  We propose a simple model of a waveguide network designed following the
growth rule of a Vicsek fractal. We show, within the framework of real space
renormalization group (RSRG) method, that such a design may lead to the
appearance of unusual electromagnetic modes. Such modes exhibit an extended
character in RSRG sense. However, they lead to a power law decay in the
end-to-end transmission of light across such a network model as the size of the
network increases. This, to our mind, may lead to an observation of power law
localization of light in a fractal waveguide network. The general occurence of
photonic band gaps and their change as a function of the parameters of the
system are also discussed.
