Weak localization of light in superdiffusive random systems

L\'evy flights constitute a broad class of random walks that occur in many fields of research, from animal foraging in biology, to economy to geophysics. The recent advent of L\'evy glasses allows to study L\'evy flights in controlled way using light waves. This raises several questions about the influence of superdiffusion on optical interference effects like weak and strong localization. Super diffusive structures have the extraordinary property that all points are connected via direct jumps, meaning that finite-size effects become an essential part of the physical problem. Here we report on the experimental observation of weak localization in L\'evy glasses and compare results with recently developed optical transport theory in the superdiffusive regime. Experimental results are in good agreement with theory and allow to unveil how light propagates inside a finite-size superdiffusive system.