes along the Brillouin zone are shown. Finally, the band structure of
an array strongly affects its scattered radiation, allowing one to manipulate
the Collective Lamb Shift as well as the decay rate (from superradiant to
subradiant) by changing the angle of the driving laser.
