We have studied the far-infrared response of GaAs/AlxGa1-xAs quantum-w
ire arrays of 200- and 300-nm periods, realized by biasing a periodic
surface-grating gate structure below the two-dimensional electron-gas
conduction threshold. We find that in our samples, which have substant
ially smaller periods than those in previous work, the resonance is ob
served at a frequency omega(r) much smaller than that of the depolariz
ation-shifted subband resonance and that the 200-nm-period wires have
a smaller omega(r) than the 300-nm-period wires of the same carrier de
nsities. The experiment demonstrates mode softening in coupled quantum
wires. We also present a theoretical model, based on the generalized
Kohn theorem, to take into account the mode softening. Our model can q
uantitatively describe the observed mode softening and explain the exp
erimental results.