Transverse and Quantum Localization of Light: A Review on Theory and Experiments

Anderson localization is an interference effect yielding a drastic reduction of diffusion-including complete hindrance-of wave packets such as sound, electromagnetic waves, and particle wave functions in the presence of strong disorder. In optics, this effect has been observed and demonstrated unquestionably only in dimensionally reduced systems. In particular, transverse localization (TL) occurs in optical fibers, which are disordered orthogonal to and translationally invariant along the propagation direction. The resonant and tube-shaped localized states act as micro-fiber-like single-mode transmission channels. Since the proposal of the first TL models in the early eighties, the fabrication technology and experimental probing techniques took giant steps forwards: TL has been observed in photo-refractive crystals, in plastic optical fibers, and also in glassy platforms, while employing direct laser writing is now possible to tailor and "design" disorder. This review covers all these aspects that are today making TL closer to applications such as quantum communication or image transport. We first discuss nonlinear optical phenomena in the TL regime, enabling steering of optical communication channels. We further report on an experiment testing the traditional, approximate way of introducing disorder into Maxwell's equations for the description of TL. We find that it does not agree with our findings for the average localization length. We present a new theory, which does not involve an approximation and which agrees with our findings. Finally, we report on some quantum aspects, showing how a single-photon state can be localized in some of its inner degrees of freedom and how quantum phenomena can be employed to secure a quantum communication channel.