Non-Hermitian focusing deep inside strongly disordered scattering media

Summary form only given. The recent intense research in the newly founded area of PT-symmetric optics [1,2] has triggered a lot of attention in theoretical and experimental studies of non-Hermitian effects in photonics. In this context of composite photonic systems that contain gain and loss, we recently demonstrated for the first time the existence of so-called “constant-intensity waves” (or CI-waves) [3], which, in the presence of inhomogeneous gain-loss media, can evolve with constant intensity - a property known so far only for plane waves in free space. We show here that engineering the complex index of refraction on similar principles leads us also to other unexpected effects with novel functionalities. In particular, we construct specific index distributions that for one specific wavelength can cause strong focusing inside disordered media. Such a focusing is the result of the non-Hermitian interference of the modes of the medium and is impossible without loss and gain.