  We present data on the optical conductivity of
URu$_{2-x}$(Fe,Os)$_{x}$Si$_{2}$. While the parent material URu$_2$Si$_2$
enters the enigmatic hidden order phase below 17.5 K, an antiferromagnetic
phase is induced by the substitution of Fe or Os onto the Ru sites. We find
that both the HO and the AFM phases exhibit an identical gap structure that is
characterized by a loss of conductivity below the gap energy with spectral
weight transferred to a narrow frequency region just above the gap, the typical
optical signature of a density wave. The AFM phase is marked by strong
increases in both transition temperature and the energy of the gap associated
with the transition. In the normal phase just above the transition the optical
scattering rate varies as $\omega^2$. We find that in both the HO and the AFM
phases, our data are consistent with elastic resonant scattering of a Fermi
liquid. This indicates that the appearance of a coherent state is a necessary
condition for either ordered phase to emerge. Our measurements favor models in
which the HO and the AFM phases are driven by the common physics of a
nesting-induced density-wave-gap.
