  In this paper, we propose a disordered heterostructure in which the
distribution of refractive index of one of its constituents follows a
L\'evy-type distribution characterized by the exponent $\alpha$. For the normal
and oblique incidences, the effect of $\alpha$ variation on the localization
length is investigated in different frequency ranges. As a result, the
controllability of Anderson localization can be achieved by changing the
exponent $\alpha$ in the disordered structure having heavy tailed distribution.
