  We study the Drude weight D and the total optical weight K for a t-t'-J model
on a square lattice that exhibits a metallic phase-modulated antiferromagnetic
ground state close to half-filling. Within a suitable 1/N expansion that
includes leading quantum-fluctuation effects, D and K are found to increase
linearly with small hole doping away from the Mott metal-insulator transition
point at half-filling. The slow zero-sound velocity near the latter transition
identifies with the velocity of the lower-energy branch of the twofold
excitation spectrum. At higher doping values, D and K eventually saturate and
then start to decrease. These features are in qualitative agreement with
optical conductivity measurements in doped antiferromagnets.
