  A better understanding of the optical properties of random photonic
structures is beneficial for many applications, such as random lasing, optical
imaging and photovoltaics. Here we investigated the light transmission
properties of disordered photonic structures in which the high refractive index
layers are aggregated in clusters. We sorted the size of the clusters from a
power law distribution tuning the exponent a of the distribution function. The
sorted high refractive layer clusters are randomly distributed within the low
refractive index layers. We studied the total light transmission, within the
photonic band gap of the corresponding periodic crystal, as a function of the
exponent in the distribution. We observed that, for a within the interval
[0,3.5], the trend can be fitted with a sigmoidal function.
