  The short burst GRB 130912A was detected by Swift, Fermi satellites and
several ground-based optical telescopes. Its X-ray light curve decayed with
time normally. The optical emission, however, displayed a long term plateau,
which is the longest one in current short GRB observations. In this work we
examine the physical origin of the X-ray and optical emission of this peculiar
event. We find that the canonical forward shock afterglow emission model can
account for the X-ray and optical data self-consistently and the energy
injection model that has been widely adopted to interpret the
shallowly-decaying afterglow emission is not needed. We also find that the
burst was born in a very-low density interstellar medium, consistent with the
compact object merger model. Significant fractions of the energy of the forward
shock have been given to accelerate the non-thermal electrons and amplify the
magnetic fields (i.e., $\epsilon_{\rm e}\sim 0.37$ and $\epsilon_{\rm B}\sim
0.16$, respectively), which are much larger than those inferred in most short
burst afterglow modeling and can explain why the long-lasting optical afterglow
plateau is rare in short GRBs.
