Dipole optical excitations on fractals are numerically simulated. It i
s shown that dipole eigen-modes of fractals are localized. The corresp
onding localization length dependence on the generalized frequency par
ameter (dispersion law) has been calculated. The value of optical spec
tral dimension found from the dispersion relations is in agreement wit
h the result obtained earlier from calculations of the density of eige
nstates.