Phase Conjugation and Focusing in Non-Hermitian fibers

Time reversal symmetry is a fundamental concept that appears in many branches of photonics, and is directly related to the technique of phase conjugation (PC) [1]. Phase conjugation is an important method that experimentally realized by using four wave mixing technique of nonlinear optics or more recently by wavefront shaping techniques. Phase conjugated wavefronts propagate backwards and thus offer an invaluable tool for a plethora of applications, especially for focusing inside complex media [2]. However, all these studies are based on the underlying conservation of energy. Once we consider non-conservative systems, such notion is impossible [3].